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

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

sample1.4s (23.1%)

Memory

6.3MiB live, 963.0MiB allocated

Samples

808.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 669.0ms

ival-div: 608.0ms (90.9% of total)

ival-sub: 47.0ms (7% of total)

exact: 7.0ms (1% of total)

ival-true: 5.0ms (0.7% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

preprocess15.0ms (0.2%)

Memory

22.2MiB live, 22.2MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`distribute-lft-neg-in`
14×	`sub-neg`
12×	`cancel-sign-sub-inv`
10×	`associate--r+`
10×	`distribute-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	18	9
2	39	6
3	63	6
4	96	6
5	104	6
6	106	6
0	5	3
0	8	3
1	13	3
2	14	3
0	14	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))

explain98.0ms (1.6%)

Memory

-20.1MiB live, 59.6MiB allocated

FPErrors

Click to see full error table

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

27.0ms

512×

valid

Compiler

Compiled 38 to 24 computations (36.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 4.0ms (52.7% of total)

ival-sub: 2.0ms (26.4% 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB 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)

simplify5.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB 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-+.f64`
4×	`lower-+.f32`
2×	`lift-/.f64`
2×	`1-exp`
2×	`lift--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
0	8	7
1	13	7
2	14	7
0	14	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)

localize20.0ms (0.3%)

Memory

-12.7MiB live, 23.6MiB 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

9.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (54.4% of total)

ival-sub: 1.0ms (27.2% 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 (- 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

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))

rewrite352.0ms (5.8%)

Memory

29.1MiB live, 617.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 912×	`lower-fma.f64`
6 912×	`lower-fma.f32`
4 474×	`lower-*.f64`
4 474×	`lower-*.f32`
3 944×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
0	8	4
1	27	4
2	129	4
3	979	4
0	8557	4

Stop Event

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

Counts

2 → 313

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

simplify21.0ms (0.3%)

Memory

-0.7MiB live, 38.2MiB allocated

Algorithm

1×	egg-herbie

Rules

192×	`lower-fma.f64`
192×	`lower-fma.f32`
144×	`lower-*.f64`
144×	`lower-*.f32`
96×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	32	30
2	75	30
3	158	30
4	412	30
5	523	30
6	576	30
7	599	30
8	601	30
0	601	30

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 10

Calls

Call 1

Inputs
-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)
(- 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))

eval42.0ms (0.7%)

Memory: -10.0MiB live, 106.8MiB allocated
Compiler: Compiled 10 399 to 762 computations (92.7% saved)

prune36.0ms (0.6%)

Memory

16.8MiB live, 95.2MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	320	3	323
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	321	3	324

Accuracy

100.0%

Counts

324 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 x #s(literal 1/3 binary64))
▶	70.2%	(.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64))))
▶	52.2%	#s(literal -1/3 binary64)

Status

Accuracy

Program

▶

100.0%

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

▶

70.2%

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

▶

52.2%

#s(literal -1/3 binary64)

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify10.0ms (0.2%)

Memory

10.6MiB live, 10.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 x #s(literal 1/3 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))
✓	cost-diff	320	(.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64))))

Rules

98×	`lower-*.f32`
94×	`lower-*.f64`
90×	`lower-fma.f32`
86×	`lower-fma.f64`
40×	`lower-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	52
0	22	50
1	40	48
2	61	48
3	95	48
4	124	48
5	133	48
6	144	48
7	144	48
0	144	48

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize71.0ms (1.2%)

Memory

-50.7MiB live, 60.7MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 x #s(literal 1/3 binary64))
✓	accuracy	100.0%	(fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))
✓	accuracy	98.8%	(/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64)))
✓	accuracy	71.1%	(.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 #s(literal 1/3 binary64) x) #s(literal 1/9 binary64))))

