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

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

sample793.0ms (13.6%)

Memory

31.1MiB live, 1 053.1MiB allocated

Samples

469.0ms	7 625×	0	valid
33.0ms	302×	1	valid
33.0ms	125×	3	valid
22.0ms	204×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 252.0ms

ival-div: 95.0ms (37.7% of total)

ival-sub: 85.0ms (33.7% of total)

ival-add: 44.0ms (17.4% of total)

adjust: 14.0ms (5.6% of total)

ival-true: 6.0ms (2.4% of total)

exact: 5.0ms (2% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

preprocess60.0ms (1%)

Memory

-30.3MiB live, 62.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	45	35
2	139	35
3	373	35
4	647	35
5	807	35
6	846	35
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)

explain79.0ms (1.4%)

Memory

37.8MiB live, 190.0MiB 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

24.0ms	458×	0	valid
6.0ms	14×	3	valid
3.0ms	30×	1	valid
1.0ms	10×	2	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-add: 7.0ms (34.7% of total)

ival-div: 6.0ms (29.7% of total)

ival-sub: 5.0ms (24.8% of total)

adjust: 1.0ms (5% 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.9MiB live, 1.9MiB 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)

simplify29.0ms (0.5%)

Memory

-9.5MiB live, 69.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 x y)
✓	cost-diff	128	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))
✓	cost-diff	384	(/.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)
(*.f64 (-.f64 x y) #s(literal 1/2 binary64))
(- x y)
(-.f64 x y)
y
2
#s(literal 2 binary64)

localize22.0ms (0.4%)

Memory

8.8MiB live, 50.3MiB 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

12.0ms	229×	0	valid
1.0ms	15×	1	valid
1.0ms	7×	3	valid
1.0ms	5×	2	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 (32.2% of total)

ival-sub: 2.0ms (32.2% of total)

adjust: 1.0ms (16.1% of total)

ival-add: 1.0ms (16.1% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

-31.1MiB live, 7.6MiB 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
1.0ms	y	@	0	(/ (- x y) 2)
0.0ms	x	@	inf	(/ (- x y) 2)
0.0ms	x	@	-inf	(/ (- x y) 2)
0.0ms	x	@	0	(+ x (/ (- x y) 2))
0.0ms	y	@	inf	(/ (- x y) 2)

rewrite376.0ms (6.4%)

Memory

6.0MiB live, 537.3MiB 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) (neg.f64 y)))
(+.f64 (.f64 y #s(literal -1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (neg.f64 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 (neg.f64 (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 (neg.f64 (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) (neg.f64 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) (neg.f64 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) (neg.f64 y)))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 y) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 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 (neg.f64 x) #s(literal -1/2 binary64) (*.f64 y #s(literal -1/2 binary64)))
(fma.f64 (neg.f64 x) #s(literal -1/2 binary64) (.f64 #s(literal 1 binary64) (.f64 y #s(literal -1/2 binary64))))
(fma.f64 (neg.f64 x) #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (neg.f64 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) (neg.f64 (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) (neg.f64 (+.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) (neg.f64 (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) (neg.f64 (+.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)))
(/.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (-.f64 x y) (+.f64 x y))) (.f64 (.f64 #s(literal 2 binary64) (+.f64 x y)) (fma.f64 x x (.f64 y y))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) #s(literal 1/2 binary64)) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (+.f64 x y) (.f64 (-.f64 x y) #s(literal 1/2 binary64))) (+.f64 x y))
(/.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 (-.f64 (.f64 x #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (neg.f64 y))) #s(literal -4 binary64))
(/.f64 (-.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 2 binary64) x) y)) (.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)))
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(.f64 (/.f64 (fma.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (fma.f64 (.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/8 binary64)) (.f64 (.f64 (-.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) x) (-.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) x)) (-.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) x))) (-.f64 (.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) x))) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (/.f64 (fma.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (fma.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) x)) (.f64 x x)) (fma.f64 x x (.f64 (.f64 (-.f64 x y) #s(literal -1/2 binary64)) (-.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) x))))) (fma.f64 x x (.f64 (.f64 (-.f64 x y) #s(literal -1/2 binary64)) (-.f64 (*.f64 (-.f64 x y) #s(literal 1/2 binary64)) x))))
(+.f64 x (neg.f64 y))
(+.f64 x (*.f64 #s(literal 1 binary64) (neg.f64 y)))
(+.f64 x (*.f64 (neg.f64 y) #s(literal 1 binary64)))
(+.f64 (neg.f64 y) x)
(+.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y)))) (neg.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y))))))
(+.f64 (/.f64 (.f64 x x) (+.f64 x y)) (neg.f64 (/.f64 (.f64 y y) (+.f64 x y))))
(+.f64 (neg.f64 (neg.f64 x)) (neg.f64 y))
(+.f64 (*.f64 #s(literal 1 binary64) (neg.f64 y)) x)
(+.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64)) x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y))) #s(literal -1 binary64)))
(-.f64 x y)
(-.f64 #s(literal 0 binary64) (-.f64 y x))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y)))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y)))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y)))
(-.f64 (+.f64 x #s(literal 0 binary64)) y)
(fma.f64 x #s(literal 1 binary64) (neg.f64 y))
(fma.f64 x #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (neg.f64 y)))
(fma.f64 x #s(literal 1 binary64) (*.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 x (/.f64 x (+.f64 x y)) (neg.f64 (/.f64 (*.f64 y y) (+.f64 x y))))
(fma.f64 x (/.f64 (.f64 x x) (fma.f64 x x (.f64 y (+.f64 x y)))) (neg.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (*.f64 y (+.f64 x y))))))
(fma.f64 y #s(literal -1 binary64) x)
(fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y (+.f64 x y)))) (neg.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y))))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 (/.f64 (.f64 y y) (+.f64 x y))))
(fma.f64 (.f64 x x) (/.f64 x (fma.f64 x x (.f64 y (+.f64 x y)))) (neg.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (*.f64 y (+.f64 x y))))))
(fma.f64 #s(literal 1 binary64) x (neg.f64 y))
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal 1 binary64) (neg.f64 y)))
(fma.f64 #s(literal 1 binary64) x (*.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (neg.f64 y) x)
(fma.f64 (neg.f64 y) #s(literal 1 binary64) x)
(fma.f64 #s(literal -1 binary64) y x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x (.f64 y (+.f64 x y)))) (neg.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y))))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 x y))) (-.f64 x y) (neg.f64 (/.f64 (*.f64 y y) (+.f64 x y))))
(fma.f64 (/.f64 (.f64 x x) (fma.f64 x (.f64 x x) (.f64 y (.f64 y y)))) (fma.f64 x x (.f64 y (-.f64 y x))) (neg.f64 (/.f64 (.f64 y y) (+.f64 x y))))
(fma.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 y (+.f64 x y)) (.f64 (.f64 y (+.f64 x y)) (.f64 y (+.f64 x y))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 y (+.f64 x y)) (-.f64 (.f64 y (+.f64 x y)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y))))))
(fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 (.f64 x x) (.f64 y (+.f64 x y))))) (-.f64 (.f64 x x) (.f64 y (+.f64 x y))) (neg.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (*.f64 y (+.f64 x y))))))
(neg.f64 (-.f64 y x))
(/.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (fma.f64 x x (.f64 y (+.f64 x y))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (neg.f64 (neg.f64 (fma.f64 x x (.f64 y (+.f64 x y))))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (fma.f64 y y (-.f64 (.f64 x x) (neg.f64 (*.f64 x y)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 x y))
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (neg.f64 (neg.f64 (+.f64 x y))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y))))
(/.f64 (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 y x)) (neg.f64 (fma.f64 x x (*.f64 y (+.f64 x y)))))
(/.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (neg.f64 (+.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 (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 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (fma.f64 x (.f64 x x) (.f64 y (.f64 y y)))) (.f64 (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 x y) (fma.f64 (.f64 y y) (fma.f64 x x (.f64 y y)) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (-.f64 x y) (+.f64 x y))) (.f64 (+.f64 x y) (fma.f64 x x (*.f64 y y))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y)))) (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (.f64 y (.f64 y y)))) (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (fma.f64 x x (*.f64 y (+.f64 x y)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x y)) (.f64 (+.f64 x y) (.f64 y y))) (*.f64 (+.f64 x y) (+.f64 x y)))
(/.f64 (neg.f64 (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 y x))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 y x))) (neg.f64 (neg.f64 (fma.f64 x x (*.f64 y (+.f64 x y))))))
(/.f64 (neg.f64 (*.f64 (+.f64 x y) (-.f64 y x))) (+.f64 x y))
(/.f64 (neg.f64 (*.f64 (+.f64 x y) (-.f64 y x))) (neg.f64 (neg.f64 (+.f64 x y))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y)))) (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y))))) (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y))))) (.f64 (.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y)))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y))))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y)))))) (fma.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y)))) (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y)))) (fma.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y)))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y)))) (.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y)))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (*.f64 y (+.f64 x y))))))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y))) (/.f64 (.f64 x x) (+.f64 x y))) (.f64 (.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (/.f64 (.f64 y y) (+.f64 x y)))) (fma.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y)) (fma.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y)) (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (*.f64 y y) (+.f64 x y))))))
(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (-.f64 (neg.f64 y) x))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y)))) (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y))))) (.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y)))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y)))))) (fma.f64 x (/.f64 (.f64 x x) (fma.f64 x x (.f64 y (+.f64 x y)))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (*.f64 y (+.f64 x y))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y))) (.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y)))) (fma.f64 x (/.f64 x (+.f64 x y)) (/.f64 (*.f64 y y) (+.f64 x y))))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (.f64 y (.f64 y y)))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (-.f64 x y) (+.f64 x y))) (+.f64 x y))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 y x))) (neg.f64 (fma.f64 x x (.f64 y (+.f64 x y)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (+.f64 x y) (-.f64 y x))) (neg.f64 (+.f64 x y)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) #s(literal 1 binary64)) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(literal 1 binary64)) (+.f64 x y))
(/.f64 (.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 #s(literal 1 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 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (fma.f64 x (.f64 x x) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y (+.f64 x y))))) (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))))
(/.f64 (.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 #s(literal 1 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 (fma.f64 x x (.f64 y y)) (.f64 (-.f64 x y) (+.f64 x y))) (/.f64 #s(literal 1 binary64) (+.f64 x y))) (fma.f64 x x (*.f64 y y)))
(/.f64 (.f64 (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 y x)) #s(literal 1 binary64)) (neg.f64 (fma.f64 x x (.f64 y (+.f64 x y)))))
(/.f64 (.f64 (.f64 (+.f64 x y) (-.f64 y x)) #s(literal 1 binary64)) (neg.f64 (+.f64 x y)))
(pow.f64 (-.f64 x y) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (-.f64 x y) #s(literal 1 binary64))
(.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y (+.f64 x y)))))
(.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y (+.f64 x y)))) #s(literal 1 binary64)))
(.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (/.f64 (-.f64 x y) (fma.f64 x x (*.f64 y (+.f64 x y)))))
(.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (.f64 (-.f64 x y) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y (+.f64 x y))))))
(*.f64 #s(literal 1 binary64) (-.f64 x y))
(.f64 (.f64 (-.f64 x y) (+.f64 x y)) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
(.f64 (.f64 (-.f64 x y) (+.f64 x y)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal 1 binary64)))
(*.f64 (+.f64 x y) (/.f64 (-.f64 x y) (+.f64 x y)))
(.f64 (+.f64 x y) (.f64 (-.f64 x y) (/.f64 #s(literal 1 binary64) (+.f64 x y))))
(*.f64 #s(literal -1 binary64) (-.f64 y x))
(.f64 (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (.f64 y (+.f64 x y))))))
(.f64 (.f64 (+.f64 x y) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x y))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y (+.f64 x y)))) (fma.f64 x (.f64 x x) (.f64 y (*.f64 y y))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (.f64 (-.f64 x y) (+.f64 x y)))
(.f64 (.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y (+.f64 x y)))))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 (-.f64 x y) (+.f64 x y))) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
(.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x (.f64 x x) (.f64 y (.f64 y y)))) (fma.f64 x x (.f64 y (-.f64 y x))))
(.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (*.f64 (-.f64 x y) (+.f64 x y))) (-.f64 x y))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (fma.f64 (.f64 y (+.f64 x y)) (.f64 (.f64 y (+.f64 x y)) (.f64 y (+.f64 x y))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 y (+.f64 x y)) (-.f64 (.f64 y (+.f64 x y)) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 (.f64 x x) (.f64 y (+.f64 x y))))) (-.f64 (.f64 x x) (.f64 y (+.f64 x y))))

