Metrics for Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, F

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 7 to 7 computations (0% saved)

sample551.0ms (9.9%)

Memory

41.9MiB live, 822.1MiB allocated

Samples

330.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 138.0ms

ival-div: 80.0ms (57.9% of total)

ival-add: 42.0ms (30.4% of total)

exact: 7.0ms (5.1% of total)

ival-true: 6.0ms (4.3% of total)

ival-assert: 3.0ms (2.2% of total)

Bogosity

preprocess18.0ms (0.3%)

Memory

-0.9MiB live, 36.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`associate--r+`
12×	`sub-neg`
10×	`distribute-lft-neg-in`
10×	`associate-+l-`
10×	`distribute-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	20	6
2	42	6
3	74	6
4	96	6
5	106	6
0	5	3
0	8	3
1	11	3
0	11	3

Stop Event

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

Calls

Call 1

Inputs
(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Outputs
(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
(+.f64 x #s(literal 1/3 binary64))

explain63.0ms (1.1%)

Memory

8.9MiB live, 120.3MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 1 binary64)`
-	-	`#s(literal 3 binary64)`
-	-	`(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))`
-	-	`(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`
-	-	`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

30.0ms

512×

valid

Compiler

Compiled 38 to 24 computations (36.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-div: 16.0ms (83.9% of total)

ival-add: 2.0ms (10.5% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))

Rules

4×	`lower-+.f32`
2×	`lift-+.f64`
2×	`lift-/.f64`
2×	`lower-+.f64`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
0	8	7
1	11	7
0	11	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
x
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 3 binary64)

Outputs
(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
(+.f64 x #s(literal 1/3 binary64))
x
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1/3 binary64)
#s(literal 1 binary64)
#s(literal 3 binary64)

localize18.0ms (0.3%)

Memory

-2.0MiB live, 35.0MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
✓	accuracy	100.0%	(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Samples

11.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

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

ival-div: 4.0ms (66.3% of total)

ival-add: 1.0ms (16.6% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Counts

2 → 12

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))>
#<alt (+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))>

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

Calls

3 calls:

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

rewrite413.0ms (7.4%)

Memory

-5.3MiB live, 667.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 708×	`lower-fma.f64`
8 708×	`lower-fma.f32`
5 116×	`lower-*.f64`
5 116×	`lower-*.f32`
3 868×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
0	8	4
1	25	4
2	126	4
3	957	4
0	8643	4

Stop Event

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

Counts

2 → 265

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Outputs
#s(literal 1/3 binary64)
(+.f64 #s(literal 1/3 binary64) x)
(+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1/3 binary64))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) x)))
(+.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(+.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) x)) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(+.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/3 binary64))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #s(literal 1/27 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #s(literal 1/27 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (.f64 x (.f64 x x))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (*.f64 x x)))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))))))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x x))))) (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 x (.f64 x (*.f64 x x)))))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (.f64 x x)) (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (neg.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)))))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x x #s(literal -1/9 binary64))) (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (*.f64 #s(literal 1/3 binary64) x)))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (.f64 x x)) (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (*.f64 x x)))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (fma.f64 x x #s(literal 1/9 binary64))) (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (*.f64 #s(literal 1/3 binary64) x)))
(+.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1/3 binary64))
(+.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal 1 binary64)))
(+.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 #s(literal 1/27 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(+.f64 (.f64 #s(literal 1/27 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) (.f64 (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x x)))) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (*.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))))
(+.f64 (.f64 (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x x)))) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (*.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))))
(+.f64 (.f64 (.f64 x x) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x)))))) (.f64 (neg.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (+.f64 #s(literal 1/3 binary64) x)))))))
(+.f64 (.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x)))))) (.f64 (.f64 #s(literal 1/3 binary64) x) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (+.f64 #s(literal 1/3 binary64) x)))))))
(+.f64 (.f64 (.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64)))))
(+.f64 (.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (.f64 (.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64)))))
(+.f64 (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (.f64 (.f64 #s(literal 1/3 binary64) x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) x))) #s(literal -1 binary64)))
(-.f64 x #s(literal -1/3 binary64))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/3 binary64) (neg.f64 x)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(-.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1/3 binary64) x)))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 (/.f64 #s(literal 1/729 binary64) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (+.f64 x #s(literal -1/3 binary64))) (/.f64 (/.f64 #s(literal 1/729 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (+.f64 x #s(literal -1/3 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1/9 binary64))) (+.f64 x #s(literal -1/3 binary64))) (/.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (+.f64 x #s(literal -1/3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 #s(literal 1/3 binary64) x)))) (+.f64 #s(literal -1/3 binary64) (neg.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/3 binary64) x)) (+.f64 #s(literal -1/3 binary64) (neg.f64 x)))
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(.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))))
(.f64 (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 #s(literal 1/3 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x x))))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x x))))))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (+.f64 #s(literal -1/9 binary64) (*.f64 x (+.f64 #s(literal 1/3 binary64) x))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/9 binary64) (*.f64 x (+.f64 #s(literal 1/3 binary64) x))))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64)))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x x))))) (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 #s(literal 1/3 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/19683 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/729 binary64)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/27 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1/729 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/19683 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/729 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/19683 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/729 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1/729 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x x))))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1/729 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/9 binary64) (*.f64 x (+.f64 #s(literal 1/3 binary64) x))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1/729 binary64)) (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) x))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1/729 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1/729 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (+.f64 x #s(literal -1/3 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1/729 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 #s(literal -1/27 binary64) (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 #s(literal 1/3 binary64) x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1/81 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (+.f64 x #s(literal -1/3 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 #s(literal -1/27 binary64) (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) x)))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 #s(literal -1/27 binary64) (.f64 x (*.f64 x x))))) (/.f64 #s(literal -1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1/729 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (-.f64 #s(literal 1/3 binary64) x)))
(.f64 (/.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1/81 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 #s(literal 1/3 binary64) x)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) x)) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/27 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x)))))) (+.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) x))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64)))) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/19683 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/729 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))))

simplify7.0ms (0.1%)

Memory

17.2MiB live, 17.2MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`lower-*.f64`
36×	`lower-*.f32`
16×	`lower-/.f32`
16×	`associate-r`
16×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	22	30
2	37	30
3	77	30
4	77	30
5	78	30
6	80	30
7	80	30
0	80	30

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 10

Calls

Call 1

Inputs
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))

Outputs
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)

eval33.0ms (0.6%)

Memory: 2.9MiB live, 80.7MiB allocated
Compiler: Compiled 7 850 to 630 computations (92% saved)

prune32.0ms (0.6%)

Memory

9.0MiB live, 86.5MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	271	4	275
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	272	4	276

Accuracy

100.0%

Counts

276 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.1%	(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
▶	70.2%	(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
▶	100.0%	(-.f64 x #s(literal -1/3 binary64))
▶	52.1%	#s(literal 1/3 binary64)

Compiler

Compiled 38 to 25 computations (34.2% saved)

simplify13.0ms (0.2%)

Memory

-12.9MiB live, 26.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 x (.f64 x x))
✓	cost-diff	(fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64))
✓	cost-diff	(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
✓	cost-diff	(fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
✓	cost-diff	(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
✓	cost-diff	(-.f64 x #s(literal -1/3 binary64))

