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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample497.0ms (11%)

Memory

41.1MiB live, 1 064.9MiB allocated

Samples

318.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 172.0ms

ival-div: 82.0ms (47.6% of total)

ival-sub: 74.0ms (43% of total)

exact: 7.0ms (4.1% of total)

ival-true: 6.0ms (3.5% of total)

ival-assert: 3.0ms (1.7% of total)

Bogosity

explain50.0ms (1.1%)

Memory

-1.8MiB live, 119.5MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`	cancellation	1	0

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	255

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

20.0ms

512×

valid

Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 5.0ms (56.7% of total)

ival-sub: 2.0ms (22.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess15.0ms (0.3%)

Memory

-6.6MiB live, 32.2MiB 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))

Compiler

Compiled 5 to 5 computations (0% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% 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 5 to 5 computations (0% saved)

simplify3.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB 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)

localize95.0ms (2.1%)

Memory

-12.3MiB live, 26.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
accuracy	0.029138404760301943	(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Samples

91.0ms

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 (54.7% of total)

ival-sub: 1.0ms (27.4% 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

2.1MiB live, 2.1MiB allocated

Counts

2 → 12

Calls

Call 1

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

Inputs

#s(alt (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())

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

Outputs
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify15.0ms (0.3%)

Memory

23.8MiB live, 23.8MiB 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))

rewrite385.0ms (8.5%)

Memory

-31.0MiB live, 225.6MiB 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

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
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eval182.0ms (4%)

Memory: -8.9MiB live, 67.5MiB allocated
Compiler: Compiled 8 097 to 759 computations (90.6% saved)

prune8.0ms (0.2%)

Memory

24.0MiB live, 24.0MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	317	6	323
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	318	6	324

Accuracy

100.0%

Counts

324 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	78.0%	(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
▶	99.9%	(fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
▶	78.0%	(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64)))
▶	78.1%	(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal -1/3 binary64) x))
▶	100.0%	(-.f64 x #s(literal 1/3 binary64))
▶	54.0%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 96 to 70 computations (27.1% saved)

simplify29.0ms (0.6%)

Memory

-23.8MiB live, 15.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))
cost-diff	0	(-.f64 x #s(literal -1/3 binary64))
cost-diff	0	(/.f64 x (-.f64 x #s(literal -1/3 binary64)))
cost-diff	896	(fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
cost-diff	0	(-.f64 #s(literal -1/3 binary64) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
cost-diff	128	(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal -1/3 binary64) x))
cost-diff	0	(-.f64 x #s(literal -1/3 binary64))
cost-diff	0	(fma.f64 x x #s(literal -1/9 binary64))
cost-diff	0	(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64)))
cost-diff	0	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
cost-diff	0	(-.f64 x #s(literal 1/3 binary64))

Rules

384×	`lower-fma.f32`
380×	`lower-fma.f64`
248×	`lower-*.f32`
246×	`lower-*.f64`
154×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	80
0	32	75
1	51	75
2	65	75
3	86	75
4	129	75
5	215	75
6	455	75
7	681	75
8	739	75
9	918	75
10	924	75
11	926	75
0	926	75

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize126.0ms (2.8%)

Memory

-3.8MiB live, 113.3MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f64 x #s(literal -1/3 binary64))
accuracy	0.03682134669805507	(fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
accuracy	0.1875	(/.f64 x (-.f64 x #s(literal -1/3 binary64)))
accuracy	0.2109375	(/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(-.f64 #s(literal -1/3 binary64) x)
accuracy	0.033535009768442016	(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
accuracy	14.052164414479659	(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal -1/3 binary64) x))
accuracy	0.0078125	(-.f64 x #s(literal -1/3 binary64))
accuracy	0.03850773826221708	(fma.f64 x x #s(literal -1/9 binary64))
accuracy	14.052164414479659	(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64)))
accuracy	29.460884018642883	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
accuracy	0.029138404760301943	(-.f64 x #s(literal 1/3 binary64))

Samples

42.0ms	211×	0	valid
41.0ms	22×	2	valid
8.0ms	23×	1	valid

Compiler

Compiled 85 to 23 computations (72.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-div: 40.0ms (51.1% of total)

const: 22.0ms (28.1% of total)

ival-sub: 6.0ms (7.7% of total)

ival-mult: 4.0ms (5.1% of total)

adjust: 3.0ms (3.8% of total)

ival-add: 2.0ms (2.6% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

21.2MiB live, 21.2MiB allocated

Counts

12 → 144

Calls

Call 1

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

Outputs
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt -1/9 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1/9 (taylor 0 x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (- (* -1 x) 1/3) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (- (* -1 x) 1/3) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (- (* -1 x) 1/3) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 3 x) (taylor 0 x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 3 (* -9 x))) (taylor 0 x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 3 (* x (- (* 27 x) 9)))) (taylor 0 x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))) (taylor 0 x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (* -3 x))) 1/3) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (* x (- (* 9 x) 3)))) 1/3) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (* 1/3 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) (taylor inf x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ -1/9 x) (taylor inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 1/27 (/ 1 x)) 1/9) x) (taylor inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 1/27 (/ 1 x)) (+ 1/9 (/ 1/81 (pow x 2)))) x) (taylor inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* 1/27 (/ 1 x)) (* 1/243 (/ 1 (pow x 3)))) (+ 1/9 (/ 1/81 (pow x 2)))) x) (taylor inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (* 1/3 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) x))) x))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ -1/9 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1/9 (* -1 (/ (- 1/27 (* 1/81 (/ 1 x))) x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1/9 (* -1 (/ (+ 1/27 (* -1 (/ (- 1/81 (* 1/243 (/ 1 x))) x))) x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

((- x 1/3) (- x (/ 1 3)) (/ (+ (* x x) -1/9) (- x -1/3)) (+ (* x x) -1/9) (- x -1/3) (/ (- 1/9 (* x x)) (- -1/3 x)) (- 1/9 (* x x)) (* x x) (- -1/3 x) (+ (* x (/ x (- x -1/3))) (/ -1/9 (- x -1/3))) (/ x (- x -1/3)) (/ -1/9 (- x -1/3)))