simplify214.0ms (3.7%)

Memory

17.1MiB live, 372.2MiB 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)
(*.f64 #s(literal -1/2 binary64) y)
(+ (* -1/2 y) (* 1/2 x))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(+ (* -1/2 y) (* 1/2 x))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(+ (* -1/2 y) (* 1/2 x))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/2 (/ y x))))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* x (+ 1/2 (* -1/2 (/ y x))))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* x (+ 1/2 (* -1/2 (/ y x))))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (- (* 1/2 (/ y x)) 1/2)))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* -1 (* x (- (* 1/2 (/ y x)) 1/2)))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* -1 (* x (- (* 1/2 (/ y x)) 1/2)))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* -1/2 y) (* 1/2 x))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(+ (* -1/2 y) (* 1/2 x))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(+ (* -1/2 y) (* 1/2 x))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* y (- (* 1/2 (/ x y)) 1/2))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* y (- (* 1/2 (/ x y)) 1/2))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* y (- (* 1/2 (/ x y)) 1/2))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(+ (* -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)
(*.f64 x #s(literal 3/2 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)
(*.f64 x #s(literal 3/2 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))
(*.f64 x #s(literal 3/2 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)
(*.f64 #s(literal -1/2 binary64) y)
(* 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)
(*.f64 #s(literal -1/2 binary64) y)
(* -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)
(neg.f64 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)
(neg.f64 y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* -1 y)
(neg.f64 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)

eval71.0ms (1.2%)

Memory: -24.1MiB live, 106.5MiB allocated
Compiler: Compiled 8 910 to 1 111 computations (87.5% saved)

prune85.0ms (1.5%)

Memory

2.6MiB live, 120.3MiB allocated

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	411	14	425
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	412	14	426