Samples

58.0ms

256×

valid

Compiler

Compiled 59 to 17 computations (71.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

const: 26.0ms (65.2% of total)

ival-mult: 6.0ms (15% of total)

ival-add: 4.0ms (10% of total)

ival-div: 2.0ms (5% of total)

ival-sub: 1.0ms (2.5% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

6 → 72

Calls

Call 1

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

Outputs
#<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 (- (pow x 3) 1/27)>
#<alt (- (pow x 3) 1/27)>
#<alt (- (pow x 3) 1/27)>
#<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 (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))>
#<alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))>
#<alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 9>
#<alt (+ 9 (* -27 x))>
#<alt (+ 9 (* x (- (* 243 (pow x 2)) 27)))>
#<alt (+ 9 (* x (- (* (pow x 2) (+ 243 (* -729 x))) 27)))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (* 1/3 (/ 1 x))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1/27 (pow x 3))) (* 1/3 (/ 1 x))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1/27 (pow x 3))) (+ (* 1/3 (/ 1 x)) (* 1/81 (/ 1 (pow x 4))))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (* 1/3 (/ 1 x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (/ (- 1/3 (* 1/27 (/ 1 (pow x 2)))) x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (/ (- (+ 1/3 (/ 1/81 (pow x 3))) (* 1/27 (/ 1 (pow x 2)))) x))) (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)))>
#<alt 1/9>
#<alt (+ 1/9 (* 1/3 x))>
#<alt (+ 1/9 (* x (+ 1/3 x)))>
#<alt (+ 1/9 (* x (+ 1/3 x)))>
#<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 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))>

Calls

18 calls:

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

rewrite362.0ms (5.9%)

Memory

23.0MiB live, 490.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 074×	`lower-fma.f32`
5 070×	`lower-fma.f64`
4 724×	`lower-*.f32`
4 720×	`lower-*.f64`
3 860×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	41
0	21	46
1	95	28
2	665	28
3	7963	28
0	8437	28

Stop Event

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

Counts

6 → 982

Calls

Call 1

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

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

simplify367.0ms (6%)

Memory

-0.5MiB live, 471.2MiB allocated

Algorithm

1×	egg-herbie

Rules

7 374×	`lower-fma.f64`
7 374×	`lower-fma.f32`
2 634×	`lower-*.f64`
2 634×	`lower-*.f32`
1 966×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	353
1	211	352
2	541	352
3	1457	344
4	4106	344
0	8187	331

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 68

Calls

Call 1

Inputs
-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
(- (pow x 3) 1/27)
(- (pow x 3) 1/27)
(- (pow x 3) 1/27)
(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)
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
9
(+ 9 (* -27 x))
(+ 9 (* x (- (* 243 (pow x 2)) 27)))
(+ 9 (* x (- (* (pow x 2) (+ 243 (* -729 x))) 27)))
(/ 1 (pow x 2))
(/ (- 1 (* 1/3 (/ 1 x))) (pow x 2))
(/ (- (+ 1 (/ 1/27 (pow x 3))) (* 1/3 (/ 1 x))) (pow x 2))
(/ (- (+ 1 (/ 1/27 (pow x 3))) (+ (* 1/3 (/ 1 x)) (* 1/81 (/ 1 (pow x 4))))) (pow x 2))
(/ 1 (pow x 2))
(/ (- 1 (* 1/3 (/ 1 x))) (pow x 2))
(/ (+ 1 (* -1 (/ (- 1/3 (* 1/27 (/ 1 (pow x 2)))) x))) (pow x 2))
(/ (+ 1 (* -1 (/ (- (+ 1/3 (/ 1/81 (pow x 3))) (* 1/27 (/ 1 (pow x 2)))) x))) (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)))
1/9
(+ 1/9 (* 1/3 x))
(+ 1/9 (* x (+ 1/3 x)))
(+ 1/9 (* x (+ 1/3 x)))
(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 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))