2.0ms

((- x 1/3) (- x (/ 1 3)) (/ (+ (* x x) -1/9) (- x -1/3)) (+ (* x x) -1/9) (- x -1/3) (/ (- 1/9 (* x x)) (- -1/3 x)) (- 1/9 (* x x)) (* x x) (- -1/3 x) (+ (* x (/ x (- x -1/3))) (/ -1/9 (- x -1/3))) (/ x (- x -1/3)) (/ -1/9 (- x -1/3)))

2.0ms

-inf

((- x 1/3) (- x (/ 1 3)) (/ (+ (* x x) -1/9) (- x -1/3)) (+ (* x x) -1/9) (- x -1/3) (/ (- 1/9 (* x x)) (- -1/3 x)) (- 1/9 (* x x)) (* x x) (- -1/3 x) (+ (* x (/ x (- x -1/3))) (/ -1/9 (- x -1/3))) (/ x (- x -1/3)) (/ -1/9 (- x -1/3)))

simplify121.0ms (2.7%)

Memory

6.1MiB live, 125.1MiB allocated

Algorithm

1×	egg-herbie

Rules

9 310×	`lower-fma.f64`
9 310×	`lower-fma.f32`
2 604×	`lower-*.f64`
2 604×	`lower-*.f32`
2 100×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	586
1	340	569
2	763	552
3	1899	544
4	4600	544
0	8113	524

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 132

Calls

Call 1

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

rewrite262.0ms (5.8%)

Memory

-22.4MiB live, 297.7MiB allocated

Rules

6 240×	`lower-fma.f32`
6 236×	`lower-fma.f64`
4 950×	`lower-/.f32`
4 942×	`lower-/.f64`
3 574×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	65
0	32	45
1	140	45
2	1121	45
0	8468	45

Stop Event

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

Counts

12 → 1 541

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
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eval285.0ms (6.3%)

Memory: 29.7MiB live, 450.3MiB allocated
Compiler: Compiled 40 214 to 2 390 computations (94.1% saved)

prune38.0ms (0.8%)

Memory

22.6MiB live, 137.3MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	1 891	2	1 893
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	1 892	7	1 899

Accuracy

100.0%

Counts

1 899 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.0%	(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
✓	99.9%	(fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
✓	78.0%	(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64)))
▶	64.9%	(/.f64 (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x))
✓	78.1%	(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal -1/3 binary64) x))
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
✓	54.0%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 69 to 50 computations (27.5% saved)

simplify242.0ms (5.4%)

Memory

-52.3MiB live, 130.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x #s(literal -1/3 binary64))
cost-diff	0	(pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	6080	(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
cost-diff	0	(fma.f64 x x #s(literal 1/9 binary64))
cost-diff	0	(pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64))
cost-diff	384	(/.f64 (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x))
cost-diff	7168	(fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))))

Rules

3 200×	`lower-fma.f32`
3 194×	`lower-fma.f64`
1 176×	`lower-*.f32`
1 174×	`lower-*.f64`
700×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	114
0	34	114
1	57	110
2	92	109
3	153	109
4	253	103
5	488	103
6	1238	99
7	3102	99
8	3793	99
9	4034	99
10	4083	99
11	4090	99
12	4093	99
13	4273	99
14	4393	99
15	4416	99
16	4428	99
17	4480	99
18	4566	99
19	4566	99
0	4566	98

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x))
(fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))))
#s(literal 1/81 binary64)
(pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64))
(fma.f64 x x #s(literal 1/9 binary64))
x
#s(literal 1/9 binary64)
#s(literal -1 binary64)
(neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))
(/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)
(-.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(*.f64 x x)
x
(pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64))
(-.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
#s(literal -1 binary64)
(/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))
#s(literal 1/9 binary64)
(-.f64 #s(literal -1/3 binary64) x)

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

localize81.0ms (1.8%)

Memory

23.1MiB live, 175.3MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f64 #s(literal -1/3 binary64) x)
accuracy	0.01953125	(pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64))
accuracy	0.2109375	(/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))
accuracy	14.105230674248102	(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
accuracy	0.03125	(fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))))
accuracy	0.20579528023380134	(pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64))
accuracy	14.052164414479659	(/.f64 (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x))
accuracy	19.301898602828096	(/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))

Samples

64.0ms

256×

valid

Compiler

Compiled 127 to 23 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-sub: 15.0ms (28.9% of total)

const: 10.0ms (19.3% of total)

ival-pow: 9.0ms (17.3% of total)

ival-mult: 6.0ms (11.6% of total)

ival-div: 4.0ms (7.7% of total)

ival-neg: 4.0ms (7.7% of total)

ival-add: 3.0ms (5.8% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.3%)

Memory

-25.5MiB live, 19.2MiB allocated

Counts

11 → 132

Calls

Call 1

Inputs
#s(alt (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (patch (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())
#s(alt (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1/9 binary64)) (patch (fma.f64 x x #s(literal 1/9 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (fma.f64 (.f64 x x) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) (patch (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())

Outputs
#s(alt 1/9 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (patch (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (patch (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (patch (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (patch (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1/9 binary64)) (patch (fma.f64 x x #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
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#s(alt (/ -1/9 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1/9 (* -1 (/ (- 1/27 (* 1/81 (/ 1 x))) x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1/9 (* -1 (/ (+ 1/27 (* -1 (/ (- 1/81 (* 1/243 (/ 1 x))) x))) x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

((+ (* 1/81 (pow (+ (* x x) 1/9) -1)) (neg (/ (pow x 4) (+ (* x x) 1/9)))) (/ (+ (* 1/81 (pow (+ (* x x) 1/9) -1)) (neg (/ (pow x 4) (+ (* x x) 1/9)))) (- -1/3 x)) (pow (+ (* x x) 1/9) -1) (+ (* x x) 1/9) (+ (* (* x x) (pow (- x -1/3) -1)) (/ 1/9 (- -1/3 x))) (* x x) (pow (- x -1/3) -1) (- x -1/3) (/ (pow x 4) (+ (* x x) 1/9)) (/ 1/9 (- -1/3 x)) (- -1/3 x))