Accuracy

99.9%

Counts

426 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	16.9%	(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)
	49.3%	(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)
▶	99.8%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
▶	99.8%	(fma.f64 (+.f64 x y) (/.f64 (-.f64 x y) (*.f64 #s(literal 2 binary64) (+.f64 x y))) x)
	51.9%	(fma.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (/.f64 #s(literal 1/2 binary64) (+.f64 x y)) x)
	51.3%	(/.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))
	31.3%	(/.f64 (-.f64 (.f64 (.f64 x x) (fma.f64 (-.f64 x y) #s(literal -1/2 binary64) x)) (.f64 (fma.f64 (-.f64 x y) #s(literal -1/2 binary64) x) (.f64 (-.f64 x y) (.f64 #s(literal 1/4 binary64) (-.f64 x y))))) (.f64 (fma.f64 (-.f64 x y) #s(literal -1/2 binary64) x) (fma.f64 (-.f64 x y) #s(literal -1/2 binary64) x)))
▶	99.8%	(-.f64 (fma.f64 x #s(literal 1/2 binary64) x) (*.f64 y #s(literal 1/2 binary64)))
	88.2%	(+.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))))
	77.7%	(+.f64 x (/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) y)) (.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 2 binary64) y))))
	99.6%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 x y))))
	57.8%	(+.f64 x (*.f64 #s(literal -1/2 binary64) y))
	51.1%	(*.f64 x #s(literal 3/2 binary64))
▶	49.3%	(*.f64 #s(literal -1/2 binary64) y)

Compiler

Compiled 448 to 226 computations (49.6% saved)

simplify814.0ms (13.9%)

Memory

-12.4MiB live, 585.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 y (.f64 y y))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 x (.f64 x x) (.f64 y (*.f64 y y)))
✓	cost-diff	0	(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)
✓	cost-diff	0	(-.f64 x y)
✓	cost-diff	0	(/.f64 (-.f64 x y) (*.f64 #s(literal 2 binary64) (+.f64 x y)))
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	1408	(fma.f64 (+.f64 x y) (/.f64 (-.f64 x y) (*.f64 #s(literal 2 binary64) (+.f64 x y))) x)
✓	cost-diff	0	(*.f64 y #s(literal 1/2 binary64))
✓	cost-diff	64	(fma.f64 x #s(literal 1/2 binary64) x)
✓	cost-diff	256	(-.f64 (fma.f64 x #s(literal 1/2 binary64) x) (*.f64 y #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) y)
✓	cost-diff	0	(-.f64 y x)
✓	cost-diff	0	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)

Rules

17 514×	`accelerator-lowering-fma.f32`
17 514×	`accelerator-lowering-fma.f64`
4 116×	`-lowering-.f32`
4 116×	`-lowering-.f64`
2 056×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	134
1	78	132
2	170	132
3	393	132
4	858	132
5	2870	132
6	6841	132
0	8080	125

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize112.0ms (1.9%)

Memory

16.7MiB live, 131.0MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.8%	(/.f64 #s(literal 1/2 binary64) (fma.f64 x x (*.f64 y (+.f64 x y))))
✓	accuracy	96.9%	(fma.f64 x x (*.f64 y (+.f64 x y)))
✓	accuracy	95.6%	(fma.f64 x (.f64 x x) (.f64 y (*.f64 y y)))
✓	accuracy	36.5%	(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)
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (+.f64 x y))
✓	accuracy	99.9%	(/.f64 (-.f64 x y) (*.f64 #s(literal 2 binary64) (+.f64 x y)))
✓	accuracy	99.8%	(fma.f64 (+.f64 x y) (/.f64 (-.f64 x y) (*.f64 #s(literal 2 binary64) (+.f64 x y))) x)
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(*.f64 y #s(literal 1/2 binary64))
✓	accuracy	99.8%	(-.f64 (fma.f64 x #s(literal 1/2 binary64) x) (*.f64 y #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) y)
✓	accuracy	100.0%	(-.f64 y x)
✓	accuracy	99.9%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)

Samples

42.0ms	214×	0	valid
12.0ms	20×	3	valid
7.0ms	7×	5	exit
6.0ms	12×	2	valid
6.0ms	3×	4	valid

Compiler

Compiled 146 to 31 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-mult: 22.0ms (43.7% of total)

ival-add: 10.0ms (19.9% of total)

ival-div: 7.0ms (13.9% of total)

adjust: 6.0ms (11.9% of total)

ival-sub: 5.0ms (9.9% of total)

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

exact: 0.0ms (0% of total)

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

series42.0ms (0.7%)