Outputs
-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)
(- (pow x 3) 1/27)
(fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))
(- (pow x 3) 1/27)
(fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))
(- (pow x 3) 1/27)
(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))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(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)
9
#s(literal 9 binary64)
(+ 9 (* -27 x))
(fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64))
(+ 9 (* x (- (* 243 (pow x 2)) 27)))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 243 binary64)) #s(literal -27 binary64)) #s(literal 9 binary64))
(+ 9 (* x (- (* (pow x 2) (+ 243 (* -729 x))) 27)))
(fma.f64 x (fma.f64 x (*.f64 x (fma.f64 x #s(literal -729 binary64) #s(literal 243 binary64))) #s(literal -27 binary64)) #s(literal 9 binary64))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (* 1/3 (/ 1 x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/3 binary64) x)) (*.f64 x x))
(/ (- (+ 1 (/ 1/27 (pow x 3))) (* 1/3 (/ 1 x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/27 binary64) (.f64 x x)) #s(literal -1/3 binary64)) x)) (.f64 x x))
(/ (- (+ 1 (/ 1/27 (pow x 3))) (+ (* 1/3 (/ 1 x)) (* 1/81 (/ 1 (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/27 binary64) (.f64 x x)) #s(literal -1/3 binary64)) x)) (/.f64 #s(literal -1/81 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (* 1/3 (/ 1 x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/3 binary64) x)) (*.f64 x x))
(/ (+ 1 (* -1 (/ (- 1/3 (* 1/27 (/ 1 (pow x 2)))) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/27 binary64) (.f64 x x)) #s(literal -1/3 binary64)) x)) (.f64 x x))
(/ (+ 1 (* -1 (/ (- (+ 1/3 (/ 1/81 (pow x 3))) (* 1/27 (/ 1 (pow x 2)))) x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 #s(literal 1/81 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -1/27 binary64) (.f64 x x)))) 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))
1/9
#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 (+ 1/3 x)))
(fma.f64 x (+.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
(+ 1/9 (* x (+ 1/3 x)))
(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)))))
(fma.f64 x (+.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(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)))))
(fma.f64 x (+.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 x (+.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))

eval163.0ms (2.7%)

Memory: 12.5MiB live, 276.4MiB allocated
Compiler: Compiled 35 280 to 1 814 computations (94.9% saved)

prune145.0ms (2.4%)

Memory

-42.4MiB live, 174.5MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1 049	1	1 050
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	1 050	3	1 053

Accuracy

100.0%

Counts

1 053 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
▶	52.8%	(.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))
✓	52.2%	#s(literal -1/3 binary64)

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify547.0ms (9%)

Memory

72.5MiB live, 600.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(fma.f64 x #s(literal -27 binary64) #s(literal 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 #s(literal -27 binary64) #s(literal 9 binary64)))

Rules

12 812×	`lower-fma.f32`
12 808×	`lower-fma.f64`
4 526×	`lower-*.f32`
4 522×	`lower-*.f64`
2 352×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
0	14	26
1	27	26
2	62	26
3	157	26
4	278	26
5	595	26
6	956	26
7	1098	26
8	1170	26
9	1224	26
10	1224	26
11	1224	26
12	3346	26
13	4293	26
14	4577	26
15	4680	26
16	4692	26
17	4694	26
18	4694	26
19	6339	26
20	6658	26
21	6682	26
22	6682	26
23	6697	26
24	7473	26
25	7474	26
26	7475	26
27	7583	26
28	7719	26
29	7761	26
30	7793	26
31	7841	26
32	7857	26
33	7980	26
0	8072	26

Stop Event

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

Calls

Call 1

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

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

localize76.0ms (1.2%)

Memory

-17.9MiB live, 57.9MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

63.0ms	252×	0	valid
0.0ms	3×	1	valid
0.0ms	1×	2	valid

Compiler

Compiled 34 to 12 computations (64.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

const: 47.0ms (83.1% of total)

ival-mult: 6.0ms (10.6% of total)

ival-add: 2.0ms (3.5% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite333.0ms (5.5%)

Memory

-34.7MiB live, 640.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 698×	`lower-fma.f32`
5 694×	`lower-fma.f64`
5 208×	`lower-*.f32`
5 204×	`lower-*.f64`
2 210×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
0	14	22
1	57	22
2	436	22
3	5160	22
0	8131	22

