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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB 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)

sample394.0ms (15.8%)

Memory

160.3MiB live, 160.3MiB allocated

Samples

223.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 107.0ms

ival-div: 59.0ms (54.9% of total)

ival-add: 34.0ms (31.6% of total)

exact: 7.0ms (6.5% of total)

ival-true: 5.0ms (4.7% of total)

ival-assert: 3.0ms (2.8% of total)

Bogosity

explain60.0ms (2.4%)

Memory

29.7MiB live, 29.7MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

17.0ms

512×

valid

Compiler

Compiled 64 to 44 computations (31.3% saved)

Precisions

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

ival-div: 4.0ms (55.9% of total)

ival-add: 2.0ms (28% of total)

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

exact: 0.0ms (0% of total)

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

preprocess13.0ms (0.5%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 5 to 5 computations (0% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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)

simplify2.0ms (0.1%)

Memory

0.4MiB live, 0.4MiB 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))

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize12.0ms (0.5%)

Memory

5.7MiB live, 5.7MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
accuracy	0.01171875	(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Samples

8.0ms

256×

valid

Compiler

Compiled 24 to 12 computations (50% saved)

Precisions

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

ival-div: 2.0ms (58.9% of total)

ival-add: 1.0ms (29.5% 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

0.4MiB live, 0.4MiB 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 (+ 1/3 x) (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 (+ 1/3 x) (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 (+ 1/3 x) (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 (* 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>) () ())) ())

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)))

simplify3.0ms (0.1%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 10

Calls

Call 1

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

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

rewrite128.0ms (5.1%)

Memory

49.8MiB live, 49.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

2 → 265

Calls

Call 1

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

Outputs
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eval26.0ms (1%)

Memory: 23.3MiB live, 23.3MiB allocated
Compiler: Compiled 6 229 to 631 computations (89.9% saved)

prune5.0ms (0.2%)

Memory

11.3MiB live, 11.3MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

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

Accuracy

100.0%

Counts

276 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(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))))
▶	66.7%	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64))) (-.f64 x #s(literal 1/3 binary64))) (.f64 (-.f64 x #s(literal 1/3 binary64)) (*.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64))))
▶	100.0%	(-.f64 x #s(literal -1/3 binary64))
▶	53.8%	#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64))

Compiler

Compiled 40 to 23 computations (42.5% saved)

simplify129.0ms (5.2%)

Memory

40.4MiB live, 40.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 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 (.f64 x x) (*.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64)))
cost-diff	128	(*.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64))
cost-diff	192	(-.f64 (.f64 (.f64 x x) (*.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64))) (-.f64 x #s(literal 1/3 binary64)))
cost-diff	1536	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64))) (-.f64 x #s(literal 1/3 binary64))) (.f64 (-.f64 x #s(literal 1/3 binary64)) (*.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64))))
cost-diff	0	(-.f64 x #s(literal -1/3 binary64))
cost-diff	0	#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	107
0	33	118
1	60	118
2	172	92
3	722	88
4	2666	88
5	7367	88
0	8805	82

Stop Event

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

Calls

Call 1

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

localize60.0ms (2.4%)

Memory

24.4MiB live, 24.4MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 x #s(literal 1/3 binary64))
accuracy	0.01171875	(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 #s(literal -1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))
accuracy	0.20703125	(/.f64 x (-.f64 x #s(literal 1/3 binary64)))
accuracy	0.03515625	(*.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64))
accuracy	0.07421875	(.f64 (-.f64 x #s(literal 1/3 binary64)) (.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64)))
accuracy	0.10546875	(.f64 (.f64 x x) (*.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64)))
accuracy	20.82166894347137	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64))) (-.f64 x #s(literal 1/3 binary64))) (.f64 (-.f64 x #s(literal 1/3 binary64)) (*.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 9 binary64))))
accuracy	0.01171875	(-.f64 x #s(literal -1/3 binary64))
accuracy	29.584231559906513	#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64))