Memory

-5.8MiB live, 36.4MiB allocated

Counts

17 → 348

Calls

Call 1

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

Outputs
#<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 (* -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 (- (* 3/2 x) (* 1/2 y))>
#<alt (- (* 3/2 x) (* 1/2 y))>
#<alt (- (* 3/2 x) (* 1/2 y))>
#<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 (* 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 (* 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 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 -1/2>
#<alt (- (/ x y) 1/2)>
#<alt (- (* x (+ (* -1 (/ x (pow y 2))) (/ 1 y))) 1/2)>
#<alt (- (* x (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))) 1/2)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ (- (* -1 y) y) x)))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* y (- (* -1 y) y)) (pow x 2))) (* 1/2 (/ (- (* -1 y) y) x))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* y (- (* -1 y) y)) (pow x 2))) (+ (* 1/2 (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3))) (* 1/2 (/ (- (* -1 y) y) x)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ (- (* -1 y) y) x)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (- (* -1 y) y)) (* 1/2 (/ (* y (- (* -1 y) y)) x))) x)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* y (- (* -1 y) y))) (* 1/2 (/ (* (pow y 2) (- (* -1 y) y)) x))) x)) (* -1/2 (- (* -1 y) y))) x)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ y x)))>
#<alt (+ 1/2 (* y (- (/ y (pow x 2)) (/ 1 x))))>
#<alt (+ 1/2 (* y (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))))>
#<alt -1/2>
#<alt (- (* 1/2 (/ (- x (* -1 x)) y)) 1/2)>
#<alt (- (+ (* -1/2 (/ (* x (- x (* -1 x))) (pow y 2))) (* 1/2 (/ (- x (* -1 x)) y))) 1/2)>
#<alt (- (+ (* -1/2 (/ (* x (- x (* -1 x))) (pow y 2))) (+ (* 1/2 (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (* 1/2 (/ (- x (* -1 x)) y)))) 1/2)>
#<alt -1/2>
#<alt (- (* -1/2 (/ (- (* -1 x) x) y)) 1/2)>
#<alt (- (* -1 (/ (+ (* -1/2 (/ (* x (- (* -1 x) x)) y)) (* 1/2 (- (* -1 x) x))) y)) 1/2)>
#<alt (- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* 1/2 (* x (- (* -1 x) x)))) y)) (* 1/2 (- (* -1 x) x))) y)) 1/2)>
#<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 x) (* 1/2 y))>
#<alt (+ (* 1/2 y) (* x (+ 1/2 (/ (pow x 2) (pow y 2)))))>
#<alt (+ (* 1/2 y) (* x (+ 1/2 (* (pow x 2) (+ (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))))))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (+ (* -1/2 (/ y x)) (* -1/2 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow x 2))))))>
#<alt (* x (+ 3/2 (+ (* -1/2 (/ y x)) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow x 2))) (* 1/2 (/ (- (pow y 3) (+ (* -1 (* y (+ (* -1 (pow y 2)) (pow y 2)))) (* -1 (pow y 3)))) (pow x 3)))))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1/2 y) (* 1/2 (/ (+ (* -1 (pow y 2)) (pow y 2)) x))) x)) 3/2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (pow y 2)) (pow y 2))) (* -1/2 (/ (- (pow y 3) (+ (* -1 (pow y 3)) (* y (+ (* -1 (pow y 2)) (pow y 2))))) x))) x)) (* -1/2 y)) x)) 3/2)))>
#<alt (+ x (* 1/2 x))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* 1/2 x) (* y (- (/ (pow y 2) (pow x 2)) 1/2))))>
#<alt (+ x (+ (* 1/2 x) (* y (- (* (pow y 2) (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) 1/2))))>
#<alt (* 1/2 y)>
#<alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))>
#<alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (+ (* -1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow y 2))) (/ x y)))))>
#<alt (* y (+ 1/2 (+ (* -1/2 (/ x y)) (+ (* -1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow y 2))) (+ (* 1/2 (/ (- (pow x 3) (+ (* -1 (* x (+ (* -1 (pow x 2)) (pow x 2)))) (* -1 (pow x 3)))) (pow y 3))) (/ x y))))))>
#<alt (* 1/2 y)>
#<alt (* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))>
#<alt (* -1 (* y (- (* -1 (/ (+ x (+ (* -1/2 x) (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) y)))) y)) 1/2)))>
#<alt (* -1 (* y (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (pow x 2)) (pow x 2))) (* -1/2 (/ (- (pow x 3) (+ (* -1 (pow x 3)) (* x (+ (* -1 (pow x 2)) (pow x 2))))) y))) y)) (* -1/2 x))) y)) 1/2)))>
#<alt (pow y 3)>
#<alt (+ (pow x 3) (pow y 3))>
#<alt (+ (pow x 3) (pow y 3))>
#<alt (+ (pow x 3) (pow y 3))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ (pow y 3) (pow x 3))))>
#<alt (* (pow x 3) (+ 1 (/ (pow y 3) (pow x 3))))>
#<alt (* (pow x 3) (+ 1 (/ (pow y 3) (pow x 3))))>
#<alt (pow x 3)>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (pow y 3) (pow x 3))) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (pow y 3) (pow x 3))) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (pow y 3) (pow x 3))) 1)))>
#<alt (pow x 3)>
#<alt (+ (pow x 3) (pow y 3))>
#<alt (+ (pow x 3) (pow y 3))>
#<alt (+ (pow x 3) (pow y 3))>
#<alt (pow y 3)>
#<alt (* (pow y 3) (+ 1 (/ (pow x 3) (pow y 3))))>
#<alt (* (pow y 3) (+ 1 (/ (pow x 3) (pow y 3))))>
#<alt (* (pow y 3) (+ 1 (/ (pow x 3) (pow y 3))))>
#<alt (pow y 3)>
#<alt (* -1 (* (pow y 3) (- (* -1 (/ (pow x 3) (pow y 3))) 1)))>
#<alt (* -1 (* (pow y 3) (- (* -1 (/ (pow x 3) (pow y 3))) 1)))>
#<alt (* -1 (* (pow y 3) (- (* -1 (/ (pow x 3) (pow y 3))) 1)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (* 2 y)>
#<alt (+ (* 2 x) (* 2 y))>
#<alt (+ (* 2 x) (* 2 y))>
#<alt (+ (* 2 x) (* 2 y))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 2 (/ y x))))>
#<alt (* x (+ 2 (* 2 (/ y x))))>
#<alt (* x (+ 2 (* 2 (/ y x))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -2 (/ y x)) 2)))>
#<alt (* -1 (* x (- (* -2 (/ y x)) 2)))>
#<alt (* -1 (* x (- (* -2 (/ y x)) 2)))>
#<alt (* 2 x)>
#<alt (+ (* 2 x) (* 2 y))>
#<alt (+ (* 2 x) (* 2 y))>
#<alt (+ (* 2 x) (* 2 y))>
#<alt (* 2 y)>
#<alt (* y (+ 2 (* 2 (/ x y))))>
#<alt (* y (+ 2 (* 2 (/ x y))))>
#<alt (* y (+ 2 (* 2 (/ x y))))>
#<alt (* 2 y)>
#<alt (* -1 (* y (- (* -2 (/ x y)) 2)))>
#<alt (* -1 (* y (- (* -2 (/ x y)) 2)))>
#<alt (* -1 (* y (- (* -2 (/ x y)) 2)))>
#<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 (/ 1/2 (pow y 2))>
#<alt (+ (* -1/2 (/ x (pow y 3))) (* 1/2 (/ 1 (pow y 2))))>
#<alt (+ (* x (- (* 1/2 (/ (pow x 2) (pow y 5))) (* 1/2 (/ 1 (pow y 3))))) (* 1/2 (/ 1 (pow y 2))))>
#<alt (+ (* x (- (* (pow x 2) (+ (* -1/2 (/ x (pow y 6))) (* 1/2 (/ 1 (pow y 5))))) (* 1/2 (/ 1 (pow y 3))))) (* 1/2 (/ 1 (pow y 2))))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ (+ 1/2 (* -1/2 (/ y x))) (pow x 2))>
#<alt (/ (- (+ 1/2 (* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow x 2)))) (* 1/2 (/ y x))) (pow x 2))>
#<alt (/ (- (+ 1/2 (* -1 (/ (+ (* -1 (* y (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))))) (* -1/2 (pow y 3))) (pow x 3)))) (+ (* -1/2 (/ (pow y 2) (pow x 2))) (+ (* 1/2 (/ y x)) (* 1/2 (/ (pow y 2) (pow x 2)))))) (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ (+ 1/2 (* -1/2 (/ y x))) (pow x 2))>
#<alt (/ (+ 1/2 (* -1 (/ (- (+ (* -1/2 (/ (pow y 2) x)) (* 1/2 (/ (pow y 2) x))) (* -1/2 y)) x))) (pow x 2))>
#<alt (/ (+ 1/2 (* -1 (/ (- (* -1 (/ (- (+ (* 1/2 (/ (pow y 3) x)) (/ (* y (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) x)) (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) x)) (* -1/2 y)) x))) (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (+ (* -1/2 (/ y (pow x 3))) (* 1/2 (/ 1 (pow x 2))))>
#<alt (+ (* y (- (* 1/2 (/ (pow y 2) (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (* 1/2 (/ 1 (pow x 2))))>
#<alt (+ (* y (- (* (pow y 2) (+ (* -1/2 (/ y (pow x 6))) (* 1/2 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (* 1/2 (/ 1 (pow x 2))))>
#<alt (/ 1/2 (pow y 2))>
#<alt (/ (+ 1/2 (* -1/2 (/ x y))) (pow y 2))>
#<alt (/ (- (+ 1/2 (* -1 (/ (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))) (pow y 2)))) (* 1/2 (/ x y))) (pow y 2))>
#<alt (/ (- (+ 1/2 (* -1 (/ (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* -1/2 (pow x 3))) (pow y 3)))) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* 1/2 (/ x y)) (* 1/2 (/ (pow x 2) (pow y 2)))))) (pow y 2))>
#<alt (/ 1/2 (pow y 2))>
#<alt (/ (+ 1/2 (* -1/2 (/ x y))) (pow y 2))>
#<alt (/ (+ 1/2 (* -1 (/ (- (+ (* -1/2 (/ (pow x 2) y)) (* 1/2 (/ (pow x 2) y))) (* -1/2 x)) y))) (pow y 2))>
#<alt (/ (+ 1/2 (* -1 (/ (- (* -1 (/ (- (+ (* 1/2 (/ (pow x 3) y)) (/ (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) y)) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) y)) (* -1/2 x)) y))) (pow y 2))>

Calls

87 calls:

Time	Variable		Point	Expression
20.0ms	y	@	inf	(+ (* x (* x x)) (* y (* y y)))
1.0ms	y	@	-inf	(/ (- x y) (* 2 (+ x y)))
1.0ms	y	@	-inf	(/ 1/2 (+ (* x x) (* y (+ x y))))
1.0ms	x	@	inf	(+ (* (+ (* x (* x x)) (* y (* y y))) (/ 1/2 (+ (* x x) (* y (+ x y))))) x)
1.0ms	y	@	inf	(* -1/2 y)

rewrite407.0ms (7%)