Stop Event

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

Counts

4 → 415

Calls

Call 1

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

Outputs
(+.f64 (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64))) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64)))
(+.f64 (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64)) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(+.f64 (fma.f64 x #s(literal 1 binary64) #s(literal -1/3 binary64)) (.f64 (.f64 x x) (*.f64 x (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))))
(+.f64 #s(literal -1/3 binary64) (fma.f64 x (.f64 (.f64 x x) #s(literal 9 binary64)) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(+.f64 (.f64 x #s(literal 1 binary64)) (fma.f64 x (.f64 #s(literal -27 binary64) (.f64 x (.f64 x x))) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64))))
(+.f64 (.f64 #s(literal -27 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64))))
(+.f64 (.f64 (.f64 x x) (*.f64 x (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))) (fma.f64 x #s(literal 1 binary64) #s(literal -1/3 binary64)))
(+.f64 (.f64 #s(literal 9 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal -1/3 binary64) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64)))))
(+.f64 (fma.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal -1/3 binary64)) (.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x))))
(+.f64 (fma.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/3 binary64))
(+.f64 (fma.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) #s(literal 9 binary64) (.f64 x #s(literal 1 binary64))) (.f64 #s(literal -27 binary64) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (fma.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) #s(literal 9 binary64) (.f64 #s(literal -27 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 729 binary64) (.f64 (.f64 x (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (.f64 x (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))))) (.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64)))) (/.f64 (.f64 #s(literal 81 binary64) (.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)))) (.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64)))))
(fma.f64 x #s(literal 1 binary64) (fma.f64 x (.f64 #s(literal -27 binary64) (.f64 x (.f64 x x))) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))
(fma.f64 x (.f64 #s(literal -27 binary64) (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -27 binary64))) (fma.f64 x #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 x (.f64 (.f64 x x) #s(literal 9 binary64)) (+.f64 #s(literal -1/3 binary64) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 x (.f64 (.f64 x x) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64))) (fma.f64 x #s(literal 1 binary64) #s(literal -1/3 binary64)))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -27 binary64)) (fma.f64 x #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 9 binary64)) (+.f64 #s(literal -1/3 binary64) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64))) (fma.f64 x #s(literal 1 binary64) #s(literal -1/3 binary64)))
(fma.f64 #s(literal -1/27 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)) (.f64 (.f64 x x) (*.f64 x (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))))
(fma.f64 #s(literal -1/27 binary64) (.f64 x #s(literal -27 binary64)) (fma.f64 x (.f64 #s(literal -27 binary64) (.f64 x (.f64 x x))) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) #s(literal 9 binary64) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64))))
(fma.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (.f64 x #s(literal -27 binary64)) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))
(fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 #s(literal -27 binary64) (.f64 x #s(literal -1/27 binary64)) (fma.f64 x (.f64 #s(literal -27 binary64) (.f64 x (.f64 x x))) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 #s(literal -27 binary64) (.f64 x (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))
(fma.f64 #s(literal 9 binary64) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64))))
(fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) (+.f64 #s(literal -1/3 binary64) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)) #s(literal -1/27 binary64) (.f64 (.f64 x x) (*.f64 x (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))))
(fma.f64 (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)) (.f64 x (.f64 x x)) (fma.f64 x #s(literal 1 binary64) #s(literal -1/3 binary64)))
(fma.f64 (.f64 x #s(literal -27 binary64)) #s(literal -1/27 binary64) (fma.f64 x (.f64 #s(literal -27 binary64) (.f64 x (.f64 x x))) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 (.f64 x #s(literal -27 binary64)) (fma.f64 x (.f64 x x) #s(literal -1/27 binary64)) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))
(fma.f64 (.f64 x #s(literal -27 binary64)) (.f64 x (.f64 x x)) (fma.f64 x #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 9 binary64) (+.f64 #s(literal -1/3 binary64) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 (.f64 x (.f64 x x)) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)) (fma.f64 x #s(literal 1 binary64) #s(literal -1/3 binary64)))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal -27 binary64)) (fma.f64 x #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal -19683 binary64)) #s(literal 729 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 729 binary64)) #s(literal -243 binary64)) #s(literal 81 binary64))) #s(literal -1/27 binary64)) (.f64 (.f64 x x) (*.f64 x (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))))
(fma.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal -19683 binary64)) #s(literal 729 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 729 binary64)) #s(literal -243 binary64)) #s(literal 81 binary64))) (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1 binary64) #s(literal -1/3 binary64)))
(fma.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 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) #s(literal 1/729 binary64))) #s(literal 9 binary64)) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64))))
(fma.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 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) #s(literal 1/729 binary64))) (.f64 x #s(literal -27 binary64))) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))
(fma.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 #s(literal 9 binary64) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) #s(literal 1/729 binary64))) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(fma.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 (.f64 x #s(literal -27 binary64)) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) #s(literal 1/729 binary64))) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64))) #s(literal -1/27 binary64)) (.f64 (.f64 x x) (*.f64 x (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64))) (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1 binary64) #s(literal -1/3 binary64)))