2.0ms

inf

((+ (* 1/81 (pow (+ (* x x) 1/9) -1)) (neg (/ (pow x 4) (+ (* x x) 1/9)))) (/ (+ (* 1/81 (pow (+ (* x x) 1/9) -1)) (neg (/ (pow x 4) (+ (* x x) 1/9)))) (- -1/3 x)) (pow (+ (* x x) 1/9) -1) (+ (* x x) 1/9) (+ (* (* x x) (pow (- x -1/3) -1)) (/ 1/9 (- -1/3 x))) (* x x) (pow (- x -1/3) -1) (- x -1/3) (/ (pow x 4) (+ (* x x) 1/9)) (/ 1/9 (- -1/3 x)) (- -1/3 x))

2.0ms

-inf

((+ (* 1/81 (pow (+ (* x x) 1/9) -1)) (neg (/ (pow x 4) (+ (* x x) 1/9)))) (/ (+ (* 1/81 (pow (+ (* x x) 1/9) -1)) (neg (/ (pow x 4) (+ (* x x) 1/9)))) (- -1/3 x)) (pow (+ (* x x) 1/9) -1) (+ (* x x) 1/9) (+ (* (* x x) (pow (- x -1/3) -1)) (/ 1/9 (- -1/3 x))) (* x x) (pow (- x -1/3) -1) (- x -1/3) (/ (pow x 4) (+ (* x x) 1/9)) (/ 1/9 (- -1/3 x)) (- -1/3 x))

simplify160.0ms (3.6%)

Memory

32.2MiB live, 219.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 224×	`lower-fma.f64`
13 224×	`lower-fma.f32`
3 864×	`lower-+.f64`
3 864×	`lower-+.f32`
3 438×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	820
1	459	795
2	1113	762
3	3259	750
4	7755	750
0	8266	710

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 126

Calls

Call 1

Inputs
1/9
(+ 1/9 (* -1 (pow x 2)))
(+ 1/9 (* -1 (pow x 2)))
(+ 1/9 (* -1 (pow x 2)))
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
9
(+ 9 (* -81 (pow x 2)))
(+ 9 (* (pow x 2) (- (* 729 (pow x 2)) 81)))
(+ 9 (* (pow x 2) (- (* (pow x 2) (+ 729 (* -6561 (pow x 2)))) 81)))
1/9
(+ 1/9 (pow x 2))
(+ 1/9 (pow x 2))
(+ 1/9 (pow x 2))
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
3
(+ 3 (* -9 x))
(+ 3 (* x (- (* 27 x) 9)))
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
(* 9 (pow x 4))
(* (pow x 4) (+ 9 (* -81 (pow x 2))))
(* (pow x 4) (+ 9 (* (pow x 2) (- (* 729 (pow x 2)) 81))))
(* (pow x 4) (+ 9 (* (pow x 2) (- (* (pow x 2) (+ 729 (* -6561 (pow x 2)))) 81))))
-1/3
(- x 1/3)
(- (* x (+ 1 (* -3 x))) 1/3)
(- (* x (+ 1 (* x (- (* 9 x) 3)))) 1/3)
-1/3
(- (* -1 x) 1/3)
(- (* -1 x) 1/3)
(- (* -1 x) 1/3)
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(/ 1 (pow x 2))
(/ (- 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))))
(/ -1/9 x)
(/ (- (* 1/27 (/ 1 x)) 1/9) x)
(/ (- (* 1/27 (/ 1 x)) (+ 1/9 (/ 1/81 (pow x 2)))) x)
(/ (- (+ (* 1/27 (/ 1 x)) (* 1/243 (/ 1 (pow x 3)))) (+ 1/9 (/ 1/81 (pow x 2)))) x)
(* -1 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(/ 1 (pow x 2))
(/ (- 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))))
(/ -1/9 x)
(* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) x))
(* -1 (/ (+ 1/9 (* -1 (/ (- 1/27 (* 1/81 (/ 1 x))) x))) x))
(* -1 (/ (+ 1/9 (* -1 (/ (+ 1/27 (* -1 (/ (- 1/81 (* 1/243 (/ 1 x))) x))) x))) x))
(* -1 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))