Memory

18.7MiB live, 757.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 930×	`accelerator-lowering-fma.f32`
4 930×	`accelerator-lowering-fma.f64`
4 404×	`/-lowering-/.f32`
4 404×	`/-lowering-/.f64`
4 292×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	119
1	187	107
2	1885	107
0	8141	100

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 663

Calls

Call 1

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

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

simplify391.0ms (6.7%)

Memory

17.0MiB live, 710.1MiB allocated

Algorithm

1×	egg-herbie

Rules

10 656×	`accelerator-lowering-fma.f32`
10 656×	`accelerator-lowering-fma.f64`
4 142×	`-lowering-.f32`
4 142×	`-lowering-.f64`
2 820×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	479	2827
1	1472	2638
2	4699	2548
0	8324	2379

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
(+ 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)))))
(* -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) (* 1/2 y))
(* 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)))))
(* 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)
(* 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)))
(+ 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)))))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
-1/2
(- (/ x y) 1/2)
(- (* x (+ (* -1 (/ x (pow y 2))) (/ 1 y))) 1/2)
(- (* x (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))) 1/2)
1/2
(+ 1/2 (* 1/2 (/ (- (* -1 y) y) x)))
(+ 1/2 (+ (* -1/2 (/ (* y (- (* -1 y) y)) (pow x 2))) (* 1/2 (/ (- (* -1 y) y) x))))
(+ 1/2 (+ (* -1/2 (/ (* y (- (* -1 y) y)) (pow x 2))) (+ (* 1/2 (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3))) (* 1/2 (/ (- (* -1 y) y) x)))))
1/2
(+ 1/2 (* 1/2 (/ (- (* -1 y) y) x)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (- (* -1 y) y)) (* 1/2 (/ (* y (- (* -1 y) y)) x))) x)))
(+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* y (- (* -1 y) y))) (* 1/2 (/ (* (pow y 2) (- (* -1 y) y)) x))) x)) (* -1/2 (- (* -1 y) y))) x)))
1/2
(+ 1/2 (* -1 (/ y x)))
(+ 1/2 (* y (- (/ y (pow x 2)) (/ 1 x))))
(+ 1/2 (* y (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))))
-1/2
(- (* 1/2 (/ (- x (* -1 x)) y)) 1/2)
(- (+ (* -1/2 (/ (* x (- x (* -1 x))) (pow y 2))) (* 1/2 (/ (- x (* -1 x)) y))) 1/2)
(- (+ (* -1/2 (/ (* x (- x (* -1 x))) (pow y 2))) (+ (* 1/2 (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (* 1/2 (/ (- x (* -1 x)) y)))) 1/2)
-1/2
(- (* -1/2 (/ (- (* -1 x) x) y)) 1/2)
(- (* -1 (/ (+ (* -1/2 (/ (* x (- (* -1 x) x)) y)) (* 1/2 (- (* -1 x) x))) y)) 1/2)
(- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* 1/2 (* x (- (* -1 x) x)))) y)) (* 1/2 (- (* -1 x) x))) y)) 1/2)
(* -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)))))
(* 1/2 y)
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 y) (* x (+ 1/2 (/ (pow x 2) (pow y 2)))))
(+ (* 1/2 y) (* x (+ 1/2 (* (pow x 2) (+ (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))))))
(* 3/2 x)
(* x (+ 3/2 (* -1/2 (/ y x))))
(* x (+ 3/2 (+ (* -1/2 (/ y x)) (* -1/2 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow x 2))))))
(* x (+ 3/2 (+ (* -1/2 (/ y x)) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow x 2))) (* 1/2 (/ (- (pow y 3) (+ (* -1 (* y (+ (* -1 (pow y 2)) (pow y 2)))) (* -1 (pow y 3)))) (pow x 3)))))))
(* 3/2 x)
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/2 y) (* 1/2 (/ (+ (* -1 (pow y 2)) (pow y 2)) x))) x)) 3/2)))
(* -1 (* x (- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (pow y 2)) (pow y 2))) (* -1/2 (/ (- (pow y 3) (+ (* -1 (pow y 3)) (* y (+ (* -1 (pow y 2)) (pow y 2))))) x))) x)) (* -1/2 y)) x)) 3/2)))
(+ x (* 1/2 x))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(+ x (+ (* 1/2 x) (* y (- (/ (pow y 2) (pow x 2)) 1/2))))
(+ x (+ (* 1/2 x) (* y (- (* (pow y 2) (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) 1/2))))
(* 1/2 y)
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (+ (* -1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow y 2))) (/ x y)))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (+ (* -1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow y 2))) (+ (* 1/2 (/ (- (pow x 3) (+ (* -1 (* x (+ (* -1 (pow x 2)) (pow x 2)))) (* -1 (pow x 3)))) (pow y 3))) (/ x y))))))
(* 1/2 y)
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 x)) y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ x (+ (* -1/2 x) (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) y)))) y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (pow x 2)) (pow x 2))) (* -1/2 (/ (- (pow x 3) (+ (* -1 (pow x 3)) (* x (+ (* -1 (pow x 2)) (pow x 2))))) y))) y)) (* -1/2 x))) y)) 1/2)))
(pow y 3)
(+ (pow x 3) (pow y 3))
(+ (pow x 3) (pow y 3))
(+ (pow x 3) (pow y 3))
(pow x 3)
(* (pow x 3) (+ 1 (/ (pow y 3) (pow x 3))))
(* (pow x 3) (+ 1 (/ (pow y 3) (pow x 3))))
(* (pow x 3) (+ 1 (/ (pow y 3) (pow x 3))))
(pow x 3)
(* -1 (* (pow x 3) (- (* -1 (/ (pow y 3) (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (pow y 3) (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (pow y 3) (pow x 3))) 1)))
(pow x 3)
(+ (pow x 3) (pow y 3))
(+ (pow x 3) (pow y 3))
(+ (pow x 3) (pow y 3))
(pow y 3)
(* (pow y 3) (+ 1 (/ (pow x 3) (pow y 3))))
(* (pow y 3) (+ 1 (/ (pow x 3) (pow y 3))))
(* (pow y 3) (+ 1 (/ (pow x 3) (pow y 3))))
(pow y 3)
(* -1 (* (pow y 3) (- (* -1 (/ (pow x 3) (pow y 3))) 1)))
(* -1 (* (pow y 3) (- (* -1 (/ (pow x 3) (pow y 3))) 1)))
(* -1 (* (pow y 3) (- (* -1 (/ (pow x 3) (pow y 3))) 1)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(* 2 y)
(+ (* 2 x) (* 2 y))
(+ (* 2 x) (* 2 y))
(+ (* 2 x) (* 2 y))
(* 2 x)
(* x (+ 2 (* 2 (/ y x))))
(* x (+ 2 (* 2 (/ y x))))
(* x (+ 2 (* 2 (/ y x))))
(* 2 x)
(* -1 (* x (- (* -2 (/ y x)) 2)))
(* -1 (* x (- (* -2 (/ y x)) 2)))
(* -1 (* x (- (* -2 (/ y x)) 2)))
(* 2 x)
(+ (* 2 x) (* 2 y))
(+ (* 2 x) (* 2 y))
(+ (* 2 x) (* 2 y))
(* 2 y)
(* y (+ 2 (* 2 (/ x y))))
(* y (+ 2 (* 2 (/ x y))))
(* y (+ 2 (* 2 (/ x y))))
(* 2 y)
(* -1 (* y (- (* -2 (/ x y)) 2)))
(* -1 (* y (- (* -2 (/ x y)) 2)))
(* -1 (* y (- (* -2 (/ x y)) 2)))
(pow y 2)
(+ (* x y) (pow y 2))
(+ (* x (+ x y)) (pow y 2))
(+ (* x (+ x y)) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y x)))
(* (pow x 2) (+ 1 (+ (/ y x) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (/ y x) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y x)))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x))))
(pow x 2)
(+ (* x y) (pow x 2))
(+ (* y (+ x y)) (pow x 2))
(+ (* y (+ x y)) (pow x 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ x y)))
(* (pow y 2) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (/ x y)))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) y))) y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) y))) y))))
(/ 1/2 (pow y 2))
(+ (* -1/2 (/ x (pow y 3))) (* 1/2 (/ 1 (pow y 2))))
(+ (* x (- (* 1/2 (/ (pow x 2) (pow y 5))) (* 1/2 (/ 1 (pow y 3))))) (* 1/2 (/ 1 (pow y 2))))
(+ (* x (- (* (pow x 2) (+ (* -1/2 (/ x (pow y 6))) (* 1/2 (/ 1 (pow y 5))))) (* 1/2 (/ 1 (pow y 3))))) (* 1/2 (/ 1 (pow y 2))))
(/ 1/2 (pow x 2))
(/ (+ 1/2 (* -1/2 (/ y x))) (pow x 2))
(/ (- (+ 1/2 (* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow x 2)))) (* 1/2 (/ y x))) (pow x 2))
(/ (- (+ 1/2 (* -1 (/ (+ (* -1 (* y (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))))) (* -1/2 (pow y 3))) (pow x 3)))) (+ (* -1/2 (/ (pow y 2) (pow x 2))) (+ (* 1/2 (/ y x)) (* 1/2 (/ (pow y 2) (pow x 2)))))) (pow x 2))
(/ 1/2 (pow x 2))
(/ (+ 1/2 (* -1/2 (/ y x))) (pow x 2))
(/ (+ 1/2 (* -1 (/ (- (+ (* -1/2 (/ (pow y 2) x)) (* 1/2 (/ (pow y 2) x))) (* -1/2 y)) x))) (pow x 2))
(/ (+ 1/2 (* -1 (/ (- (* -1 (/ (- (+ (* 1/2 (/ (pow y 3) x)) (/ (* y (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) x)) (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) x)) (* -1/2 y)) x))) (pow x 2))
(/ 1/2 (pow x 2))
(+ (* -1/2 (/ y (pow x 3))) (* 1/2 (/ 1 (pow x 2))))
(+ (* y (- (* 1/2 (/ (pow y 2) (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (* 1/2 (/ 1 (pow x 2))))
(+ (* y (- (* (pow y 2) (+ (* -1/2 (/ y (pow x 6))) (* 1/2 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (* 1/2 (/ 1 (pow x 2))))
(/ 1/2 (pow y 2))
(/ (+ 1/2 (* -1/2 (/ x y))) (pow y 2))
(/ (- (+ 1/2 (* -1 (/ (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))) (pow y 2)))) (* 1/2 (/ x y))) (pow y 2))
(/ (- (+ 1/2 (* -1 (/ (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* -1/2 (pow x 3))) (pow y 3)))) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* 1/2 (/ x y)) (* 1/2 (/ (pow x 2) (pow y 2)))))) (pow y 2))
(/ 1/2 (pow y 2))
(/ (+ 1/2 (* -1/2 (/ x y))) (pow y 2))
(/ (+ 1/2 (* -1 (/ (- (+ (* -1/2 (/ (pow x 2) y)) (* 1/2 (/ (pow x 2) y))) (* -1/2 x)) y))) (pow y 2))
(/ (+ 1/2 (* -1 (/ (- (* -1 (/ (- (+ (* 1/2 (/ (pow x 3) y)) (/ (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) y)) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) y)) (* -1/2 x)) y))) (pow y 2))