Rules

220×	`lower-fma.f32`
212×	`lower-fma.f64`
140×	`lower-+.f32`
138×	`lower-+.f64`
66×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	93
0	30	85
1	56	83
2	98	83
3	145	83
4	173	83
5	190	83
6	196	83
0	196	83

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal 1/3 binary64)
(-.f64 x #s(literal -1/3 binary64))
x
#s(literal -1/3 binary64)
(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
x
(*.f64 x x)
#s(literal 1/27 binary64)
(fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(+.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
#s(literal 1/9 binary64)
(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64))
x
(.f64 x (.f64 x x))
(*.f64 x x)
#s(literal -1/81 binary64)
(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))
(fma.f64 x x #s(literal 1/9 binary64))
#s(literal 1/9 binary64)
(+.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)

Outputs
#s(literal 1/3 binary64)
(-.f64 x #s(literal -1/3 binary64))
(+.f64 x #s(literal 1/3 binary64))
x
#s(literal -1/3 binary64)
(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
x
(*.f64 x x)
#s(literal 1/27 binary64)
(fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(+.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
#s(literal 1/9 binary64)
(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
(/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1/81 binary64)) (*.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))
(fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal -1/81 binary64))
x
(.f64 x (.f64 x x))
(*.f64 x x)
#s(literal -1/81 binary64)
(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))
(*.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))
(fma.f64 x x #s(literal 1/9 binary64))
#s(literal 1/9 binary64)
(+.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)

localize191.0ms (3.4%)

Memory

-3.4MiB live, 151.9MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64))
✓	accuracy	99.9%	(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	67.1%	(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/3 binary64))
✓	accuracy	100.0%	(fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
✓	accuracy	71.0%	(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
✓	accuracy	100.0%	(-.f64 x #s(literal -1/3 binary64))

Samples

162.0ms

256×

valid

Compiler

Compiled 104 to 21 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 147.0ms

ival-sub: 112.0ms (76.3% of total)

const: 14.0ms (9.5% of total)

ival-mult: 8.0ms (5.5% of total)

ival-div: 6.0ms (4.1% of total)

ival-add: 6.0ms (4.1% of total)

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

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

series7.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (-.f64 x #s(literal -1/3 binary64))>
#<alt (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))>
#<alt (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))>
#<alt (*.f64 x x)>
#<alt (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))>
#<alt (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))>
#<alt (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64))>
#<alt (.f64 x (.f64 x x))>
#<alt (+.f64 x #s(literal -1/3 binary64))>
#<alt (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))>

Outputs
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt 1/27>
#<alt (+ 1/27 (pow x 3))>
#<alt (+ 1/27 (pow x 3))>
#<alt (+ 1/27 (pow x 3))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<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 1/9>
#<alt (+ 1/9 (* -1/3 x))>
#<alt (+ 1/9 (* x (- x 1/3)))>
#<alt (+ 1/9 (* x (- x 1/3)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 1/3 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 1/3 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x))))>
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt -1/81>
#<alt (- (pow x 4) 1/81)>
#<alt (- (pow x 4) 1/81)>
#<alt (- (pow x 4) 1/81)>
#<alt (pow x 4)>
#<alt (* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))>
#<alt (pow x 4)>
#<alt (* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt -1/3>
#<alt (- x 1/3)>
#<alt (- x 1/3)>
#<alt (- x 1/3)>
#<alt x>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt -1/27>
#<alt (- (* 1/9 x) 1/27)>
#<alt (- (* x (+ 1/9 (* -1/3 x))) 1/27)>
#<alt (- (* x (+ 1/9 (* x (- x 1/3)))) 1/27)>
#<alt (pow x 3)>
#<alt (* (pow x 3) (- 1 (* 1/3 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))))>
#<alt (pow x 3)>
#<alt (* -1 (* (pow x 3) (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1)))>

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ (+ (* x (* x (* x x))) -1/81) (* (+ (* x x) 1/9) (+ x -1/3)))
1.0ms	x	@	inf	(/ (+ (* x (* x x)) 1/27) (+ (* x (+ x -1/3)) 1/9))
1.0ms	x	@	0	(/ (+ (* x (* x x)) 1/27) (+ (* x (+ x -1/3)) 1/9))
1.0ms	x	@	inf	(/ (+ (* x (* x (* x x))) -1/81) (* (+ (* x x) 1/9) (+ x -1/3)))
0.0ms	x	@	-inf	(/ (+ (* x (* x x)) 1/27) (+ (* x (+ x -1/3)) 1/9))

rewrite1.0s (18.3%)

Memory

-50.4MiB live, 669.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

9 322×	`lower-fma.f32`
9 314×	`lower-fma.f64`
5 450×	`lower-*.f32`
5 444×	`lower-*.f64`
4 152×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	72
0	29	43
1	138	42
2	1035	42
0	8996	42

Stop Event

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

Counts

10 → 1 257

Calls

Call 1

Inputs
(-.f64 x #s(literal -1/3 binary64))
(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
(*.f64 x x)
(fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64))
(.f64 x (.f64 x x))
(+.f64 x #s(literal -1/3 binary64))
(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))