(fma.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/729 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64))) #s(literal 9 binary64)) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(fma.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/729 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64))) (.f64 x #s(literal -27 binary64))) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64)))
(fma.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/729 binary64)) (/.f64 #s(literal 9 binary64) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64))) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64))))
(fma.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/729 binary64)) (/.f64 (.f64 x #s(literal -27 binary64)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64))) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))
(fma.f64 #s(literal 1 binary64) x (fma.f64 x (.f64 #s(literal -27 binary64) (.f64 x (.f64 x x))) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 9 binary64)) (+.f64 #s(literal -1/3 binary64) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64))) (fma.f64 x #s(literal 1 binary64) #s(literal -1/3 binary64)))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 x #s(literal -27 binary64))) (fma.f64 x #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -27 binary64) (fma.f64 x #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 (fma.f64 #s(literal -27 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64)) x (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal -27 binary64)) (.f64 x x) (fma.f64 x #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 (.f64 x #s(literal 9 binary64)) (.f64 x x) (+.f64 #s(literal -1/3 binary64) (.f64 x (fma.f64 #s(literal -27 binary64) (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 (.f64 x #s(literal -1/27 binary64)) #s(literal -27 binary64) (fma.f64 x (.f64 #s(literal -27 binary64) (.f64 x (.f64 x x))) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64))))
(fma.f64 (.f64 x (fma.f64 x (.f64 x x) #s(literal -1/27 binary64))) #s(literal -27 binary64) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))
(fma.f64 (.f64 x (.f64 #s(literal -27 binary64) (fma.f64 x (.f64 x (.f64 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))) (fma.f64 #s(literal 9 binary64) (.f64 x (*.f64 x x)) #s(literal -1/3 binary64)))
(fma.f64 (.f64 x (.f64 #s(literal -27 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) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1/27 binary64)) #s(literal 1/729 binary64))) (fma.f64 #s(literal 9 binary64) (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))
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(pow.f64 (/.f64 (-.f64 #s(literal 9 binary64) (.f64 x #s(literal -27 binary64))) (-.f64 #s(literal 81 binary64) (.f64 (*.f64 x x) #s(literal 729 binary64)))) #s(literal -1 binary64))
(.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal -19683 binary64)) #s(literal 729 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 729 binary64)) #s(literal -243 binary64)) #s(literal 81 binary64))))
(.f64 (fma.f64 (.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64))))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))
(.f64 (neg.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal -19683 binary64)) #s(literal 729 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 729 binary64)) #s(literal -243 binary64)) #s(literal 81 binary64)))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 729 binary64)) #s(literal -243 binary64)) #s(literal 81 binary64))) (fma.f64 x (.f64 (.f64 x x) #s(literal -19683 binary64)) #s(literal 729 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 729 binary64)) #s(literal -243 binary64)) #s(literal 81 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (.f64 x x) #s(literal -19683 binary64)) #s(literal 729 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64))) (fma.f64 (.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64))) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 81 binary64) (.f64 (.f64 x x) #s(literal 729 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 9 binary64) (.f64 x #s(literal -27 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64)) (fma.f64 (*.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64))) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal -19683 binary64)) #s(literal 729 binary64)) (fma.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64))))) (fma.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (-.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (.f64 (.f64 x x) #s(literal 729 binary64))) (.f64 #s(literal 531441 binary64) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (/.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal -19683 binary64)) #s(literal 729 binary64)) (.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 729 binary64)) #s(literal -243 binary64)) #s(literal 81 binary64)) (+.f64 (fma.f64 (.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64)) (.f64 x #s(literal -243 binary64))))) (+.f64 (fma.f64 (.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64)) (*.f64 x #s(literal -243 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 729 binary64) #s(literal -81 binary64)) (fma.f64 x (.f64 (.f64 x x) #s(literal -19683 binary64)) #s(literal -729 binary64))) (fma.f64 x (*.f64 x #s(literal 729 binary64)) (fma.f64 x #s(literal -243 binary64) #s(literal 81 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 729 binary64)) #s(literal -243 binary64)) #s(literal 81 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal -7625597484987 binary64) #s(literal 387420489 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal 531441 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -14348907 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 729 binary64)) #s(literal -243 binary64)) #s(literal 81 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (*.f64 x x) #s(literal -19683 binary64)) #s(literal -729 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 531441 binary64) (.f64 x (.f64 x (.f64 x x))) (fma.f64 (.f64 x x) #s(literal 59049 binary64) #s(literal 6561 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64)) (fma.f64 #s(literal 531441 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -6561 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 729 binary64)) #s(literal 81 binary64))))