Outputs
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(+ 1/9 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(+ 1/9 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
9
#s(literal 9 binary64)
(+ 9 (* -81 (pow x 2)))
(fma.f64 #s(literal -81 binary64) (*.f64 x x) #s(literal 9 binary64))
(+ 9 (* (pow x 2) (- (* 729 (pow x 2)) 81)))
(fma.f64 (fma.f64 #s(literal 729 binary64) (.f64 x x) #s(literal -81 binary64)) (.f64 x x) #s(literal 9 binary64))
(+ 9 (* (pow x 2) (- (* (pow x 2) (+ 729 (* -6561 (pow x 2)))) 81)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -6561 binary64) (.f64 x x) #s(literal 729 binary64)) (.f64 x x) #s(literal -81 binary64)) (*.f64 x x) #s(literal 9 binary64))
1/9
#s(literal 1/9 binary64)
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
-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))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
3
#s(literal 3 binary64)
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(+ 3 (* x (- (* 27 x) 9)))
(fma.f64 (fma.f64 #s(literal 27 binary64) x #s(literal -9 binary64)) x #s(literal 3 binary64))
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -81 binary64) x #s(literal 27 binary64)) x #s(literal -9 binary64)) x #s(literal 3 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(-.f64 x #s(literal -1/3 binary64))
(+ 1/3 x)
(-.f64 x #s(literal -1/3 binary64))
(+ 1/3 x)
(-.f64 x #s(literal -1/3 binary64))
(* 9 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64))
(* (pow x 4) (+ 9 (* -81 (pow x 2))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -81 binary64) (.f64 x x) #s(literal 9 binary64)))
(* (pow x 4) (+ 9 (* (pow x 2) (- (* 729 (pow x 2)) 81))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 729 binary64) (.f64 x x) #s(literal -81 binary64)) (*.f64 x x) #s(literal 9 binary64)))
(* (pow x 4) (+ 9 (* (pow x 2) (- (* (pow x 2) (+ 729 (* -6561 (pow x 2)))) 81))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -6561 binary64) (.f64 x x) #s(literal 729 binary64)) (.f64 x x) #s(literal -81 binary64)) (.f64 x x) #s(literal 9 binary64)))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- (* x (+ 1 (* -3 x))) 1/3)
(fma.f64 (fma.f64 #s(literal -3 binary64) x #s(literal 1 binary64)) x #s(literal -1/3 binary64))
(- (* x (+ 1 (* x (- (* 9 x) 3)))) 1/3)
(fma.f64 (fma.f64 (fma.f64 #s(literal 9 binary64) x #s(literal -3 binary64)) x #s(literal 1 binary64)) x #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- (* -1 x) 1/3)
(-.f64 #s(literal -1/3 binary64) x)
(- (* -1 x) 1/3)
(-.f64 #s(literal -1/3 binary64) x)
(- (* -1 x) 1/3)
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 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))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/9 binary64) (*.f64 x x))) x) x)
(/ (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (.f64 x x))) (/.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
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))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/9 binary64) x) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x)
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -1/3 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x)) x) #s(literal -1 binary64)) x)
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))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) x x) x #s(literal -1/9 binary64))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))))
(fma.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x) #s(literal -1/9 binary64))
(/ -1/9 x)
(/.f64 #s(literal -1/9 binary64) x)
(/ (- (* 1/27 (/ 1 x)) 1/9) x)
(/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x)
(/ (- (* 1/27 (/ 1 x)) (+ 1/9 (/ 1/81 (pow x 2)))) x)
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/27 binary64) (/.f64 #s(literal 1/81 binary64) x)) x) #s(literal 1/9 binary64)) x)
(/ (- (+ (* 1/27 (/ 1 x)) (* 1/243 (/ 1 (pow x 3)))) (+ 1/9 (/ 1/81 (pow x 2)))) x)
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/27 binary64) (/.f64 (-.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1/243 binary64) x)) x)) x) #s(literal 1/9 binary64)) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 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 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/9 binary64) (*.f64 x x))) x) x)
(/ (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (.f64 x x))) (/.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
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))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/9 binary64) x) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -1/3 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x)) x) #s(literal -1 binary64)) x)
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))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) x x) x #s(literal -1/9 binary64))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))))
(fma.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x) #s(literal -1/9 binary64))
(/ -1/9 x)
(/.f64 #s(literal -1/9 binary64) x)
(* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x)
(* -1 (/ (+ 1/9 (* -1 (/ (- 1/27 (* 1/81 (/ 1 x))) x))) x))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/27 binary64) (/.f64 #s(literal 1/81 binary64) x)) x) #s(literal 1/9 binary64)) x)
(* -1 (/ (+ 1/9 (* -1 (/ (+ 1/27 (* -1 (/ (- 1/81 (* 1/243 (/ 1 x))) x))) x))) x))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/27 binary64) (/.f64 (-.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1/243 binary64) x)) x)) x) #s(literal 1/9 binary64)) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)

rewrite234.0ms (5.2%)

Memory

21.1MiB live, 253.9MiB allocated

Rules

6 938×	`lower-fma.f32`
6 932×	`lower-fma.f64`
3 908×	`lower-/.f32`
3 902×	`lower-/.f64`
3 826×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	89
0	34	96
1	151	81
2	1097	48
0	8770	48

Stop Event

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

Counts

11 → 833

Calls

Call 1

Inputs
(fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))))
(/.f64 (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x))
(pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64))
(fma.f64 x x #s(literal 1/9 binary64))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(*.f64 x x)
(pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64))
(-.f64 x #s(literal -1/3 binary64))
(/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))
(/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))
(-.f64 #s(literal -1/3 binary64) x)

Outputs
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eval210.0ms (4.7%)

Memory: -18.4MiB live, 251.6MiB allocated
Compiler: Compiled 29 895 to 2 644 computations (91.2% saved)

prune23.0ms (0.5%)

Memory

-7.6MiB live, 80.3MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	1 083	3	1 086
Fresh	0	0	0
Picked	2	0	2
Done	0	5	5
Total	1 085	8	1 093

Accuracy

100.0%

Counts

1 093 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.0%	(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
✓	99.9%	(fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
▶	64.9%	(/.f64 (fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/81 binary64) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 2 binary64)))) (fma.f64 (/.f64 x (-.f64 x #s(literal -1/3 binary64))) x (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))))
✓	78.0%	(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64)))
▶	64.9%	(/.f64 (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x))
✓	78.1%	(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal -1/3 binary64) x))
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
✓	54.0%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 98 to 68 computations (30.6% saved)

simplify223.0ms (5%)

Memory

8.3MiB live, 119.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x #s(literal -1/3 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	320	(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
cost-diff	0	(-.f64 x #s(literal -1/3 binary64))
cost-diff	0	(pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64))
cost-diff	0	(fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/81 binary64) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 2 binary64))))
cost-diff	0	(/.f64 (fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/81 binary64) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 2 binary64)))) (fma.f64 (/.f64 x (-.f64 x #s(literal -1/3 binary64))) x (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))))
cost-diff	0	(fma.f64 x x #s(literal 1/9 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64)))
cost-diff	384	(/.f64 (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x))
cost-diff	1408	(fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))))

Rules

5 876×	`lower-fma.f32`
5 866×	`lower-fma.f64`
2 340×	`lower-*.f32`
2 338×	`lower-*.f64`
1 864×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	214
0	56	210
1	88	209
2	128	209
3	206	209
4	329	203
5	587	203
6	1482	199
7	3460	199
8	4397	199
9	4764	199
10	4998	199
11	5295	199
12	5340	199
13	6105	199
14	6886	199
15	7292	199
16	8000	199
0	8204	198