Outputs
(+ x (* 1/2 x))
(*.f64 x #s(literal 3/2 binary64))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 x #s(literal 3/2 binary64) (*.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 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) 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 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(* 3/2 x)
(*.f64 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)))
(* 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 x #s(literal 3/2 binary64))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* -1 x)
(neg.f64 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 y (/.f64 x y)))
(* y (+ 1 (* -1 (/ x y))))
(-.f64 y (*.f64 y (/.f64 x y)))
(* y (+ 1 (* -1 (/ x y))))
(-.f64 y (*.f64 y (/.f64 x y)))
y
(* -1 (* y (- (/ x y) 1)))
(-.f64 y (*.f64 y (/.f64 x y)))
(* -1 (* y (- (/ x y) 1)))
(-.f64 y (*.f64 y (/.f64 x y)))
(* -1 (* y (- (/ x y) 1)))
(-.f64 y (*.f64 y (/.f64 x y)))
y
(+ y (* -1 x))
(-.f64 y x)
(+ y (* -1 x))
(-.f64 y x)
(+ y (* -1 x))
(-.f64 y x)
(* -1 x)
(neg.f64 x)
(* x (- (/ y x) 1))
(-.f64 (*.f64 x (/.f64 y x)) x)
(* x (- (/ y x) 1))
(-.f64 (*.f64 x (/.f64 y x)) x)
(* x (- (/ y x) 1))
(-.f64 (*.f64 x (/.f64 y x)) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(-.f64 (*.f64 x (/.f64 y x)) x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(-.f64 (*.f64 x (/.f64 y x)) x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(-.f64 (*.f64 x (/.f64 y x)) x)
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* -1/2 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)
(- (* 3/2 x) (* 1/2 y))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(- (* 3/2 x) (* 1/2 y))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(- (* 3/2 x) (* 1/2 y))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(* 3/2 x)
(*.f64 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)))
(* 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 x #s(literal 3/2 binary64))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(+ x (* 1/2 x))
(*.f64 x #s(literal 3/2 binary64))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 x #s(literal 3/2 binary64) (*.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 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) 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 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 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 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(* 3/2 x)
(*.f64 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)))
(* 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 x #s(literal 3/2 binary64))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(+ x (* 1/2 x))
(*.f64 x #s(literal 3/2 binary64))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 x #s(literal 3/2 binary64) (*.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 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) 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 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 x (/.f64 #s(literal 3/2 binary64) y) #s(literal -1/2 binary64)))
y
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
x
(* x (+ 1 (/ y x)))
(fma.f64 x (/.f64 y x) x)
(* x (+ 1 (/ y x)))
(fma.f64 x (/.f64 y x) x)
(* x (+ 1 (/ y x)))
(fma.f64 x (/.f64 y x) x)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 x (/.f64 y x) x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 x (/.f64 y x) x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 x (/.f64 y x) x)
x
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
y
(* y (+ 1 (/ x y)))
(fma.f64 y (/.f64 x y) y)
(* y (+ 1 (/ x y)))
(fma.f64 y (/.f64 x y) y)
(* y (+ 1 (/ x y)))
(fma.f64 y (/.f64 x y) y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 y (/.f64 x y) y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 y (/.f64 x y) y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 y (/.f64 x y) y)
-1/2
#s(literal -1/2 binary64)
(- (/ x y) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 x y))
(- (* x (+ (* -1 (/ x (pow y 2))) (/ 1 y))) 1/2)
(fma.f64 x (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x (*.f64 y y))) #s(literal -1/2 binary64))
(- (* x (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))) 1/2)
(fma.f64 x (fma.f64 x (+.f64 (/.f64 x (.f64 y (.f64 y y))) (/.f64 #s(literal -1 binary64) (*.f64 y y))) (/.f64 #s(literal 1 binary64) y)) #s(literal -1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ (- (* -1 y) y) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (neg.f64 y) y) x) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/2 (/ (* y (- (* -1 y) y)) (pow x 2))) (* 1/2 (/ (- (* -1 y) y) x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (neg.f64 y) y) x) (fma.f64 (.f64 #s(literal -1/2 binary64) y) (/.f64 (-.f64 (neg.f64 y) y) (.f64 x x)) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (/ (* y (- (* -1 y) y)) (pow x 2))) (+ (* 1/2 (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3))) (* 1/2 (/ (- (* -1 y) y) x)))))
(fma.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 y x) #s(literal -2 binary64) (/.f64 (.f64 (.f64 y y) (-.f64 (neg.f64 y) y)) (.f64 x (.f64 x x)))) (fma.f64 (.f64 #s(literal -1/2 binary64) y) (/.f64 (-.f64 (neg.f64 y) y) (.f64 x x)) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ (- (* -1 y) y) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (neg.f64 y) y) x) #s(literal 1/2 binary64))
(+ 1/2 (* -1 (/ (+ (* -1/2 (- (* -1 y) y)) (* 1/2 (/ (* y (- (* -1 y) y)) x))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 y (/.f64 (-.f64 (neg.f64 y) y) x)) (.f64 #s(literal -1/2 binary64) (-.f64 (neg.f64 y) y))) x))
(+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* y (- (* -1 y) y))) (* 1/2 (/ (* (pow y 2) (- (* -1 y) y)) x))) x)) (* -1/2 (- (* -1 y) y))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 (neg.f64 y) y) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 y (.f64 y (/.f64 (-.f64 (neg.f64 y) y) x))) (.f64 y (.f64 #s(literal -1/2 binary64) (-.f64 (neg.f64 y) y)))) x)) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1 (/ y x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 y x))
(+ 1/2 (* y (- (/ y (pow x 2)) (/ 1 x))))
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(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 1/2 binary64)) (*.f64 x x))
(/ (+ 1/2 (* -1 (/ (- (* -1 (/ (- (+ (* 1/2 (/ (pow y 3) x)) (/ (* y (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) x)) (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) x)) (* -1/2 y)) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) y (/.f64 (/.f64 (.f64 y (.f64 #s(literal 1/2 binary64) (.f64 y y))) x) x)) x)) (.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(+ (* -1/2 (/ y (pow x 3))) (* 1/2 (/ 1 (pow x 2))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 1/2 binary64)) (*.f64 x x))
(+ (* y (- (* 1/2 (/ (pow y 2) (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (* 1/2 (/ 1 (pow x 2))))
(fma.f64 y (fma.f64 (.f64 y y) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+ (* y (- (* (pow y 2) (+ (* -1/2 (/ y (pow x 6))) (* 1/2 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (* 1/2 (/ 1 (pow x 2))))
(fma.f64 y (fma.f64 (.f64 y y) (fma.f64 #s(literal -1/2 binary64) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ (+ 1/2 (* -1/2 (/ x y))) (pow y 2))
(/.f64 (fma.f64 x (/.f64 #s(literal -1/2 binary64) y) #s(literal 1/2 binary64)) (*.f64 y y))
(/ (- (+ 1/2 (* -1 (/ (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))) (pow y 2)))) (* 1/2 (/ x y))) (pow y 2))
(/.f64 (fma.f64 x (/.f64 #s(literal -1/2 binary64) y) #s(literal 1/2 binary64)) (*.f64 y y))
(/ (- (+ 1/2 (* -1 (/ (+ (* -1 (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* -1/2 (pow x 3))) (pow y 3)))) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* 1/2 (/ x y)) (* 1/2 (/ (pow x 2) (pow y 2)))))) (pow y 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 y (.f64 y y))) (fma.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (.f64 y y))) (.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x (.f64 y y)) (/.f64 x y)))))) (.f64 y y))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ (+ 1/2 (* -1/2 (/ x y))) (pow y 2))
(/.f64 (fma.f64 x (/.f64 #s(literal -1/2 binary64) y) #s(literal 1/2 binary64)) (*.f64 y y))
(/ (+ 1/2 (* -1 (/ (- (+ (* -1/2 (/ (pow x 2) y)) (* 1/2 (/ (pow x 2) y))) (* -1/2 x)) y))) (pow y 2))
(/.f64 (fma.f64 x (/.f64 #s(literal -1/2 binary64) y) #s(literal 1/2 binary64)) (*.f64 y y))
(/ (+ 1/2 (* -1 (/ (- (* -1 (/ (- (+ (* 1/2 (/ (pow x 3) y)) (/ (* x (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) y)) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) y)) (* -1/2 x)) y))) (pow y 2))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 (/.f64 (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))) y) y)) y)) (*.f64 y y))