simplify228.0ms (3.7%)

Memory

27.8MiB live, 293.2MiB allocated

Algorithm

1×	egg-herbie

Rules

5 462×	`lower-fma.f64`
5 462×	`lower-fma.f32`
2 142×	`lower-*.f64`
2 142×	`lower-*.f32`
1 064×	`associate-*r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	258
1	157	250
2	426	250
3	1291	250
4	3419	242
5	7271	242
0	8094	220

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval196.0ms (3.2%)

Memory: -3.8MiB live, 112.4MiB allocated
Compiler: Compiled 15 403 to 1 219 computations (92.1% saved)

prune341.0ms (5.6%)

Memory

-13.3MiB live, 117.6MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	462	1	463
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	463	3	466

Accuracy

100.0%

Counts

466 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
▶	99.4%	(*.f64 #s(literal -1/27 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))
✓	52.2%	#s(literal -1/3 binary64)

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify498.0ms (8.2%)

Memory

14.1MiB live, 287.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64))
✓	cost-diff	512	(*.f64 #s(literal -1/27 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))

Rules

18 686×	`associate-r`
11 188×	`lower-*.f32`
11 186×	`lower-*.f64`
2 636×	`*-commutative`
2 182×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	14
0	9	14
1	19	13
2	30	11
3	35	11
4	60	11
5	131	11
6	306	11
7	335	11
8	335	11
9	751	11
10	818	11
11	818	11
12	818	11
13	1911	11
14	2106	11
15	2106	11
16	2106	11
17	5349	11
18	5349	11
19	5349	11
20	6153	11
21	6153	11
22	6153	11
0	15058	11

Stop Event

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

Calls

Call 1

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

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

localize70.0ms (1.1%)

Memory

-26.7MiB live, 48.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64))
✓	accuracy	99.4%	(*.f64 #s(literal -1/27 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))

Samples

15.0ms	252×	0	valid
0.0ms	3×	1	valid
0.0ms	1×	2	valid

Compiler

Compiled 18 to 9 computations (50% saved)

Precisions

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

const: 5.0ms (49.8% of total)

ival-mult: 3.0ms (29.9% of total)

ival-add: 1.0ms (10% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

2 → 24

Calls

Call 1

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

Outputs
#<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 9>
#<alt (+ 9 (* -27 x))>
#<alt (+ 9 (* -27 x))>
#<alt (+ 9 (* -27 x))>
#<alt (* -27 x)>
#<alt (* x (- (* 9 (/ 1 x)) 27))>
#<alt (* x (- (* 9 (/ 1 x)) 27))>
#<alt (* x (- (* 9 (/ 1 x)) 27))>
#<alt (* -27 x)>
#<alt (* -1 (* x (- 27 (* 9 (/ 1 x)))))>
#<alt (* -1 (* x (- 27 (* 9 (/ 1 x)))))>
#<alt (* -1 (* x (- 27 (* 9 (/ 1 x)))))>

Calls

6 calls:

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

rewrite365.0ms (6%)

Memory

2.9MiB live, 675.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 540×	`lower-fma.f32`
6 538×	`lower-fma.f64`
5 056×	`lower-/.f64`
5 056×	`lower-/.f32`
4 230×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	10
0	9	10
1	34	9
2	202	7
3	1535	7
0	8264	7