Stop Event

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

Calls

Call 1

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

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

localize181.0ms (4%)

Memory

-14.8MiB live, 283.4MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f64 #s(literal -1/3 binary64) x)
accuracy	0.01953125	(/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64)))
accuracy	0.2109375	(/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))
accuracy	14.105230674248102	(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
accuracy	0.2109375	(/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))
accuracy	0.53515625	(pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64))
accuracy	14.048258164479659	(/.f64 (fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/81 binary64) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 2 binary64)))) (fma.f64 (/.f64 x (-.f64 x #s(literal -1/3 binary64))) x (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))))
accuracy	18.604301093059647	(fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/81 binary64) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 2 binary64))))
accuracy	0.03125	(fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))))
accuracy	0.20579528023380134	(/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64)))
accuracy	14.052164414479659	(/.f64 (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x))
accuracy	19.301898602828096	(/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))

Samples

121.0ms	212×	0	valid
20.0ms	22×	2	valid
13.0ms	22×	1	valid

Compiler

Compiled 231 to 37 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 134.0ms

const: 41.0ms (30.7% of total)

ival-pow2: 41.0ms (30.7% of total)

ival-div: 16.0ms (12% of total)

ival-mult: 11.0ms (8.2% of total)

ival-pow: 8.0ms (6% of total)

ival-add: 8.0ms (6% of total)

adjust: 4.0ms (3% of total)

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

exact: 1.0ms (0.7% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

series18.0ms (0.4%)

Memory

15.1MiB live, 53.5MiB allocated

Counts

15 → 180

Calls

Call 1

Inputs
#s(alt (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (patch (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1/9 binary64)) (patch (fma.f64 x x #s(literal 1/9 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/81 binary64) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 2 binary64)))) (fma.f64 (/.f64 x (-.f64 x #s(literal -1/3 binary64))) x (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))) (patch (/.f64 (fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/81 binary64) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 2 binary64)))) (fma.f64 (/.f64 x (-.f64 x #s(literal -1/3 binary64))) x (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))) #<representation binary64>) () ())
#s(alt (fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/81 binary64) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 2 binary64)))) (patch (fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/81 binary64) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (patch (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) (patch (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())

Outputs
#s(alt 1/9 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (patch (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (patch (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (patch (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (patch (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) (patch (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) (patch (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6)))))) (taylor -inf x) (#s(alt (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) (patch (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1/9 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 1/81 (/ 1 x)) 1/27) x)) 1/9) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/243 (/ 1 x)) 1/81) x)) 1/27) x)) 1/9) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ -1/9 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1/9 (* -1 (/ (- 1/27 (* 1/81 (/ 1 x))) x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1/9 (* -1 (/ (+ 1/27 (* -1 (/ (- 1/81 (* 1/243 (/ 1 x))) x))) x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

inf

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

3.0ms

-inf

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

2.0ms

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

simplify211.0ms (4.7%)

Memory

-2.9MiB live, 119.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 898×	`lower-fma.f64`
7 898×	`lower-fma.f32`
4 416×	`lower-*.f64`
4 416×	`lower-*.f32`
1 928×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	249	1209
1	718	1171
2	1794	1118
3	5312	1118
0	8276	1055

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 172

Calls

Call 1

Inputs
1/9
(+ 1/9 (* -1 (pow x 2)))
(+ 1/9 (* -1 (pow x 2)))
(+ 1/9 (* -1 (pow x 2)))
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
9
(+ 9 (* -81 (pow x 2)))
(+ 9 (* (pow x 2) (- (* 729 (pow x 2)) 81)))
(+ 9 (* (pow x 2) (- (* (pow x 2) (+ 729 (* -6561 (pow x 2)))) 81)))
1/9
(+ 1/9 (pow x 2))
(+ 1/9 (pow x 2))
(+ 1/9 (pow x 2))
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/9
(- (* 2/3 x) 1/9)
(- (* x (+ 2/3 (* -3 x))) 1/9)
(- (* x (+ 2/3 (* x (- (* 12 x) 3)))) 1/9)
9
(+ 9 (* -54 x))
(+ 9 (* x (- (* 243 x) 54)))
(+ 9 (* x (- (* x (+ 243 (* -972 x))) 54)))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
3
(+ 3 (* -9 x))
(+ 3 (* x (- (* 27 x) 9)))
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))
(* 9 (pow x 4))
(* (pow x 4) (+ 9 (* -81 (pow x 2))))
(* (pow x 4) (+ 9 (* (pow x 2) (- (* 729 (pow x 2)) 81))))
(* (pow x 4) (+ 9 (* (pow x 2) (- (* (pow x 2) (+ 729 (* -6561 (pow x 2)))) 81))))
1/3
(+ 1/3 (* -1 x))
(+ 1/3 (* x (- (* 3 x) 1)))
(+ 1/3 (* x (- (* x (+ 3 (* -9 x))) 1)))
-1/3
(- x 1/3)
(- (* x (+ 1 (* -3 x))) 1/3)
(- (* x (+ 1 (* x (- (* 9 x) 3)))) 1/3)
-1/3
(- (* -1 x) 1/3)
(- (* -1 x) 1/3)
(- (* -1 x) 1/3)
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(/ 1 (pow x 2))
(/ (- 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 2/3 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1/3 (pow x 2))) (* 2/3 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1/3 (pow x 2))) (+ (* 2/3 (/ 1 x)) (* 4/27 (/ 1 (pow x 3))))))
(/ 1 (pow x 2))
(/ (- 1 (* 2/3 (/ 1 x))) (pow x 2))
(/ (- (+ 1 (/ 1/3 (pow x 2))) (* 2/3 (/ 1 x))) (pow x 2))
(/ (- (+ 1 (/ 1/3 (pow x 2))) (+ (* 2/3 (/ 1 x)) (* 4/27 (/ 1 (pow x 3))))) (pow x 2))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x)
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))))
(/ 1/9 x)
(/ (- 1/9 (* 1/27 (/ 1 x))) x)
(/ (- (+ 1/9 (/ 1/81 (pow x 2))) (* 1/27 (/ 1 x))) x)
(/ (- (+ 1/9 (/ 1/81 (pow x 2))) (+ (* 1/27 (/ 1 x)) (* 1/243 (/ 1 (pow x 3))))) x)
(/ -1/9 x)
(/ (- (* 1/27 (/ 1 x)) 1/9) x)
(/ (- (* 1/27 (/ 1 x)) (+ 1/9 (/ 1/81 (pow x 2)))) x)
(/ (- (+ (* 1/27 (/ 1 x)) (* 1/243 (/ 1 (pow x 3)))) (+ 1/9 (/ 1/81 (pow x 2)))) x)
(* -1 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(/ 1 (pow x 2))
(/ (- 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(pow x 2)
(* (pow x 2) (- 1 (* 2/3 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 2/3 (* 1/3 (/ 1 x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ 2/3 (* -1 (/ (- 1/3 (* 4/27 (/ 1 x))) x))) x))))
(/ 1 (pow x 2))
(/ (- 1 (* 2/3 (/ 1 x))) (pow x 2))
(/ (+ 1 (* -1 (/ (- 2/3 (* 1/3 (/ 1 x))) x))) (pow x 2))
(/ (+ 1 (* -1 (/ (+ 2/3 (* -1 (/ (- 1/3 (* 4/27 (/ 1 x))) x))) x))) (pow x 2))
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)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x))
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))))
(/ 1/9 x)
(* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x))
(* -1 (/ (- (* -1 (/ (- (* 1/81 (/ 1 x)) 1/27) x)) 1/9) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/243 (/ 1 x)) 1/81) x)) 1/27) x)) 1/9) x))
(/ -1/9 x)
(* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) x))
(* -1 (/ (+ 1/9 (* -1 (/ (- 1/27 (* 1/81 (/ 1 x))) x))) x))
(* -1 (/ (+ 1/9 (* -1 (/ (+ 1/27 (* -1 (/ (- 1/81 (* 1/243 (/ 1 x))) x))) x))) x))
(* -1 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))