Samples

31.0ms	213×	0	valid
9.0ms	21×	2	valid
7.0ms	22×	1	valid

Compiler

Compiled 214 to 40 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

const: 10.0ms (29.1% of total)

ival-div: 8.0ms (23.3% of total)

ival-mult: 8.0ms (23.3% of total)

ival-sub: 4.0ms (11.6% of total)

adjust: 2.0ms (5.8% of total)

ival-add: 2.0ms (5.8% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.4%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

11 → 132

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((+ x (/ 1 3)) (- x -1/3) (/ (- (* (* x x) (* (- x 1/3) 9)) (- x 1/3)) (* (- x 1/3) (* (- x 1/3) 9))) (- (* (* x x) (* (- x 1/3) 9)) (- x 1/3)) (* (- x 1/3) 9) (* (* x x) (* (- x 1/3) 9)) (+ (* x (/ x (- x 1/3))) (/ -1/9 (- x 1/3))) (/ x (- x 1/3)) (- x 1/3) (/ -1/9 (- x 1/3)) (* (- x 1/3) (* (- x 1/3) 9)))
2.0ms	x	@	inf	((+ x (/ 1 3)) (- x -1/3) (/ (- (* (* x x) (* (- x 1/3) 9)) (- x 1/3)) (* (- x 1/3) (* (- x 1/3) 9))) (- (* (* x x) (* (- x 1/3) 9)) (- x 1/3)) (* (- x 1/3) 9) (* (* x x) (* (- x 1/3) 9)) (+ (* x (/ x (- x 1/3))) (/ -1/9 (- x 1/3))) (/ x (- x 1/3)) (- x 1/3) (/ -1/9 (- x 1/3)) (* (- x 1/3) (* (- x 1/3) 9)))
2.0ms	x	@	0	((+ x (/ 1 3)) (- x -1/3) (/ (- (* (* x x) (* (- x 1/3) 9)) (- x 1/3)) (* (- x 1/3) (* (- x 1/3) 9))) (- (* (* x x) (* (- x 1/3) 9)) (- x 1/3)) (* (- x 1/3) 9) (* (* x x) (* (- x 1/3) 9)) (+ (* x (/ x (- x 1/3))) (/ -1/9 (- x 1/3))) (/ x (- x 1/3)) (- x 1/3) (/ -1/9 (- x 1/3)) (* (- x 1/3) (* (- x 1/3) 9)))

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

2.0ms

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

simplify114.0ms (4.6%)

Memory

38.4MiB live, 38.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	162	721
1	434	713
2	1121	706
3	3405	690
0	8655	631

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 122

Calls

Call 1

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

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

rewrite123.0ms (4.9%)

Memory

55.7MiB live, 55.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	92
0	33	92
1	128	88
2	1093	88
0	8525	84

Stop Event

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

Counts

11 → 643

Calls

Call 1

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

Outputs
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eval130.0ms (5.2%)

Memory: 94.1MiB live, 94.1MiB allocated
Compiler: Compiled 30 699 to 2 698 computations (91.2% saved)

prune31.0ms (1.3%)

Memory

40.0MiB live, 40.0MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1 054	2	1 056
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	1 056	4	1 060

Accuracy

100.0%

Counts

1 060 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.6%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) x) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))))
✓	100.0%	(-.f64 x #s(literal -1/3 binary64))
▶	76.7%	(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
✓	53.8%	#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64))

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify32.0ms (1.3%)

Memory

2.6MiB live, 2.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
cost-diff	0	(-.f64 #s(literal 1/3 binary64) x)
cost-diff	128	(/.f64 (-.f64 #s(literal 1/3 binary64) x) (-.f64 #s(literal 1/9 binary64) (*.f64 x x)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) x) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (-.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	448	(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	66
0	18	66
1	32	62
2	51	62
3	116	62
4	254	62
5	448	62
6	884	62
7	1200	62
8	1459	62
9	1475	62
10	1502	62
0	1502	59