Outputs
(+.f64 x #s(literal 1/3 binary64))
(+.f64 #s(literal 1/3 binary64) x)
(+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1 binary64)))
(+.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(+.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 #s(literal 1/27 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(+.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/3 binary64))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #s(literal 1/27 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (.f64 x (.f64 x x))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #s(literal 1/27 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))) #s(literal -1/81 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))) (.f64 x (.f64 x (*.f64 x x)))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))) #s(literal -1/81 binary64)))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (.f64 x x)) (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (-.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64)))))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (-.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64)))) (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (.f64 x x)))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))))) #s(literal 1/729 binary64))) (.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))))) (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))))) #s(literal 1/729 binary64))) (-.f64 #s(literal 1/81 binary64) (.f64 (fma.f64 x #s(literal 1/9 binary64) #s(literal -1/27 binary64)) x))))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))))) #s(literal 1/729 binary64))) (-.f64 #s(literal 1/81 binary64) (.f64 (fma.f64 x #s(literal 1/9 binary64) #s(literal -1/27 binary64)) x))) (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))))) #s(literal 1/729 binary64))) (.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))))))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/81 binary64))) (.f64 x x)) (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 (.f64 x x) (*.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/81 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/81 binary64))) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 (.f64 x x) (*.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/81 binary64))) #s(literal -1/9 binary64)))
(+.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1/3 binary64))
(+.f64 (.f64 #s(literal 1/27 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(+.f64 (.f64 #s(literal -1/81 binary64) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (.f64 #s(literal -1/81 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))))
(+.f64 (.f64 (.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))))
(+.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (.f64 (.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))))
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(.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1/729 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1/81 binary64)) (.f64 (.f64 x x) #s(literal -1/9 binary64))) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal 1/3 binary64)))))))
(.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1/729 binary64)) (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1/81 binary64)) (.f64 (*.f64 x x) #s(literal -1/9 binary64))) (+.f64 x #s(literal 1/3 binary64)))))
(.f64 (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1/9 binary64)) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal 1/3 binary64)))))))
(.f64 (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1/3 binary64)) (fma.f64 x x #s(literal -1/9 binary64)))))
(*.f64 (fma.f64 x (neg.f64 x) #s(literal -1/9 binary64)) (+.f64 #s(literal 1/3 binary64) (neg.f64 x)))
(*.f64 (+.f64 #s(literal 1/3 binary64) (neg.f64 x)) (fma.f64 x (neg.f64 x) #s(literal -1/9 binary64)))
(.f64 (fma.f64 (.f64 x (fma.f64 x x #s(literal 1/9 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 x x) #s(literal -1/27 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (.f64 x (fma.f64 x x #s(literal 1/9 binary64)))) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 x x) #s(literal -1/27 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 x x) #s(literal -1/27 binary64)) (*.f64 x (fma.f64 x x #s(literal 1/9 binary64))))))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))))
(.f64 (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal 1/3 binary64)))))
(.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1/81 binary64)) (.f64 (.f64 x x) #s(literal -1/9 binary64)))))
(.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1/9 binary64))))
(.f64 (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal 1/3 binary64))))))
(.f64 (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal 1/3 binary64))))))
(.f64 (.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1/729 binary64)) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1/81 binary64)) (.f64 (.f64 x x) #s(literal -1/9 binary64)))))
(.f64 (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1/9 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64))) (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64))) (*.f64 (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))
(.f64 (/.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64))) (/.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1/81 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1/729 binary64)))) (/.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1/81 binary64)) (.f64 (*.f64 x x) #s(literal -1/9 binary64)))))
(.f64 (/.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1/81 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(.f64 (/.f64 (+.f64 x #s(literal -1/3 binary64)) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1/729 binary64)))) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (+.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1/81 binary64)) (.f64 (*.f64 x x) #s(literal -1/9 binary64)))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1/9 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 #s(literal -1/27 binary64) (.f64 x (*.f64 x x)))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 (.f64 x x) (.f64 x (neg.f64 x)) #s(literal 1/81 binary64))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1/3 binary64)))
(.f64 (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal 1/3 binary64))))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))))) #s(literal 1/729 binary64)))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 (fma.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1/81 binary64)) (*.f64 (fma.f64 x #s(literal 1/9 binary64) #s(literal -1/27 binary64)) x))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/81 binary64)))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/9 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 #s(literal -1/27 binary64) (.f64 x (*.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) (.f64 x (neg.f64 x)) #s(literal 1/81 binary64))) (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 #s(literal -1 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal 1/3 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal 1/3 binary64))))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))))) #s(literal 1/729 binary64)))) (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 (fma.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1/81 binary64)) (*.f64 (fma.f64 x #s(literal 1/9 binary64) #s(literal -1/27 binary64)) x))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) (fma.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/81 binary64)))) (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/9 binary64))))
(*.f64 (/.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))
(.f64 (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)))) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(.f64 (.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1/3 binary64)))

simplify567.0ms (10.2%)

Memory

27.6MiB live, 538.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14 434×	`lower-fma.f64`
14 434×	`lower-fma.f32`
3 040×	`lower-*.f64`
3 040×	`lower-*.f32`
1 698×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	522
1	235	506
2	665	494
3	2398	462
4	6748	462
0	8088	452

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 112

Calls

Call 1

Inputs
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
1/27
(+ 1/27 (pow x 3))
(+ 1/27 (pow x 3))
(+ 1/27 (pow x 3))
(pow x 3)
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(pow x 3)
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(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)
1/9
(+ 1/9 (* -1/3 x))
(+ 1/9 (* x (- x 1/3)))
(+ 1/9 (* x (- x 1/3)))
(pow x 2)
(* (pow x 2) (- 1 (* 1/3 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 1/3 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x))))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
-1/81
(- (pow x 4) 1/81)
(- (pow x 4) 1/81)
(- (pow x 4) 1/81)
(pow x 4)
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(pow x 4)
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
-1/27
(- (* 1/9 x) 1/27)
(- (* x (+ 1/9 (* -1/3 x))) 1/27)
(- (* x (+ 1/9 (* x (- x 1/3)))) 1/27)
(pow x 3)
(* (pow x 3) (- 1 (* 1/3 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))))
(pow x 3)
(* -1 (* (pow x 3) (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1)))

Outputs
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
1/27
#s(literal 1/27 binary64)
(+ 1/27 (pow x 3))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
(+ 1/27 (pow x 3))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
(+ 1/27 (pow x 3))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
(* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 x (*.f64 x x) #s(literal 1/27 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* -1/3 x))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
(+ 1/9 (* x (- x 1/3)))
(fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(+ 1/9 (* x (- x 1/3)))
(fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/3 (/ 1 x))))
(*.f64 x (+.f64 x #s(literal -1/3 binary64)))
(* (pow x 2) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -1/3 binary64) (/.f64 #s(literal 1/9 binary64) x))))
(* (pow x 2) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -1/3 binary64) (/.f64 #s(literal 1/9 binary64) x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/3 (/ 1 x))))
(*.f64 x (+.f64 x #s(literal -1/3 binary64)))
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -1/3 binary64) (/.f64 #s(literal 1/9 binary64) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -1/3 binary64) (/.f64 #s(literal 1/9 binary64) x))))
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
-1/81
#s(literal -1/81 binary64)
(- (pow x 4) 1/81)
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/81 binary64))
(- (pow x 4) 1/81)
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/81 binary64))
(- (pow x 4) 1/81)
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/81 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/81 binary64))
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/81 binary64))
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/81 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/81 binary64))
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/81 binary64))
(* (pow x 4) (- 1 (* 1/81 (/ 1 (pow x 4)))))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/81 binary64))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(+.f64 x #s(literal -1/3 binary64))
(- x 1/3)
(+.f64 x #s(literal -1/3 binary64))
(- x 1/3)
(+.f64 x #s(literal -1/3 binary64))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal -1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal -1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal -1/3 binary64))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/3 binary64))
-1/27
#s(literal -1/27 binary64)
(- (* 1/9 x) 1/27)
(fma.f64 x #s(literal 1/9 binary64) #s(literal -1/27 binary64))
(- (* x (+ 1/9 (* -1/3 x))) 1/27)
(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
(- (* x (+ 1/9 (* x (- x 1/3)))) 1/27)
(fma.f64 x (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (- 1 (* 1/3 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 x #s(literal -1/3 binary64)))
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 x (+.f64 #s(literal -1/3 binary64) (/.f64 #s(literal 1/9 binary64) x))))
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))))
(fma.f64 (*.f64 x x) (+.f64 x (+.f64 #s(literal -1/3 binary64) (/.f64 #s(literal 1/9 binary64) x))) #s(literal -1/27 binary64))
(pow x 3)
(.f64 x (.f64 x x))
(* -1 (* (pow x 3) (- (* 1/3 (/ 1 x)) 1)))
(.f64 (.f64 x x) (+.f64 x #s(literal -1/3 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1)))
(.f64 (.f64 x x) (+.f64 x (+.f64 #s(literal -1/3 binary64) (/.f64 #s(literal 1/9 binary64) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1)))
(fma.f64 (*.f64 x x) (+.f64 x (+.f64 #s(literal -1/3 binary64) (/.f64 #s(literal 1/9 binary64) x))) #s(literal -1/27 binary64))

eval240.0ms (4.3%)

Memory: -12.4MiB live, 461.8MiB allocated
Compiler: Compiled 50 354 to 2 722 computations (94.6% saved)

prune156.0ms (2.8%)

Memory

-10.9MiB live, 279.8MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1 508	1	1 509
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	1 509	4	1 513

Accuracy

100.0%

Counts

1 513 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	70.2%	(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
▶	52.4%	(/.f64 #s(literal -1/81 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
✓	100.0%	(-.f64 x #s(literal -1/3 binary64))
✓	52.1%	#s(literal 1/3 binary64)