Outputs
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(+ 1/9 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(+ 1/9 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
9
#s(literal 9 binary64)
(+ 9 (* -81 (pow x 2)))
(fma.f64 #s(literal -81 binary64) (*.f64 x x) #s(literal 9 binary64))
(+ 9 (* (pow x 2) (- (* 729 (pow x 2)) 81)))
(fma.f64 (fma.f64 #s(literal 729 binary64) (.f64 x x) #s(literal -81 binary64)) (.f64 x x) #s(literal 9 binary64))
(+ 9 (* (pow x 2) (- (* (pow x 2) (+ 729 (* -6561 (pow x 2)))) 81)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -6561 binary64) (.f64 x x) #s(literal 729 binary64)) (.f64 x x) #s(literal -81 binary64)) (*.f64 x x) #s(literal 9 binary64))
1/9
#s(literal 1/9 binary64)
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
-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))
-1/9
#s(literal -1/9 binary64)
(- (* 2/3 x) 1/9)
(fma.f64 #s(literal 2/3 binary64) x #s(literal -1/9 binary64))
(- (* x (+ 2/3 (* -3 x))) 1/9)
(fma.f64 (fma.f64 #s(literal -3 binary64) x #s(literal 2/3 binary64)) x #s(literal -1/9 binary64))
(- (* x (+ 2/3 (* x (- (* 12 x) 3)))) 1/9)
(fma.f64 (fma.f64 (fma.f64 #s(literal 12 binary64) x #s(literal -3 binary64)) x #s(literal 2/3 binary64)) x #s(literal -1/9 binary64))
9
#s(literal 9 binary64)
(+ 9 (* -54 x))
(fma.f64 #s(literal -54 binary64) x #s(literal 9 binary64))
(+ 9 (* x (- (* 243 x) 54)))
(fma.f64 (fma.f64 #s(literal 243 binary64) x #s(literal -54 binary64)) x #s(literal 9 binary64))
(+ 9 (* x (- (* x (+ 243 (* -972 x))) 54)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -972 binary64) x #s(literal 243 binary64)) x #s(literal -54 binary64)) x #s(literal 9 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(-.f64 x #s(literal -1/3 binary64))
(+ 1/3 x)
(-.f64 x #s(literal -1/3 binary64))
(+ 1/3 x)
(-.f64 x #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
3
#s(literal 3 binary64)
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(+ 3 (* x (- (* 27 x) 9)))
(fma.f64 (fma.f64 #s(literal 27 binary64) x #s(literal -9 binary64)) x #s(literal 3 binary64))
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -81 binary64) x #s(literal 27 binary64)) x #s(literal -9 binary64)) x #s(literal 3 binary64))
(* 9 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64))
(* (pow x 4) (+ 9 (* -81 (pow x 2))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -81 binary64) (.f64 x x) #s(literal 9 binary64)))
(* (pow x 4) (+ 9 (* (pow x 2) (- (* 729 (pow x 2)) 81))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 729 binary64) (.f64 x x) #s(literal -81 binary64)) (*.f64 x x) #s(literal 9 binary64)))
(* (pow x 4) (+ 9 (* (pow x 2) (- (* (pow x 2) (+ 729 (* -6561 (pow x 2)))) 81))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -6561 binary64) (.f64 x x) #s(literal 729 binary64)) (.f64 x x) #s(literal -81 binary64)) (.f64 x x) #s(literal 9 binary64)))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* -1 x))
(-.f64 #s(literal 1/3 binary64) x)
(+ 1/3 (* x (- (* 3 x) 1)))
(fma.f64 (fma.f64 #s(literal 3 binary64) x #s(literal -1 binary64)) x #s(literal 1/3 binary64))
(+ 1/3 (* x (- (* x (+ 3 (* -9 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) x #s(literal -1 binary64)) x #s(literal 1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- (* x (+ 1 (* -3 x))) 1/3)
(fma.f64 (fma.f64 #s(literal -3 binary64) x #s(literal 1 binary64)) x #s(literal -1/3 binary64))
(- (* x (+ 1 (* x (- (* 9 x) 3)))) 1/3)
(fma.f64 (fma.f64 (fma.f64 #s(literal 9 binary64) x #s(literal -3 binary64)) x #s(literal 1 binary64)) x #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- (* -1 x) 1/3)
(-.f64 #s(literal -1/3 binary64) x)
(- (* -1 x) 1/3)
(-.f64 #s(literal -1/3 binary64) x)
(- (* -1 x) 1/3)
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 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))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/9 binary64) (*.f64 x x))) x) x)
(/ (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1/9 binary64) (.f64 x x))) (/.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
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))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 2/3 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal -2/3 binary64) x) x x) x)
(* (pow x 2) (- (+ 1 (/ 1/3 (pow x 2))) (* 2/3 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 (-.f64 #s(literal -2/3 binary64) (/.f64 #s(literal -1/3 binary64) x)) x) x x) x)
(* (pow x 2) (- (+ 1 (/ 1/3 (pow x 2))) (+ (* 2/3 (/ 1 x)) (* 4/27 (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (-.f64 (/.f64 (/.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 4/27 binary64) x)) x) x) (/.f64 #s(literal 2/3 binary64) x)) x x) x)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (* 2/3 (/ 1 x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2/3 binary64) x)) x) x)
(/ (- (+ 1 (/ 1/3 (pow x 2))) (* 2/3 (/ 1 x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)) (*.f64 x x))
(/ (- (+ 1 (/ 1/3 (pow x 2))) (+ (* 2/3 (/ 1 x)) (* 4/27 (/ 1 (pow x 3))))) (pow x 2))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 4/27 binary64) x)) x) x)) (/.f64 #s(literal 2/3 binary64) x)) (*.f64 x x))