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize40.0ms (1.6%)

Memory

14.0MiB live, 14.0MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 #s(literal 1/3 binary64) x)
accuracy	0.0078125	(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
accuracy	0.0859375	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) x) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))))
accuracy	14.936484256986494	(/.f64 (-.f64 #s(literal 1/3 binary64) x) (-.f64 #s(literal 1/9 binary64) (*.f64 x x)))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))
accuracy	0.00390625	(-.f64 #s(literal 1/3 binary64) x)
accuracy	0.0078125	(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
accuracy	14.924953961441545	(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)))

Samples

30.0ms

256×

valid

Compiler

Compiled 134 to 24 computations (82.1% saved)

Precisions

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

const: 7.0ms (37.4% of total)

ival-div: 5.0ms (26.7% of total)

ival-mult: 4.0ms (21.3% of total)

ival-sub: 3.0ms (16% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

2.5MiB live, 2.5MiB allocated

Counts

7 → 84

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify116.0ms (4.7%)

Memory

28.0MiB live, 28.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	110	422
1	311	390
2	702	386
3	1893	382
4	4473	382
5	6482	382
0	8098	370

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 80

Calls

Call 1

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

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

rewrite147.0ms (5.9%)

Memory

52.3MiB live, 52.3MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	47
0	18	43
1	81	27
2	552	27
3	6474	27
0	8796	27

Stop Event

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

Counts

7 → 1 217

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
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#<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>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
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#<batchref>
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eval200.0ms (8%)

Memory: 133.8MiB live, 133.8MiB allocated
Compiler: Compiled 35 439 to 3 395 computations (90.4% saved)

prune43.0ms (1.7%)

Memory

58.7MiB live, 58.7MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1 606	2	1 608
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	1 607	5	1 612

Accuracy

100.0%

Counts

1 612 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.6%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x #s(literal 1/3 binary64)) (fma.f64 x x #s(literal -1/9 binary64))))
▶	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ (- 1/3 x) (- 1/9 (* x x))) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
✓	100.0%	(-.f64 x #s(literal -1/3 binary64))
✓	76.7%	(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
✓	53.8%	#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64))

Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify48.0ms (1.9%)

Memory

2.9MiB live, 2.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x x #s(literal -1/9 binary64))
cost-diff	0	(-.f64 x #s(literal 1/3 binary64))
cost-diff	0	(/.f64 (-.f64 x #s(literal 1/3 binary64)) (fma.f64 x x #s(literal -1/9 binary64)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x #s(literal 1/3 binary64)) (fma.f64 x x #s(literal -1/9 binary64))))
cost-diff	0	(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
cost-diff	0	#s(approx (/ (- 1/3 x) (- 1/9 (* x x))) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (- 1/3 x) (- 1/9 (* x x))) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	67
0	25	67
1	47	67
2	71	65
3	114	65
4	201	63
5	352	63
6	599	63
7	1118	63
8	1570	63
9	1629	63
10	1689	63
11	1717	63
12	1725	63
13	1734	63
14	1738	63
0	1738	63

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize52.0ms (2.1%)

Memory

17.1MiB live, 17.1MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 x #s(literal 1/3 binary64))
accuracy	0.0078125	(fma.f64 x x #s(literal -1/9 binary64))
accuracy	0.0859375	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x #s(literal 1/3 binary64)) (fma.f64 x x #s(literal -1/9 binary64))))
accuracy	14.936484256986494	(/.f64 (-.f64 x #s(literal 1/3 binary64)) (fma.f64 x x #s(literal -1/9 binary64)))
accuracy	0	(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
accuracy	0.0859375	(/.f64 #s(literal 1 binary64) #s(approx (/ (- 1/3 x) (- 1/9 (* x x))) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
accuracy	29.5773787180437	#s(approx (/ (- 1/3 x) (- 1/9 (* x x))) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))