Stop Event

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

Counts

2 → 319

Calls

Call 1

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

Outputs
(+.f64 x #s(literal -1/3 binary64))
(+.f64 #s(literal -1/3 binary64) x)
(+.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 (*.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)))
(fma.f64 #s(literal -1/27 binary64) (*.f64 x #s(literal -27 binary64)) #s(literal -1/3 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal -1/3 binary64))
(fma.f64 #s(literal -27 binary64) (*.f64 #s(literal -1/27 binary64) x) #s(literal -1/3 binary64))
(fma.f64 (*.f64 x #s(literal -27 binary64)) #s(literal -1/27 binary64) #s(literal -1/3 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal -1/3 binary64))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal 1/3 binary64)))))
(fma.f64 (*.f64 #s(literal -1/27 binary64) x) #s(literal -27 binary64) #s(literal -1/3 binary64))
(/.f64 #s(literal -1/27 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64))))
(/.f64 (fma.f64 x (.f64 x x) #s(literal -1/27 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)) (+.f64 #s(literal 1/9 binary64) (-.f64 (.f64 x x) (*.f64 x #s(literal -1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64))) #s(literal -1/27 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (-.f64 (.f64 x x) (.f64 x #s(literal -1/3 binary64)))) (fma.f64 x (*.f64 x x) #s(literal -1/27 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64)))
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(.f64 (pow.f64 (/.f64 (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64)) (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -6561 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 729 binary64)) #s(literal 81 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 729 binary64) #s(literal 243 binary64)) #s(literal 81 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -7625597484987 binary64) #s(literal 387420489 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal 531441 binary64)) (.f64 (.f64 x (*.f64 x x)) #s(literal 14348907 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 729 binary64) #s(literal 243 binary64)) #s(literal 81 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal -19683 binary64) #s(literal -729 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -7625597484987 binary64) #s(literal 387420489 binary64)) (fma.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal 531441 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 14348907 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (-.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (.f64 x (.f64 x #s(literal 729 binary64)))) (.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)))))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -7625597484987 binary64) #s(literal 387420489 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 729 binary64) #s(literal 243 binary64)) #s(literal 81 binary64)) (+.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (.f64 x #s(literal -243 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal 531441 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 14348907 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (.f64 x #s(literal -243 binary64))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64)) (fma.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal -19683 binary64) #s(literal -729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (-.f64 (fma.f64 x #s(literal 243 binary64) #s(literal 81 binary64)) (.f64 x (.f64 x #s(literal 729 binary64)))) (.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 729 binary64) #s(literal 243 binary64)) #s(literal 81 binary64)) (+.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (.f64 x #s(literal -243 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal -19683 binary64) #s(literal -729 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (*.f64 x #s(literal -243 binary64))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64)) (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 59049 binary64) #s(literal 6561 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal -19683 binary64) #s(literal 729 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 59049 binary64) #s(literal 6561 binary64)))) (fma.f64 x (fma.f64 x #s(literal 729 binary64) #s(literal 243 binary64)) #s(literal 81 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 59049 binary64) #s(literal 6561 binary64)))) (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -19683 binary64) #s(literal 729 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 59049 binary64) #s(literal 6561 binary64)))) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 729 binary64) #s(literal 243 binary64)) #s(literal 81 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (neg.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 59049 binary64) #s(literal 6561 binary64)))) (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 387420489 binary64)) #s(literal -531441 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (+.f64 #s(literal 81 binary64) (.f64 #s(literal -729 binary64) (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 59049 binary64) #s(literal 6561 binary64)))) (-.f64 #s(literal 9 binary64) (.f64 x #s(literal -27 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -6561 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal -19683 binary64) #s(literal -729 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal 81 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 729 binary64)) (fma.f64 x #s(literal -243 binary64) #s(literal 81 binary64))))))
(.f64 (/.f64 (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -6561 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal -19683 binary64) #s(literal 729 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal 81 binary64))) (fma.f64 x (fma.f64 x #s(literal 729 binary64) #s(literal 243 binary64)) #s(literal 81 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -6561 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 729 binary64)) #s(literal 81 binary64))) (fma.f64 x #s(literal -27 binary64) #s(literal -9 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -6561 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -19683 binary64) #s(literal 729 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal 81 binary64))) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 729 binary64) #s(literal 243 binary64)) #s(literal 81 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -6561 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (neg.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 729 binary64)) #s(literal 81 binary64))) (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 531441 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -6561 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (+.f64 #s(literal 81 binary64) (.f64 #s(literal -729 binary64) (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal 81 binary64))) (-.f64 #s(literal 9 binary64) (*.f64 x #s(literal -27 binary64)))))
(.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (fma.f64 (.f64 x (*.f64 x x)) #s(literal -19683 binary64) #s(literal 729 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 729 binary64) #s(literal 243 binary64)) #s(literal 81 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (neg.f64 (fma.f64 (.f64 x (*.f64 x x)) #s(literal -19683 binary64) #s(literal 729 binary64))))) (/.f64 #s(literal -1 binary64) (fma.f64 x (fma.f64 x #s(literal 729 binary64) #s(literal 243 binary64)) #s(literal 81 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (neg.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 729 binary64)) #s(literal -81 binary64)) (+.f64 #s(literal 81 binary64) (.f64 #s(literal -729 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 9 binary64) (.f64 x #s(literal -27 binary64)))))

simplify41.0ms (0.7%)