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
(* 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))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/9 binary64) x) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x)
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -1/3 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x)) x) #s(literal -1 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 x x) #s(literal -1/9 binary64))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))))
(fma.f64 (.f64 (+.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) x) x (fma.f64 (/.f64 #s(literal -1/729 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 x x) #s(literal -1/9 binary64)))
(/ 1/9 x)
(/.f64 #s(literal 1/9 binary64) x)
(/ (- 1/9 (* 1/27 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 1/9 binary64) (/.f64 #s(literal 1/27 binary64) x)) x)
(/ (- (+ 1/9 (/ 1/81 (pow x 2))) (* 1/27 (/ 1 x))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal 1/27 binary64)) x) #s(literal -1/9 binary64)) x)
(/ (- (+ 1/9 (/ 1/81 (pow x 2))) (+ (* 1/27 (/ 1 x)) (* 1/243 (/ 1 (pow x 3))))) x)
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -1/27 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/243 binary64) x) #s(literal 1/81 binary64)) x)) x) #s(literal -1/9 binary64)) x)
(/ -1/9 x)
(/.f64 #s(literal -1/9 binary64) x)
(/ (- (* 1/27 (/ 1 x)) 1/9) x)
(/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x)
(/ (- (* 1/27 (/ 1 x)) (+ 1/9 (/ 1/81 (pow x 2)))) x)
(/.f64 (-.f64 #s(literal -1/9 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal 1/27 binary64)) x)) x)
(/ (- (+ (* 1/27 (/ 1 x)) (* 1/243 (/ 1 (pow x 3)))) (+ 1/9 (/ 1/81 (pow x 2)))) x)
(/.f64 (-.f64 #s(literal -1/9 binary64) (/.f64 (-.f64 #s(literal -1/27 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/243 binary64) x) #s(literal 1/81 binary64)) x)) x)) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(fma.f64 (neg.f64 x) x #s(literal 1/9 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 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/9 binary64) (*.f64 x x))) x) x)
(/ (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1/9 binary64) (.f64 x x))) (/.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
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))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 2/3 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal -2/3 binary64) x) x x) x)
(* (pow x 2) (+ 1 (* -1 (/ (- 2/3 (* 1/3 (/ 1 x))) x))))
(*.f64 (fma.f64 (/.f64 (-.f64 #s(literal -2/3 binary64) (/.f64 #s(literal -1/3 binary64) x)) x) x x) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ 2/3 (* -1 (/ (- 1/3 (* 4/27 (/ 1 x))) x))) x))))
(*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 4/27 binary64) x)) x) #s(literal 2/3 binary64)) x) x x) x)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (* 2/3 (/ 1 x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2/3 binary64) x)) x) x)
(/ (+ 1 (* -1 (/ (- 2/3 (* 1/3 (/ 1 x))) x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)) (*.f64 x x))
(/ (+ 1 (* -1 (/ (+ 2/3 (* -1 (/ (- 1/3 (* 4/27 (/ 1 x))) x))) x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2/3 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 4/27 binary64) x)) x)) x)) x) x)
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))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/9 binary64) x) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -1/3 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x)) x) #s(literal -1 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 x x) #s(literal -1/9 binary64))
(* (pow x 2) (- (+ 1 (/ 1/81 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6))))))
(fma.f64 (.f64 (+.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) x) x (fma.f64 (/.f64 #s(literal -1/729 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 x x) #s(literal -1/9 binary64)))
(/ 1/9 x)
(/.f64 #s(literal 1/9 binary64) x)
(* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x))
(/.f64 (-.f64 #s(literal 1/9 binary64) (/.f64 #s(literal 1/27 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 1/81 (/ 1 x)) 1/27) x)) 1/9) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal 1/27 binary64)) x) #s(literal -1/9 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/243 (/ 1 x)) 1/81) x)) 1/27) x)) 1/9) x))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -1/27 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/243 binary64) x) #s(literal 1/81 binary64)) x)) x) #s(literal -1/9 binary64)) x)
(/ -1/9 x)
(/.f64 #s(literal -1/9 binary64) x)
(* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x)
(* -1 (/ (+ 1/9 (* -1 (/ (- 1/27 (* 1/81 (/ 1 x))) x))) x))
(/.f64 (-.f64 #s(literal -1/9 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal 1/27 binary64)) x)) x)
(* -1 (/ (+ 1/9 (* -1 (/ (+ 1/27 (* -1 (/ (- 1/81 (* 1/243 (/ 1 x))) x))) x))) x))
(/.f64 (-.f64 #s(literal -1/9 binary64) (/.f64 (-.f64 #s(literal -1/27 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/243 binary64) x) #s(literal 1/81 binary64)) x)) x)) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)