eval178.0ms (3.1%)

Memory: -1.7MiB live, 311.6MiB allocated
Compiler: Compiled 32 803 to 2 795 computations (91.5% saved)

prune112.0ms (1.9%)

Memory

8.7MiB live, 244.4MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1 149	2	1 151
Fresh	8	1	9
Picked	3	2	5
Done	0	0	0
Total	1 160	5	1 165

Accuracy

100.0%

Counts

1 165 → 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)
▶	57.8%	(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))
▶	51.1%	(*.f64 x #s(literal 3/2 binary64))
✓	49.3%	(*.f64 #s(literal -1/2 binary64) y)

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify5.0ms (0.1%)

Memory

-27.8MiB live, 11.0MiB 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 x #s(literal 3/2 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
(* x 3/2)
x
3/2
(+ (* x 3/2) (* -1/2 y))
x
3/2
(* -1/2 y)
-1/2
y
(+ (* y -1/2) x)
y
-1/2
x

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

localize32.0ms (0.5%)

Memory

25.6MiB live, 66.6MiB 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 x #s(literal 3/2 binary64))

Samples

18.0ms	229×	0	valid
2.0ms	15×	1	valid
1.0ms	7×	3	valid
1.0ms	5×	2	valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

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

ival-mult: 8.0ms (66.4% of total)

ival-add: 3.0ms (24.9% of total)

adjust: 1.0ms (8.3% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

6.7MiB live, 6.7MiB allocated

Counts

4 → 72

Calls

Call 1

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

Outputs
#<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 (* -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
2.0ms	x	@	inf	(* x 3/2)
0.0ms	x	@	-inf	(* x 3/2)
0.0ms	x	@	0	(* x 3/2)
0.0ms	y	@	0	(+ (* x 3/2) (* -1/2 y))
0.0ms	x	@	0	(+ (* x 3/2) (* -1/2 y))

rewrite410.0ms (7%)

Memory

-18.3MiB live, 614.0MiB 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	3047	18
0	8265	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 264

Calls

Call 1

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

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

simplify310.0ms (5.3%)

Memory

11.3MiB live, 382.1MiB 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`
2 292×	`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	3269	318
6	4571	318
7	5107	318
8	5318	318
9	5479	318
10	7149	318
0	8013	282

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

eval38.0ms (0.7%)

Memory: 2.0MiB live, 76.0MiB allocated
Compiler: Compiled 10 279 to 795 computations (92.3% saved)

prune37.0ms (0.6%)

Memory

2.9MiB live, 84.1MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	335	6	341