Memory

9.8MiB live, 91.9MiB allocated

Algorithm

1×	egg-herbie

Rules

400×	`lower-fma.f64`
400×	`lower-fma.f32`
288×	`lower-*.f64`
288×	`lower-*.f32`
194×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	82
1	61	82
2	142	82
3	333	82
4	862	82
5	1010	82
6	1099	82
7	1148	82
8	1152	82
0	1152	73

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 22

Calls

Call 1

Inputs
-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)))
9
(+ 9 (* -27 x))
(+ 9 (* -27 x))
(+ 9 (* -27 x))
(* -27 x)
(* x (- (* 9 (/ 1 x)) 27))
(* x (- (* 9 (/ 1 x)) 27))
(* x (- (* 9 (/ 1 x)) 27))
(* -27 x)
(* -1 (* x (- 27 (* 9 (/ 1 x)))))
(* -1 (* x (- 27 (* 9 (/ 1 x)))))
(* -1 (* x (- 27 (* 9 (/ 1 x)))))

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

eval47.0ms (0.8%)

Memory: 7.1MiB live, 139.7MiB allocated
Compiler: Compiled 9 708 to 1 065 computations (89% saved)

prune40.0ms (0.7%)

Memory

8.6MiB live, 125.0MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	341	3	344

Accuracy

100.0%

Counts

344 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
✓	99.4%	(*.f64 #s(literal -1/27 binary64) (fma.f64 x #s(literal -27 binary64) #s(literal 9 binary64)))
✓	52.2%	#s(literal -1/3 binary64)

Compiler

Compiled 55 to 32 computations (41.8% saved)

regimes8.0ms (0.1%)

Memory

-27.6MiB live, 14.4MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
3.0ms	x

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

10.2MiB live, 10.2MiB 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
52.2%	1	`x`
52.2%	1	`(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`

Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0.1%)

Memory

-18.9MiB live, 19.5MiB 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)

soundness147.0ms (2.4%)

Memory

3.2MiB live, 162.3MiB allocated

Rules

6 912×	`lower-fma.f64`
6 912×	`lower-fma.f32`
4 474×	`lower-*.f64`
4 474×	`lower-*.f32`
3 944×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
0	8	4
1	27	4
2	129	4
3	979	4
0	8557	4
0	13	30
1	32	30
2	75	30
3	158	30
4	412	30
5	523	30
6	576	30
7	599	30
8	601	30
0	601	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)

preprocess19.0ms (0.3%)

Memory: 8.6MiB live, 47.1MiB allocated
Compiler: Compiled 22 to 18 computations (18.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample1.4s (23.1%)

preprocess15.0ms (0.2%)

explain98.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize20.0ms (0.3%)

series1.0ms (0%)

rewrite352.0ms (5.8%)

simplify21.0ms (0.3%)

eval42.0ms (0.7%)

prune36.0ms (0.6%)

simplify10.0ms (0.2%)

localize71.0ms (1.2%)

series7.0ms (0.1%)

rewrite362.0ms (5.9%)

simplify367.0ms (6%)

eval163.0ms (2.7%)

prune145.0ms (2.4%)

simplify547.0ms (9%)

localize76.0ms (1.2%)

series3.0ms (0.1%)

rewrite333.0ms (5.5%)

simplify228.0ms (3.7%)

eval196.0ms (3.2%)

prune341.0ms (5.6%)

simplify498.0ms (8.2%)

localize70.0ms (1.1%)

series1.0ms (0%)

rewrite365.0ms (6%)

simplify41.0ms (0.7%)

eval47.0ms (0.8%)

prune40.0ms (0.7%)

regimes8.0ms (0.1%)

regimes3.0ms (0%)

simplify8.0ms (0.1%)

soundness147.0ms (2.4%)

preprocess19.0ms (0.3%)

end0.0ms (0%)

Profiling