rewrite256.0ms (5.7%)

Memory

-0.6MiB live, 279.1MiB allocated

Rules

5 574×	`lower-fma.f32`
5 564×	`lower-fma.f64`
5 012×	`lower-/.f32`
4 994×	`lower-/.f64`
3 894×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	144
0	56	155
1	241	129
2	2064	91
0	8541	91

Stop Event

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

Counts

15 → 900

Calls

Call 1

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

Outputs
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eval265.0ms (5.9%)

Memory: 39.9MiB live, 418.5MiB allocated
Compiler: Compiled 45 615 to 3 896 computations (91.5% saved)

prune39.0ms (0.9%)

Memory

-15.8MiB live, 102.0MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	1 478	2	1 480
Fresh	0	0	0
Picked	2	1	3
Done	0	5	5
Total	1 480	8	1 488

Accuracy

100.0%

Counts

1 488 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	78.0%	(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
✓	99.9%	(fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
	64.9%	(/.f64 (fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (*.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))) (fma.f64 (/.f64 x (-.f64 x #s(literal -1/3 binary64))) x (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))))
✓	78.0%	(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64)))
	76.5%	(/.f64 (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (.f64 (.f64 x x) (/.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)))))) (-.f64 #s(literal -1/3 binary64) x))
✓	78.1%	(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal -1/3 binary64) x))
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
✓	54.0%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 316 to 125 computations (60.4% saved)

regimes9.0ms (0.2%)

Memory

17.9MiB live, 17.9MiB allocated

Counts

14 → 1

Calls

Call 1

Inputs
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
(-.f64 x #s(literal 1/3 binary64))
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64)))
(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal -1/3 binary64) x))
(fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.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))) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(/.f64 (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (.f64 (.f64 x x) (/.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)))))) (-.f64 #s(literal -1/3 binary64) x))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(/.f64 (fma.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x))
(/.f64 (fma.f64 #s(literal 1/81 binary64) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))) (-.f64 #s(literal -1/3 binary64) x))
(/.f64 (fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (*.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)) (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))) (fma.f64 (/.f64 x (-.f64 x #s(literal -1/3 binary64))) x (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))))
(/.f64 (fma.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/81 binary64) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 2 binary64)))) (fma.f64 (/.f64 x (-.f64 x #s(literal -1/3 binary64))) x (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x))))

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

Calls

2 calls:

4.0ms	x
4.0ms	(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Results

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

Compiler

Compiled 6 to 6 computations (0% saved)

regimes8.0ms (0.2%)

Memory

-30.7MiB live, 6.8MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
1.0ms	x

Results

Accuracy	Segments	Branch
54.0%	1	`x`
54.0%	1	`(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`

Compiler

Compiled 6 to 6 computations (0% saved)

simplify31.0ms (0.7%)

Memory

-12.8MiB live, 46.8MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative-binary64-+.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`1-exp-binary32-exp.f32`
2×	`-commutative-binary64-.f64`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	8
1	14	8
2	18	8
3	20	8
4	21	8

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness139.0ms (3.1%)

Memory

-2.0MiB live, 111.1MiB 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	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
0	5	4
0	8	4
1	27	4
2	129	4
3	979	4
0	8557	4

Stop Event

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

Compiler

Compiled 14 to 14 computations (0% saved)

preprocess41.0ms (0.9%)

Memory: 27.3MiB live, 71.4MiB allocated
Compiler: Compiled 20 to 20 computations (0% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	80
0	32	75
1	51	75
2	65	75
3	86	75
4	129	75
5	215	75
6	455	75
7	681	75
8	739	75
9	918	75
10	924	75
11	926	75
0	926	75

Iter	Nodes	Cost
0	21	80
0	32	75
1	51	75
2	65	75
3	86	75
4	129	75
5	215	75
6	455	75
7	681	75
8	739	75
9	918	75
10	924	75
11	926	75
0	926	75

start0.0ms (0%)

analyze0.0ms (0%)

sample497.0ms (11%)

explain50.0ms (1.1%)

preprocess15.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize95.0ms (2.1%)

series1.0ms (0%)

simplify15.0ms (0.3%)

rewrite385.0ms (8.5%)

eval182.0ms (4%)

prune8.0ms (0.2%)

simplify29.0ms (0.6%)

localize126.0ms (2.8%)

series10.0ms (0.2%)

simplify121.0ms (2.7%)

rewrite262.0ms (5.8%)

eval285.0ms (6.3%)

prune38.0ms (0.8%)

simplify242.0ms (5.4%)

localize81.0ms (1.8%)

series13.0ms (0.3%)

simplify160.0ms (3.6%)

rewrite234.0ms (5.2%)

eval210.0ms (4.7%)

prune23.0ms (0.5%)

simplify223.0ms (5%)

localize181.0ms (4%)

series18.0ms (0.4%)

simplify211.0ms (4.7%)

rewrite256.0ms (5.7%)

eval265.0ms (5.9%)

prune39.0ms (0.9%)

regimes9.0ms (0.2%)

regimes8.0ms (0.2%)

simplify31.0ms (0.7%)

soundness139.0ms (3.1%)

preprocess41.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	80
0	32	75
1	51	75
2	65	75
3	86	75
4	129	75
5	215	75
6	455	75
7	681	75
8	739	75
9	918	75
10	924	75
11	926	75
0	926	75