Compiler

Compiled 31 to 22 computations (29% saved)

simplify11.0ms (0.2%)

Memory

13.1MiB live, 13.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 x #s(literal -1/3 binary64))
✓	cost-diff	(fma.f64 x x #s(literal 1/9 binary64))
✓	cost-diff	(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))
✓	cost-diff	(/.f64 #s(literal -1/81 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))

Rules

210×	`lower-fma.f32`
208×	`lower-fma.f64`
128×	`lower-+.f32`
126×	`lower-+.f64`
62×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	29
0	13	29
1	24	29
2	53	29
3	107	29
4	150	29
5	173	29
6	181	29
0	181	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal -1/81 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
#s(literal -1/81 binary64)
(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))
(fma.f64 x x #s(literal 1/9 binary64))
x
#s(literal 1/9 binary64)
(+.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)

Outputs
(/.f64 #s(literal -1/81 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
#s(literal -1/81 binary64)
(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))
(fma.f64 x x #s(literal 1/9 binary64))
x
#s(literal 1/9 binary64)
(+.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)

localize41.0ms (0.7%)

Memory

-10.3MiB live, 63.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal -1/3 binary64))
✓	accuracy	100.0%	(fma.f64 x x #s(literal 1/9 binary64))
✓	accuracy	99.9%	(/.f64 #s(literal -1/81 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
✓	accuracy	99.9%	(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))

Samples

30.0ms

256×

valid

Compiler

Compiled 34 to 11 computations (67.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

const: 12.0ms (61.7% of total)

ival-mult: 3.0ms (15.4% of total)

ival-div: 2.0ms (10.3% of total)

ival-add: 2.0ms (10.3% of total)

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

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

series1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal -1/81 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))>
#<alt (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))>
#<alt (fma.f64 x x #s(literal 1/9 binary64))>
#<alt (+.f64 x #s(literal -1/3 binary64))>

Outputs
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 (* x (+ 1 (* 27 (pow x 3)))))>
#<alt (+ 1/3 (* x (+ 1 (* (pow x 3) (+ 27 (* 81 x))))))>
#<alt (/ -1/81 (pow x 3))>
#<alt (* -1 (/ (+ 1/81 (* 1/243 (/ 1 x))) (pow x 3)))>
#<alt (/ (- (* -1 (/ (+ 1/243 (* 1/6561 (/ 1 (pow x 3)))) x)) 1/81) (pow x 3))>
#<alt (/ (- (* -1 (/ (+ 1/6561 (* 1/19683 (/ 1 x))) (pow x 4))) (+ 1/81 (* 1/243 (/ 1 x)))) (pow x 3))>
#<alt (/ -1/81 (pow x 3))>
#<alt (* -1 (/ (+ 1/81 (* 1/243 (/ 1 x))) (pow x 3)))>
#<alt (* -1 (/ (+ 1/81 (+ (/ 1/6561 (pow x 4)) (* 1/243 (/ 1 x)))) (pow x 3)))>
#<alt (* -1 (/ (+ 1/81 (* -1 (/ (- (* -1 (/ (+ 1/6561 (* 1/19683 (/ 1 x))) (pow x 3))) 1/243) x))) (pow x 3)))>
#<alt -1/27>
#<alt (- (* 1/9 x) 1/27)>
#<alt (- (* x (+ 1/9 (* -1/3 x))) 1/27)>
#<alt (- (* x (+ 1/9 (* x (- x 1/3)))) 1/27)>
#<alt (pow x 3)>
#<alt (* (pow x 3) (- 1 (* 1/3 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))))>
#<alt (pow x 3)>
#<alt (* -1 (* (pow x 3) (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1)))>
#<alt 1/9>
#<alt (+ 1/9 (pow x 2))>
#<alt (+ 1/9 (pow x 2))>
#<alt (+ 1/9 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt -1/3>
#<alt (- x 1/3)>
#<alt (- x 1/3)>
#<alt (- x 1/3)>
#<alt x>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/ -1/81 (* (+ (* x x) 1/9) (+ x -1/3)))
0.0ms	x	@	-inf	(/ -1/81 (* (+ (* x x) 1/9) (+ x -1/3)))
0.0ms	x	@	0	(/ -1/81 (* (+ (* x x) 1/9) (+ x -1/3)))
0.0ms	x	@	inf	(+ (* x x) 1/9)
0.0ms	x	@	-inf	(+ (* x x) 1/9)

rewrite341.0ms (6.1%)

Memory

9.7MiB live, 514.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 846×	`lower-*.f32`
4 844×	`lower-*.f64`
3 352×	`lower-fma.f32`
3 350×	`lower-fma.f64`
2 886×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
0	13	25
1	60	25
2	434	25
3	5472	25
0	8074	25

Stop Event

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

Counts

4 → 509

Calls

Call 1

Inputs
(/.f64 #s(literal -1/81 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))
(fma.f64 x x #s(literal 1/9 binary64))
(+.f64 x #s(literal -1/3 binary64))

Outputs
(+.f64 (.f64 (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (.f64 x x)) (.f64 (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64)))) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64))))
(+.f64 (.f64 (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64))) (.f64 (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (*.f64 x x)))
(+.f64 (.f64 (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x x #s(literal -1/9 binary64)))) x) (.f64 (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x x #s(literal -1/9 binary64)))) #s(literal 1/3 binary64)))
(+.f64 (.f64 (.f64 x x) (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))))) (.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))))))
(+.f64 (.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))))) (.f64 (.f64 x x) (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))))))
(+.f64 (.f64 x (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x x #s(literal -1/9 binary64))))) (.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x x #s(literal -1/9 binary64))))))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (*.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -81 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/81 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 x (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x x #s(literal -1/9 binary64)))) (.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/81 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x x #s(literal -1/9 binary64))))))
(fma.f64 (.f64 x x) (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))))))
(fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (.f64 (.f64 x x) (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))))))
(fma.f64 (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (.f64 x x) (.f64 (/.f64 #s(literal -1/81 binary64) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64))))
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simplify468.0ms (8.4%)

Memory

-13.0MiB live, 518.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 632×	`lower-fma.f64`
10 632×	`lower-fma.f32`
3 652×	`lower-*.f64`
3 652×	`lower-*.f32`
2 508×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	336
1	320	328
2	938	319
3	3124	302
4	7998	302
0	8005	281

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 46

Calls

Call 1

Inputs
1/3
(+ 1/3 x)
(+ 1/3 (* x (+ 1 (* 27 (pow x 3)))))
(+ 1/3 (* x (+ 1 (* (pow x 3) (+ 27 (* 81 x))))))
(/ -1/81 (pow x 3))
(* -1 (/ (+ 1/81 (* 1/243 (/ 1 x))) (pow x 3)))
(/ (- (* -1 (/ (+ 1/243 (* 1/6561 (/ 1 (pow x 3)))) x)) 1/81) (pow x 3))
(/ (- (* -1 (/ (+ 1/6561 (* 1/19683 (/ 1 x))) (pow x 4))) (+ 1/81 (* 1/243 (/ 1 x)))) (pow x 3))
(/ -1/81 (pow x 3))
(* -1 (/ (+ 1/81 (* 1/243 (/ 1 x))) (pow x 3)))
(* -1 (/ (+ 1/81 (+ (/ 1/6561 (pow x 4)) (* 1/243 (/ 1 x)))) (pow x 3)))
(* -1 (/ (+ 1/81 (* -1 (/ (- (* -1 (/ (+ 1/6561 (* 1/19683 (/ 1 x))) (pow x 3))) 1/243) x))) (pow x 3)))
-1/27
(- (* 1/9 x) 1/27)
(- (* x (+ 1/9 (* -1/3 x))) 1/27)
(- (* x (+ 1/9 (* x (- x 1/3)))) 1/27)
(pow x 3)
(* (pow x 3) (- 1 (* 1/3 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))))
(pow x 3)
(* -1 (* (pow x 3) (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1)))
1/9
(+ 1/9 (pow x 2))
(+ 1/9 (pow x 2))
(+ 1/9 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))

