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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

1.0MiB live, 1.0MiB 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)

sample504.0ms (19.6%)

Memory

9.8MiB live, 922.4MiB allocated

Samples

293.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 143.0ms

ival-div: 79.0ms (55.1% of total)

ival-sub: 48.0ms (33.5% of total)

exact: 7.0ms (4.9% of total)

ival-true: 6.0ms (4.2% of total)

ival-assert: 3.0ms (2.1% of total)

Bogosity

explain52.0ms (2%)

Memory

27.4MiB live, 104.4MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

21.0ms

512×

valid

Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions

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

ival-div: 4.0ms (51.3% of total)

ival-sub: 2.0ms (25.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess16.0ms (0.6%)

Memory

-15.3MiB live, 27.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 5 to 5 computations (0% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 5 computations (0% saved)

simplify3.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize16.0ms (0.6%)

Memory

-11.3MiB live, 26.9MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
accuracy	0.0078125	(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Samples

12.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

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

ival-div: 2.0ms (53.9% of total)

ival-sub: 1.0ms (26.9% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Counts

2 → 12

Calls

Call 1

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

Inputs

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

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

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

Calls

3 calls:

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

simplify16.0ms (0.6%)

Memory

-16.4MiB live, 21.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 10

Calls

Call 1

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

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

rewrite148.0ms (5.8%)

Memory

18.4MiB live, 295.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

2 → 313

Calls

Call 1

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

Outputs
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eval57.0ms (2.2%)

Memory: -17.5MiB live, 145.5MiB allocated
Compiler: Compiled 8 097 to 759 computations (90.6% saved)

prune6.0ms (0.2%)

Memory

21.7MiB live, 21.7MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	319	4	323
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	320	4	324

Accuracy

100.0%

Counts

324 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.9%	(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
▶	65.5%	(/.f64 #s(literal 1 binary64) (/.f64 (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)))))
▶	100.0%	(-.f64 x #s(literal 1/3 binary64))
▶	47.0%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 40 to 25 computations (37.5% saved)

simplify142.0ms (5.5%)

Memory

13.4MiB live, 167.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x #s(literal -1/3 binary64))
cost-diff	0	(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
cost-diff	0	(/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64)))
cost-diff	0	(fma.f64 x x #s(literal 1/9 binary64))
cost-diff	1088	(/.f64 (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))))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 (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)))))
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: 2 (0.0ms)

Iter	Nodes	Cost
0	21	110
0	34	98
1	54	90
2	91	89
3	245	89
4	1021	89
5	5099	89
6	6521	89
7	6754	89
8	7548	89
0	8019	89

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

localize73.0ms (2.8%)

Memory

6.2MiB live, 126.3MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(-.f64 x #s(literal -1/3 binary64))
accuracy	0.4341110292326519	(/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	14.974689669838432	(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
accuracy	15.090206584652446	(/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	0.01171875	(fma.f64 x x #s(literal 1/9 binary64))
accuracy	0.04296875	(*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64)))
accuracy	0.1171875	(/.f64 #s(literal 1 binary64) (/.f64 (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)))))
accuracy	21.773189293171978	(/.f64 (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))))
accuracy	0.0078125	(-.f64 x #s(literal 1/3 binary64))
accuracy	33.944802592443445	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Samples

47.0ms	244×	0	valid
8.0ms	7×	1	valid
3.0ms	5×	2	valid

Compiler

Compiled 124 to 24 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

const: 13.0ms (28.6% of total)

ival-mult: 11.0ms (24.2% of total)

ival-div: 9.0ms (19.8% of total)

ival-sub: 8.0ms (17.6% of total)

ival-add: 4.0ms (8.8% of total)

adjust: 1.0ms (2.2% of total)

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

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

exact: 0.0ms (0% of total)

series16.0ms (0.6%)