Samples

38.0ms	249×	0	valid
1.0ms	4×	1	valid
1.0ms	3×	2	valid

Compiler

Compiled 112 to 33 computations (70.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

const: 10.0ms (34.7% of total)

ival-div: 7.0ms (24.3% of total)

ival-mult: 4.0ms (13.9% of total)

ival-sub: 4.0ms (13.9% of total)

ival-add: 3.0ms (10.4% of total)

exact: 1.0ms (3.5% of total)

adjust: 0.0ms (0% of total)

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

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

series6.0ms (0.2%)

Memory

2.6MiB live, 2.6MiB allocated

Counts

7 → 84

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify121.0ms (4.8%)

Memory

23.3MiB live, 23.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	418
1	221	402
2	509	402
3	1466	394
4	3739	394
5	6152	394
6	7546	394
7	7969	394
0	8016	364

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite134.0ms (5.4%)

Memory

49.6MiB live, 49.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	59
0	25	59
1	135	41
2	1010	41
0	8837	41

Stop Event

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

Counts

7 → 876

Calls

Call 1

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

Outputs
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eval127.0ms (5.1%)

Memory: 83.8MiB live, 83.8MiB allocated
Compiler: Compiled 20 225 to 2 809 computations (86.1% saved)

prune29.0ms (1.2%)

Memory

37.1MiB live, 37.1MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	954	0	954
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	954	5	959

Accuracy

100.0%

Counts

959 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.6%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x #s(literal 1/3 binary64)) (fma.f64 x x #s(literal -1/9 binary64))))
✓	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ (- 1/3 x) (- 1/9 (* x x))) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
✓	100.0%	(-.f64 x #s(literal -1/3 binary64))
✓	76.7%	(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
✓	53.8%	#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64))

Compiler

Compiled 117 to 65 computations (44.4% saved)

regimes8.0ms (0.3%)

Memory

4.2MiB live, 4.2MiB allocated

Counts

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

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

Calls

2 calls:

4.0ms	x
3.0ms	(+.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)

regimes4.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB 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:

2.0ms	x
1.0ms	(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Results

Accuracy	Segments	Branch
53.8%	1	`x`
53.8%	1	`(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`

Compiler

Compiled 6 to 6 computations (0% saved)

simplify28.0ms (1.1%)

Memory

18.4MiB live, 18.4MiB allocated

Algorithm

1×	egg-herbie

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))

soundness91.0ms (3.6%)

Memory

1.6MiB live, 1.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 14 to 14 computations (0% saved)

preprocess29.0ms (1.1%)

Memory: 22.7MiB live, 22.7MiB allocated
Compiler: Compiled 20 to 20 computations (0% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample394.0ms (15.8%)

explain60.0ms (2.4%)

preprocess13.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify2.0ms (0.1%)

localize12.0ms (0.5%)

series1.0ms (0%)

simplify3.0ms (0.1%)

rewrite128.0ms (5.1%)

eval26.0ms (1%)

prune5.0ms (0.2%)

simplify129.0ms (5.2%)

localize60.0ms (2.4%)

series10.0ms (0.4%)

simplify114.0ms (4.6%)

rewrite123.0ms (4.9%)

eval130.0ms (5.2%)

prune31.0ms (1.3%)

simplify32.0ms (1.3%)

localize40.0ms (1.6%)

series6.0ms (0.2%)

simplify116.0ms (4.7%)

rewrite147.0ms (5.9%)

eval200.0ms (8%)

prune43.0ms (1.7%)

simplify48.0ms (1.9%)

localize52.0ms (2.1%)

series6.0ms (0.2%)

simplify121.0ms (4.8%)

rewrite134.0ms (5.4%)

eval127.0ms (5.1%)

prune29.0ms (1.2%)

regimes8.0ms (0.3%)

regimes4.0ms (0.1%)

simplify28.0ms (1.1%)

soundness91.0ms (3.6%)

preprocess29.0ms (1.1%)

end0.0ms (0%)

Profiling