Outputs
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 (* x (+ 1 (* 27 (pow x 3)))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 27 binary64) (.f64 x x)) #s(literal 1 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* x (+ 1 (* (pow x 3) (+ 27 (* 81 x))))))
(fma.f64 x (fma.f64 x (.f64 (fma.f64 x #s(literal 81 binary64) #s(literal 27 binary64)) (.f64 x x)) #s(literal 1 binary64)) #s(literal 1/3 binary64))
(/ -1/81 (pow x 3))
(/.f64 #s(literal -1/81 binary64) (.f64 x (.f64 x x)))
(* -1 (/ (+ 1/81 (* 1/243 (/ 1 x))) (pow x 3)))
(/.f64 (-.f64 #s(literal -1/81 binary64) (/.f64 #s(literal 1/243 binary64) x)) (.f64 x (.f64 x x)))
(/ (- (* -1 (/ (+ 1/243 (* 1/6561 (/ 1 (pow x 3)))) x)) 1/81) (pow x 3))
(/.f64 (+.f64 #s(literal -1/81 binary64) (/.f64 (+.f64 #s(literal -1/243 binary64) (/.f64 #s(literal -1/6561 binary64) (.f64 x (.f64 x x)))) x)) (.f64 x (.f64 x x)))
(/ (- (* -1 (/ (+ 1/6561 (* 1/19683 (/ 1 x))) (pow x 4))) (+ 1/81 (* 1/243 (/ 1 x)))) (pow x 3))
(/.f64 (+.f64 #s(literal -1/81 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -1/6561 binary64) (/.f64 #s(literal -1/19683 binary64) x)) (.f64 x (.f64 x x))) #s(literal -1/243 binary64)) x)) (.f64 x (.f64 x x)))
(/ -1/81 (pow x 3))
(/.f64 #s(literal -1/81 binary64) (.f64 x (.f64 x x)))
(* -1 (/ (+ 1/81 (* 1/243 (/ 1 x))) (pow x 3)))
(/.f64 (-.f64 #s(literal -1/81 binary64) (/.f64 #s(literal 1/243 binary64) x)) (.f64 x (.f64 x x)))
(* -1 (/ (+ 1/81 (+ (/ 1/6561 (pow x 4)) (* 1/243 (/ 1 x)))) (pow x 3)))
(/.f64 (+.f64 (-.f64 #s(literal -1/81 binary64) (/.f64 #s(literal 1/243 binary64) x)) (/.f64 #s(literal -1/6561 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (*.f64 x x)))
(* -1 (/ (+ 1/81 (* -1 (/ (- (* -1 (/ (+ 1/6561 (* 1/19683 (/ 1 x))) (pow x 3))) 1/243) x))) (pow x 3)))
(/.f64 (+.f64 #s(literal -1/81 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -1/6561 binary64) (/.f64 #s(literal -1/19683 binary64) x)) (.f64 x (.f64 x x))) #s(literal -1/243 binary64)) x)) (.f64 x (.f64 x x)))
-1/27
#s(literal -1/27 binary64)
(- (* 1/9 x) 1/27)
(fma.f64 x #s(literal 1/9 binary64) #s(literal -1/27 binary64))
(- (* x (+ 1/9 (* -1/3 x))) 1/27)
(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
(- (* x (+ 1/9 (* x (- x 1/3)))) 1/27)
(fma.f64 x (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (- 1 (* 1/3 (/ 1 x))))
(.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64))))
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))
(*.f64 x (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x (fma.f64 x (/.f64 #s(literal -1/27 binary64) (.f64 x (.f64 x x))) #s(literal -1/3 binary64))))))
(pow x 3)
(.f64 x (.f64 x x))
(* -1 (* (pow x 3) (- (* 1/3 (/ 1 x)) 1)))
(.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1)))
(*.f64 x (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1)))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x (fma.f64 x (/.f64 #s(literal -1/27 binary64) (.f64 x (.f64 x x))) #s(literal -1/3 binary64))))))
1/9
#s(literal 1/9 binary64)
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(+.f64 x #s(literal -1/3 binary64))
(- x 1/3)
(+.f64 x #s(literal -1/3 binary64))
(- x 1/3)
(+.f64 x #s(literal -1/3 binary64))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal -1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal -1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal -1/3 binary64))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/3 binary64))

eval97.0ms (1.7%)

Memory: 26.4MiB live, 139.9MiB allocated
Compiler: Compiled 14 734 to 1 791 computations (87.8% saved)

prune64.0ms (1.1%)

Memory

5.5MiB live, 135.5MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	554	1	555
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	555	4	559

Accuracy

100.0%

Counts

559 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	70.2%	(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
▶	52.6%	(/.f64 #s(literal -1/81 binary64) (fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64)))
✓	100.0%	(-.f64 x #s(literal -1/3 binary64))
✓	52.1%	#s(literal 1/3 binary64)

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify8.0ms (0.1%)

Memory

-29.5MiB live, 8.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

✓

cost-diff

(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))

✓

cost-diff

(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))

✓

cost-diff

(/.f64 #s(literal -1/81 binary64) (fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64)))

Rules

44×	`lower-fma.f32`
40×	`lower-fma.f64`
28×	`lower-+.f64`
28×	`lower-+.f32`
22×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
0	13	25
1	23	25
2	40	25
3	46	25
0	46	25

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal -1/81 binary64) (fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64)))
#s(literal -1/81 binary64)
(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
x
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
#s(literal -1/3 binary64)
#s(literal 1/9 binary64)
#s(literal -1/27 binary64)

Outputs
(/.f64 #s(literal -1/81 binary64) (fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64)))
#s(literal -1/81 binary64)
(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
x
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
#s(literal -1/3 binary64)
#s(literal 1/9 binary64)
#s(literal -1/27 binary64)

localize46.0ms (0.8%)

Memory

12.9MiB live, 55.2MiB allocated

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

✓

accuracy

99.9%

(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))

✓

accuracy

99.7%

(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))

✓

accuracy

98.9%

(/.f64 #s(literal -1/81 binary64) (fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64)))

Samples

35.0ms

256×

valid

Compiler

Compiled 32 to 12 computations (62.5% saved)

Precisions

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

const: 20.0ms (72.9% of total)

ival-mult: 3.0ms (10.9% of total)

ival-div: 2.0ms (7.3% of total)

ival-add: 2.0ms (7.3% of total)

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

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

series3.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

#<alt (/.f64 #s(literal -1/81 binary64) (fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64)))>