Accuracy

100.0%

Counts

341 → 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)
✓	57.8%	(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))
✓	51.1%	(*.f64 x #s(literal 3/2 binary64))
✓	49.3%	(*.f64 #s(literal -1/2 binary64) y)
▶	11.9%	x

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify3.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
x

Outputs
x

localize8.0ms (0.1%)

Memory

-27.2MiB live, 11.7MiB allocated

Samples

6.0ms

256×

valid

Compiler

Compiled 3 to 4 computations (-33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

series0.0ms (0%)

Memory

0.0MiB live, 0.0MiB allocated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite7.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify3.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

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

prune6.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	5	5
Total	6	6

Accuracy

100.0%

Counts

6 → 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)
✓	57.8%	(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))
✓	51.1%	(*.f64 x #s(literal 3/2 binary64))
✓	49.3%	(*.f64 #s(literal -1/2 binary64) y)
✓	11.9%	x

Compiler

Compiled 251 to 90 computations (64.1% saved)

regimes28.0ms (0.5%)

Memory

-10.0MiB live, 27.4MiB allocated

Counts

18 → 1

Calls

Call 1

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

15.0ms	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))
6.0ms	y
6.0ms	x

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)

regimes9.0ms (0.2%)

Memory

14.1MiB live, 14.1MiB allocated

Counts

6 → 1

Calls

Call 1

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

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)

regimes19.0ms (0.3%)

Memory

-29.2MiB live, 13.2MiB allocated

Counts

5 → 3

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
77.6%	3	`x`
81.8%	3	`y`
64.3%	3	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes2.0ms (0%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

3 → 3

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
80.2%	3	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes5.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
49.3%	1	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`
49.3%	1	`x`
49.3%	1	`y`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0.1%)

Memory

11.3MiB live, 11.3MiB 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	x
1.0ms	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))
1.0ms	y

Results

Accuracy	Segments	Branch
11.9%	1	`y`
11.9%	1	`x`
11.9%	1	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch22.0ms (0.4%)

Memory

1.0MiB live, 39.7MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	1.180208338290647e-19	6.584431477153592e-18
11.0ms	-9.872859165942661e+58	-4.4834734649824224e+55

Samples

10.0ms	219×	0	valid
1.0ms	9×	2	valid
1.0ms	12×	1	valid

Compiler

Compiled 207 to 161 computations (22.2% saved)

Precisions

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

ival-div: 2.0ms (35.6% of total)

ival-sub: 2.0ms (35.6% of total)

ival-add: 1.0ms (17.8% 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)

bsearch24.0ms (0.4%)

Memory

-10.2MiB live, 66.6MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	1.180208338290647e-19	6.584431477153592e-18
13.0ms	-7.032146348287423e+76	-6.395858713496665e+70

Samples

12.0ms	233×	0	valid
1.0ms	16×	1	valid
1.0ms	7×	2	valid

Compiler

Compiled 204 to 171 computations (16.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-sub: 3.0ms (44.2% of total)

ival-div: 2.0ms (29.4% of total)

ival-add: 1.0ms (14.7% 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)

simplify19.0ms (0.3%)

Memory

-37.8MiB live, 21.7MiB 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	47
1	32	47
2	37	47
3	39	47
4	40	47

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 (-.f64 y x) #s(literal -1/2 binary64) x)
(if (<=.f64 y #s(literal -320000000000000003275221446530736367881740420330391863296 binary64)) (fma.f64 y #s(literal -1/2 binary64) x) (if (<=.f64 y #s(literal 4984604984193435/41538374868278621028243970633760768 binary64)) (*.f64 x #s(literal 3/2 binary64)) (fma.f64 y #s(literal -1/2 binary64) x)))
(if (<=.f64 y #s(literal -86000000000000001640216906213847645774579117778673337318348706820390912 binary64)) (.f64 #s(literal -1/2 binary64) y) (if (<=.f64 y #s(literal 2271629875608987/1298074214633706907132624082305024 binary64)) (.f64 x #s(literal 3/2 binary64)) (*.f64 #s(literal -1/2 binary64) y)))
(*.f64 #s(literal -1/2 binary64) y)
x

Outputs
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
(if (<=.f64 y #s(literal -320000000000000003275221446530736367881740420330391863296 binary64)) (fma.f64 y #s(literal -1/2 binary64) x) (if (<=.f64 y #s(literal 4984604984193435/41538374868278621028243970633760768 binary64)) (*.f64 x #s(literal 3/2 binary64)) (fma.f64 y #s(literal -1/2 binary64) x)))
(if (<=.f64 y #s(literal -86000000000000001640216906213847645774579117778673337318348706820390912 binary64)) (.f64 #s(literal -1/2 binary64) y) (if (<=.f64 y #s(literal 2271629875608987/1298074214633706907132624082305024 binary64)) (.f64 x #s(literal 3/2 binary64)) (*.f64 #s(literal -1/2 binary64) y)))
(*.f64 #s(literal -1/2 binary64) y)
x

soundness969.0ms (16.6%)

Memory

37.9MiB live, 570.5MiB allocated

Rules

10 656×	`accelerator-lowering-fma.f32`
10 656×	`accelerator-lowering-fma.f64`
8 340×	`accelerator-lowering-fma.f32`
8 340×	`accelerator-lowering-fma.f64`
7 504×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	479	2827
1	1472	2638
2	4699	2548
0	8324	2379
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	39	318
1	109	318
2	291	318
3	720	318
4	1675	318
5	3269	318
6	4571	318
7	5107	318
8	5318	318
9	5479	318
10	7149	318
0	8013	282
0	6	15
1	45	15
2	397	15
3	5077	15
0	8178	14

Stop Event

1×	done
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 129 to 74 computations (42.6% saved)

preprocess88.0ms (1.5%)

Memory: -24.7MiB live, 193.9MiB allocated
Compiler: Compiled 144 to 70 computations (51.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	41
1	45	35
2	139	35
3	373	35
4	647	35
5	807	35
6	846	35
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	16	41
1	45	35
2	139	35
3	373	35
4	647	35
5	807	35
6	846	35
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%)

sample793.0ms (13.6%)

preprocess60.0ms (1%)

explain79.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify29.0ms (0.5%)

localize22.0ms (0.4%)

series4.0ms (0.1%)

rewrite376.0ms (6.4%)

simplify214.0ms (3.7%)

eval71.0ms (1.2%)

prune85.0ms (1.5%)

simplify814.0ms (13.9%)

localize112.0ms (1.9%)

series42.0ms (0.7%)

rewrite407.0ms (7%)

simplify391.0ms (6.7%)

eval178.0ms (3.1%)

prune112.0ms (1.9%)

simplify5.0ms (0.1%)

localize32.0ms (0.5%)

series4.0ms (0.1%)

rewrite410.0ms (7%)

simplify310.0ms (5.3%)

eval38.0ms (0.7%)

prune37.0ms (0.6%)

simplify3.0ms (0.1%)

localize8.0ms (0.1%)

series0.0ms (0%)

rewrite7.0ms (0.1%)

simplify3.0ms (0%)

eval0.0ms (0%)

prune6.0ms (0.1%)

regimes28.0ms (0.5%)

regimes9.0ms (0.2%)

regimes19.0ms (0.3%)

regimes2.0ms (0%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch22.0ms (0.4%)

bsearch24.0ms (0.4%)

simplify19.0ms (0.3%)

soundness969.0ms (16.6%)

preprocess88.0ms (1.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	41
1	45	35
2	139	35
3	373	35
4	647	35
5	807	35
6	846	35
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