#<alt (fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))>

#<alt (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))>

Outputs
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 (* x (+ 1 (* -9 (pow x 2)))))>
#<alt (+ 1/3 (* x (+ 1 (* (pow x 2) (- (* -27 x) 9)))))>
#<alt (/ 1/27 (pow x 2))>
#<alt (/ (+ 1/27 (* 1/81 (/ 1 x))) (pow x 2))>
#<alt (/ (- (+ 1/27 (* 1/81 (/ 1 x))) (/ 1/729 (pow x 3))) (pow x 2))>
#<alt (/ (+ 1/27 (+ (* -1 (/ (+ 1/729 (* 1/2187 (/ 1 x))) (pow x 3))) (* 1/81 (/ 1 x)))) (pow x 2))>
#<alt (/ 1/27 (pow x 2))>
#<alt (/ (+ 1/27 (* 1/81 (/ 1 x))) (pow x 2))>
#<alt (/ (+ 1/27 (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) 1/81) x))) (pow x 2))>
#<alt (/ (+ 1/27 (* -1 (/ (- (+ (/ 1/2187 (pow x 3)) (* 1/729 (/ 1 (pow x 2)))) 1/81) x))) (pow x 2))>
#<alt -1/27>
#<alt (- (* 1/9 x) 1/27)>
#<alt (- (* x (+ 1/9 (* -1/3 x))) 1/27)>
#<alt (- (* x (+ 1/9 (* -1/3 x))) 1/27)>
#<alt (* -1/3 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/9 (/ 1 x)) 1/3))>
#<alt (* (pow x 2) (- (* 1/9 (/ 1 x)) (+ 1/3 (/ 1/27 (pow x 2)))))>
#<alt (* (pow x 2) (- (* 1/9 (/ 1 x)) (+ 1/3 (/ 1/27 (pow x 2)))))>
#<alt (* -1/3 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/9 (/ 1 x)) 1/3))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3))>
#<alt 1/9>
#<alt (+ 1/9 (* -1/3 x))>
#<alt (+ 1/9 (* -1/3 x))>
#<alt (+ 1/9 (* -1/3 x))>
#<alt (* -1/3 x)>
#<alt (* x (- (* 1/9 (/ 1 x)) 1/3))>
#<alt (* x (- (* 1/9 (/ 1 x)) 1/3))>
#<alt (* x (- (* 1/9 (/ 1 x)) 1/3))>
#<alt (* -1/3 x)>
#<alt (* -1 (* x (- 1/3 (* 1/9 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/3 (* 1/9 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/3 (* 1/9 (/ 1 x)))))>

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+ (* x -1/3) 1/9)
0.0ms	x	@	-inf	(/ -1/81 (+ (* x (+ (* x -1/3) 1/9)) -1/27))
0.0ms	x	@	inf	(/ -1/81 (+ (* x (+ (* x -1/3) 1/9)) -1/27))
0.0ms	x	@	0	(/ -1/81 (+ (* x (+ (* x -1/3) 1/9)) -1/27))
0.0ms	x	@	inf	(+ (* x (+ (* x -1/3) 1/9)) -1/27)

rewrite399.0ms (7.1%)

Memory

1.8MiB live, 549.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 210×	`lower-fma.f32`
6 206×	`lower-fma.f64`
4 836×	`lower-*.f64`
4 836×	`lower-*.f32`
3 308×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	13	20
1	59	20
2	411	20
3	4263	20
0	8816	20

Stop Event

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

Counts

3 → 291

Calls

Call 1

Inputs

(/.f64 #s(literal -1/81 binary64) (fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64)))

(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))

(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))

Outputs
(+.f64 (.f64 (/.f64 #s(literal -1/81 binary64) (fma.f64 (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))))) #s(literal -1/19683 binary64))) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)))))) (.f64 (/.f64 #s(literal -1/81 binary64) (fma.f64 (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))))) #s(literal -1/19683 binary64))) (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 x #s(literal 1/27 binary64)) #s(literal 1/729 binary64))))
(+.f64 (.f64 (/.f64 #s(literal -1/81 binary64) (fma.f64 (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))))) #s(literal -1/19683 binary64))) (fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 x #s(literal 1/27 binary64)) #s(literal 1/729 binary64))) (.f64 (/.f64 #s(literal -1/81 binary64) (fma.f64 (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))))) #s(literal -1/19683 binary64))) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)))))))
(+.f64 (.f64 (/.f64 #s(literal -1/81 binary64) (fma.f64 (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) #s(literal -1/729 binary64))) (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)))) (.f64 (/.f64 #s(literal -1/81 binary64) (fma.f64 (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) (*.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) #s(literal -1/729 binary64))) #s(literal 1/27 binary64)))
(+.f64 (.f64 (/.f64 #s(literal -1/81 binary64) (fma.f64 (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) #s(literal -1/729 binary64))) (.f64 x (.f64 x #s(literal -1/3 binary64)))) (.f64 (/.f64 #s(literal -1/81 binary64) (fma.f64 (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) (.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) #s(literal -1/729 binary64))) (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64))))
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(neg.f64 (/.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))))
(/.f64 (fma.f64 (.f64 x #s(literal -1/27 binary64)) (.f64 x x) #s(literal 1/729 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64))) (+.f64 #s(literal 1/81 binary64) (.f64 #s(literal -1/9 binary64) (*.f64 x x)))))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x #s(literal -1/27 binary64)) (.f64 x x) #s(literal 1/729 binary64))) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64))))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64))) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)))
(/.f64 (fma.f64 (.f64 #s(literal -1/19683 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/387420489 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)) (-.f64 (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/531441 binary64)) (.f64 #s(literal -1/19683 binary64) (.f64 x (*.f64 x x))))))
(/.f64 (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/531441 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)) (fma.f64 (.f64 x #s(literal -1/27 binary64)) (.f64 x x) #s(literal -1/729 binary64))))
(/.f64 (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/531441 binary64)) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)) (fma.f64 (.f64 #s(literal 1/81 binary64) (.f64 x x)) (.f64 x x) (fma.f64 #s(literal 1/729 binary64) (.f64 x x) #s(literal 1/6561 binary64)))))
(/.f64 (+.f64 #s(literal 1/81 binary64) (.f64 #s(literal -1/9 binary64) (.f64 x x))) (+.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/3 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal 1/81 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/6561 binary64)) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)) (fma.f64 x (*.f64 x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/9 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))) (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)) #s(literal 1/81 binary64))) (*.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x #s(literal -1/27 binary64)) (*.f64 x x) #s(literal 1/729 binary64)) #s(literal 1 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)))
(/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64)) #s(literal 1 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/19683 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/387420489 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/531441 binary64)) (.f64 #s(literal -1/19683 binary64) (.f64 x (.f64 x x)))) (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/531441 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x #s(literal -1/27 binary64)) (*.f64 x x) #s(literal -1/729 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/531441 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/81 binary64) (.f64 x x)) (.f64 x x) (fma.f64 #s(literal 1/729 binary64) (*.f64 x x) #s(literal 1/6561 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/81 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/6561 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/9 binary64)) #s(literal 1/81 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x #s(literal -1/27 binary64)) (.f64 x x) #s(literal 1/729 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64)))) (neg.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/81 binary64) (.f64 #s(literal -1/9 binary64) (.f64 x x)))) (neg.f64 (+.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)))) (/.f64 #s(literal 1/531441 binary64) (.f64 (.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))))) (fma.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/9 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))) (/.f64 (.f64 x (.f64 x #s(literal 1/9 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))) (fma.f64 (/.f64 #s(literal -1/81 binary64) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/81 binary64) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64))) (.f64 (/.f64 (.f64 x (*.f64 x #s(literal 1/9 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))) (/.f64 #s(literal -1/81 binary64) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/9 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))) (/.f64 (.f64 x (.f64 x #s(literal 1/9 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)))) (.f64 (/.f64 #s(literal -1/81 binary64) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/81 binary64) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64))))) (fma.f64 (*.f64 x #s(literal 1/9 binary64)) (/.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))) (/.f64 #s(literal -1/81 binary64) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/19683 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/387420489 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)))) (-.f64 (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/531441 binary64)) (.f64 #s(literal -1/19683 binary64) (.f64 x (*.f64 x x)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/531441 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)))) (fma.f64 (.f64 x #s(literal -1/27 binary64)) (.f64 x x) #s(literal -1/729 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/531441 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)))) (fma.f64 (.f64 #s(literal 1/81 binary64) (.f64 x x)) (.f64 x x) (fma.f64 #s(literal 1/729 binary64) (.f64 x x) #s(literal 1/6561 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/81 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/6561 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)))) (fma.f64 x (*.f64 x #s(literal 1/9 binary64)) #s(literal 1/81 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64))) (+.f64 #s(literal 1/81 binary64) (.f64 #s(literal -1/9 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x #s(literal -1/27 binary64)) (*.f64 x x) #s(literal 1/729 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64))))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x #s(literal -1/27 binary64)) (*.f64 x x) #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)))))
(.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64))) (fma.f64 (.f64 x #s(literal -1/27 binary64)) (*.f64 x x) #s(literal 1/729 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x #s(literal -1/27 binary64)) (*.f64 x x) #s(literal 1/729 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))) (fma.f64 x (.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64))) #s(literal -1 binary64)))
(.f64 (+.f64 #s(literal 1/81 binary64) (.f64 #s(literal -1/9 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))))
(.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64)) (fma.f64 x (*.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64))) (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x #s(literal -1/27 binary64)) (.f64 x x) #s(literal 1/729 binary64)) (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (fma.f64 x #s(literal 1/27 binary64) #s(literal 1/81 binary64)) (.f64 (fma.f64 x #s(literal 1/27 binary64) #s(literal 1/81 binary64)) (fma.f64 x #s(literal 1/27 binary64) #s(literal 1/81 binary64)))))) (fma.f64 (fma.f64 x #s(literal 1/27 binary64) #s(literal 1/81 binary64)) (-.f64 (fma.f64 x #s(literal 1/27 binary64) #s(literal 1/81 binary64)) (.f64 x (.f64 x #s(literal 1/9 binary64)))) (.f64 (.f64 #s(literal 1/81 binary64) (.f64 x x)) (.f64 x x))))
(.f64 (/.f64 (fma.f64 (.f64 x #s(literal -1/27 binary64)) (.f64 x x) #s(literal 1/729 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)) (+.f64 (fma.f64 x (.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64)) (.f64 x #s(literal -1/27 binary64))))) (+.f64 (fma.f64 x (.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64)) (.f64 x #s(literal -1/27 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/9 binary64)) #s(literal -1/81 binary64)) (fma.f64 (.f64 x #s(literal -1/27 binary64)) (.f64 x x) #s(literal -1/729 binary64))) (fma.f64 x (*.f64 x #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/27 binary64) #s(literal 1/81 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)) (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/531441 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/81 binary64) (.f64 x x)) (.f64 x x) (fma.f64 #s(literal 1/729 binary64) (.f64 x x) #s(literal 1/6561 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal -1/9 binary64)) (fma.f64 (.f64 #s(literal 1/81 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/6561 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)) (fma.f64 (.f64 #s(literal -1/19683 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/387420489 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/531441 binary64)) (.f64 #s(literal -1/19683 binary64) (.f64 x (*.f64 x x))))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/9 binary64) #s(literal 1/27 binary64)) #s(literal 1/81 binary64)) (fma.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/531441 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x #s(literal -1/27 binary64)) (.f64 x x) #s(literal -1/729 binary64))))

simplify485.0ms (8.7%)

Memory

23.7MiB live, 456.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 862×	`lower-fma.f64`
7 862×	`lower-fma.f32`
2 862×	`lower-*.f64`
2 862×	`lower-*.f32`
1 506×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	268
1	204	262
2	479	262
3	1311	258
4	3130	258
5	6009	258
0	8062	231

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
1/3
(+ 1/3 x)
(+ 1/3 (* x (+ 1 (* -9 (pow x 2)))))
(+ 1/3 (* x (+ 1 (* (pow x 2) (- (* -27 x) 9)))))
(/ 1/27 (pow x 2))
(/ (+ 1/27 (* 1/81 (/ 1 x))) (pow x 2))
(/ (- (+ 1/27 (* 1/81 (/ 1 x))) (/ 1/729 (pow x 3))) (pow x 2))
(/ (+ 1/27 (+ (* -1 (/ (+ 1/729 (* 1/2187 (/ 1 x))) (pow x 3))) (* 1/81 (/ 1 x)))) (pow x 2))
(/ 1/27 (pow x 2))
(/ (+ 1/27 (* 1/81 (/ 1 x))) (pow x 2))
(/ (+ 1/27 (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) 1/81) x))) (pow x 2))
(/ (+ 1/27 (* -1 (/ (- (+ (/ 1/2187 (pow x 3)) (* 1/729 (/ 1 (pow x 2)))) 1/81) x))) (pow x 2))
-1/27
(- (* 1/9 x) 1/27)
(- (* x (+ 1/9 (* -1/3 x))) 1/27)
(- (* x (+ 1/9 (* -1/3 x))) 1/27)
(* -1/3 (pow x 2))
(* (pow x 2) (- (* 1/9 (/ 1 x)) 1/3))
(* (pow x 2) (- (* 1/9 (/ 1 x)) (+ 1/3 (/ 1/27 (pow x 2)))))
(* (pow x 2) (- (* 1/9 (/ 1 x)) (+ 1/3 (/ 1/27 (pow x 2)))))
(* -1/3 (pow x 2))
(* (pow x 2) (- (* 1/9 (/ 1 x)) 1/3))
(* (pow x 2) (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3))
(* (pow x 2) (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3))
1/9
(+ 1/9 (* -1/3 x))
(+ 1/9 (* -1/3 x))
(+ 1/9 (* -1/3 x))
(* -1/3 x)
(* x (- (* 1/9 (/ 1 x)) 1/3))
(* x (- (* 1/9 (/ 1 x)) 1/3))
(* x (- (* 1/9 (/ 1 x)) 1/3))
(* -1/3 x)
(* -1 (* x (- 1/3 (* 1/9 (/ 1 x)))))
(* -1 (* x (- 1/3 (* 1/9 (/ 1 x)))))
(* -1 (* x (- 1/3 (* 1/9 (/ 1 x)))))

Outputs
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 (* x (+ 1 (* -9 (pow x 2)))))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal -9 binary64)) #s(literal 1 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* x (+ 1 (* (pow x 2) (- (* -27 x) 9)))))
(fma.f64 x (fma.f64 (*.f64 x x) (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64)) #s(literal 1 binary64)) #s(literal 1/3 binary64))
(/ 1/27 (pow x 2))
(/.f64 #s(literal 1/27 binary64) (*.f64 x x))
(/ (+ 1/27 (* 1/81 (/ 1 x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/27 binary64) (/.f64 #s(literal 1/81 binary64) x)) (*.f64 x x))
(/ (- (+ 1/27 (* 1/81 (/ 1 x))) (/ 1/729 (pow x 3))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/27 binary64) (/.f64 (+.f64 #s(literal 1/81 binary64) (/.f64 #s(literal -1/729 binary64) (.f64 x x))) x)) (.f64 x x))
(/ (+ 1/27 (+ (* -1 (/ (+ 1/729 (* 1/2187 (/ 1 x))) (pow x 3))) (* 1/81 (/ 1 x)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1/27 binary64) (/.f64 (+.f64 #s(literal -1/81 binary64) (/.f64 (+.f64 #s(literal 1/729 binary64) (/.f64 #s(literal 1/2187 binary64) x)) (.f64 x x))) x)) (.f64 x x))
(/ 1/27 (pow x 2))
(/.f64 #s(literal 1/27 binary64) (*.f64 x x))
(/ (+ 1/27 (* 1/81 (/ 1 x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/27 binary64) (/.f64 #s(literal 1/81 binary64) x)) (*.f64 x x))
(/ (+ 1/27 (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) 1/81) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/27 binary64) (/.f64 (+.f64 #s(literal 1/81 binary64) (/.f64 #s(literal -1/729 binary64) (.f64 x x))) x)) (.f64 x x))
(/ (+ 1/27 (* -1 (/ (- (+ (/ 1/2187 (pow x 3)) (* 1/729 (/ 1 (pow x 2)))) 1/81) x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1/27 binary64) (/.f64 (+.f64 #s(literal -1/81 binary64) (/.f64 (+.f64 #s(literal 1/729 binary64) (/.f64 #s(literal 1/2187 binary64) x)) (.f64 x x))) x)) (.f64 x x))
-1/27
#s(literal -1/27 binary64)
(- (* 1/9 x) 1/27)
(fma.f64 x #s(literal 1/9 binary64) #s(literal -1/27 binary64))
(- (* x (+ 1/9 (* -1/3 x))) 1/27)
(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
(- (* x (+ 1/9 (* -1/3 x))) 1/27)
(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
(* -1/3 (pow x 2))
(.f64 x (.f64 x #s(literal -1/3 binary64)))
(* (pow x 2) (- (* 1/9 (/ 1 x)) 1/3))
(*.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)))
(* (pow x 2) (- (* 1/9 (/ 1 x)) (+ 1/3 (/ 1/27 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
(* (pow x 2) (- (* 1/9 (/ 1 x)) (+ 1/3 (/ 1/27 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
(* -1/3 (pow x 2))
(.f64 x (.f64 x #s(literal -1/3 binary64)))
(* (pow x 2) (- (* 1/9 (/ 1 x)) 1/3))
(*.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)))
(* (pow x 2) (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3))
(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
(* (pow x 2) (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3))
(fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* -1/3 x))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
(+ 1/9 (* -1/3 x))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
(+ 1/9 (* -1/3 x))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
(* -1/3 x)
(*.f64 x #s(literal -1/3 binary64))
(* x (- (* 1/9 (/ 1 x)) 1/3))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
(* x (- (* 1/9 (/ 1 x)) 1/3))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
(* x (- (* 1/9 (/ 1 x)) 1/3))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
(* -1/3 x)
(*.f64 x #s(literal -1/3 binary64))
(* -1 (* x (- 1/3 (* 1/9 (/ 1 x)))))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
(* -1 (* x (- 1/3 (* 1/9 (/ 1 x)))))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))
(* -1 (* x (- 1/3 (* 1/9 (/ 1 x)))))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64))

eval73.0ms (1.3%)

Memory: -26.8MiB live, 103.0MiB allocated
Compiler: Compiled 10 310 to 1 058 computations (89.7% saved)

prune39.0ms (0.7%)

Memory

13.6MiB live, 90.4MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	327	0	327
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	327	4	331

Accuracy

100.0%

Counts

331 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	70.2%	(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
✓	52.6%	(/.f64 #s(literal -1/81 binary64) (fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64)))
✓	100.0%	(-.f64 x #s(literal -1/3 binary64))
✓	52.1%	#s(literal 1/3 binary64)

Compiler

Compiled 89 to 48 computations (46.1% saved)

regimes6.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(literal 1/3 binary64)
(-.f64 x #s(literal -1/3 binary64))
(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
(/.f64 #s(literal -1/81 binary64) (fma.f64 x (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) #s(literal -1/27 binary64)))
(/.f64 #s(literal -1/81 binary64) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))
(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1/27 binary64)) (fma.f64 x (+.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1/81 binary64)) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (+.f64 x #s(literal -1/3 binary64))))

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

Calls

2 calls:

3.0ms	x
2.0ms	(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory

5.6MiB live, 5.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/3 binary64)

Outputs
#s(literal 1/3 binary64)

Calls

2 calls:

1.0ms	x
1.0ms	(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Results

Accuracy	Segments	Branch
52.1%	1	`x`
52.1%	1	`(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`

Compiler

Compiled 8 to 6 computations (25% saved)

simplify32.0ms (0.6%)

Memory

-28.1MiB live, 10.4MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	6	4
2	11	4
3	13	4
4	14	4

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness112.0ms (2%)

Memory

1.4MiB live, 84.0MiB allocated

Rules

8 708×	`lower-fma.f64`
8 708×	`lower-fma.f32`
5 116×	`lower-*.f64`
5 116×	`lower-*.f32`
3 868×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
0	8	4
1	25	4
2	126	4
3	957	4
0	8643	4
0	8	30
1	22	30
2	37	30
3	77	30
4	77	30
5	78	30
6	80	30
7	80	30
0	80	30

Stop Event

1×	done
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 11 to 9 computations (18.2% saved)

preprocess20.0ms (0.4%)

Memory: 17.2MiB live, 56.0MiB allocated
Compiler: Compiled 22 to 18 computations (18.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample551.0ms (9.9%)

preprocess18.0ms (0.3%)

explain63.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize18.0ms (0.3%)

series1.0ms (0%)

rewrite413.0ms (7.4%)

simplify7.0ms (0.1%)

eval33.0ms (0.6%)

prune32.0ms (0.6%)

simplify13.0ms (0.2%)

localize191.0ms (3.4%)

series7.0ms (0.1%)

rewrite1.0s (18.3%)

simplify567.0ms (10.2%)

eval240.0ms (4.3%)

prune156.0ms (2.8%)

simplify11.0ms (0.2%)

localize41.0ms (0.7%)

series1.0ms (0%)

rewrite341.0ms (6.1%)

simplify468.0ms (8.4%)

eval97.0ms (1.7%)

prune64.0ms (1.1%)

simplify8.0ms (0.1%)

localize46.0ms (0.8%)

series3.0ms (0.1%)

rewrite399.0ms (7.1%)

simplify485.0ms (8.7%)

eval73.0ms (1.3%)

prune39.0ms (0.7%)

regimes6.0ms (0.1%)

regimes3.0ms (0%)

simplify32.0ms (0.6%)

soundness112.0ms (2%)

preprocess20.0ms (0.4%)

end0.0ms (0%)

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