Memory

-15.6MiB live, 22.6MiB allocated

Counts

12 → 144

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 #s(literal 1 binary64) (/.f64 (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))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (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))))) #<representation binary64>) () ())
#s(alt (/.f64 (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)))) (patch (/.f64 (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)))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1/9 binary64)) (patch (fma.f64 x x #s(literal 1/9 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #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 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 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 (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 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 binary64) (/.f64 (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))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (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))))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (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))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (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))))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (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))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (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))))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (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))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (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))))) #<representation binary64>) () ())) ())
#s(alt -3 (taylor 0 x) (#s(alt (/.f64 (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)))) (patch (/.f64 (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* -9 x) 3) (taylor 0 x) (#s(alt (/.f64 (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)))) (patch (/.f64 (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (- (* -27 x) 9)) 3) (taylor 0 x) (#s(alt (/.f64 (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)))) (patch (/.f64 (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (- (* x (- (* -81 x) 27)) 9)) 3) (taylor 0 x) (#s(alt (/.f64 (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)))) (patch (/.f64 (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)))) #<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 (+ 1/9 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1/9 binary64)) (patch (fma.f64 x x #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1/9 binary64)) (patch (fma.f64 x x #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1/9 binary64)) (patch (fma.f64 x x #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/27 (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/9 x) 1/27) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1/9 (* -1/3 x))) 1/27) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1/9 (* x (- x 1/3)))) 1/27) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (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 (* 9 x) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 9 (* -27 x))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 9 (* x (- (* 243 (pow x 2)) 27)))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 9 (* x (- (* (pow x 2) (+ 243 (* -729 x))) 27)))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/9 (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* 1/3 x)) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
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#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 (pow x 3) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.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 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 (pow x 2))) 1/3) x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 (pow x 2))) (+ 1/3 (/ 1/81 (pow x 3)))) x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ -1/27 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 1/81 (/ 1 x)) 1/27) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) 1/81) x)) 1/27) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) (+ 1/81 (/ 1/2187 (pow x 3)))) x)) 1/27) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	((- x (/ 1 3)) (- x 1/3) (/ 1 (/ (+ (* x x) 1/9) (* (+ (* x x) 1/9) (- x 1/3)))) (/ (+ (* x x) 1/9) (* (+ (* x x) 1/9) (- x 1/3))) (+ (* x x) 1/9) (* (+ (* x x) 1/9) (- x 1/3)) (* x x) (/ x (+ (* x (- x -1/3)) 1/9)) (+ (* x (- x -1/3)) 1/9) (- x -1/3) (+ (* (* x x) (/ x (+ (* x (- x -1/3)) 1/9))) (/ -1/27 (+ (* x (- x -1/3)) 1/9))) (/ -1/27 (+ (* x (- x -1/3)) 1/9)))
3.0ms	x	@	inf	((- x (/ 1 3)) (- x 1/3) (/ 1 (/ (+ (* x x) 1/9) (* (+ (* x x) 1/9) (- x 1/3)))) (/ (+ (* x x) 1/9) (* (+ (* x x) 1/9) (- x 1/3))) (+ (* x x) 1/9) (* (+ (* x x) 1/9) (- x 1/3)) (* x x) (/ x (+ (* x (- x -1/3)) 1/9)) (+ (* x (- x -1/3)) 1/9) (- x -1/3) (+ (* (* x x) (/ x (+ (* x (- x -1/3)) 1/9))) (/ -1/27 (+ (* x (- x -1/3)) 1/9))) (/ -1/27 (+ (* x (- x -1/3)) 1/9)))
3.0ms	x	@	-inf	((- x (/ 1 3)) (- x 1/3) (/ 1 (/ (+ (* x x) 1/9) (* (+ (* x x) 1/9) (- x 1/3)))) (/ (+ (* x x) 1/9) (* (+ (* x x) 1/9) (- x 1/3))) (+ (* x x) 1/9) (* (+ (* x x) 1/9) (- x 1/3)) (* x x) (/ x (+ (* x (- x -1/3)) 1/9)) (+ (* x (- x -1/3)) 1/9) (- x -1/3) (+ (* (* x x) (/ x (+ (* x (- x -1/3)) 1/9))) (/ -1/27 (+ (* x (- x -1/3)) 1/9))) (/ -1/27 (+ (* x (- x -1/3)) 1/9)))

Time

Variable

Point

Expression

6.0ms

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

3.0ms

inf

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

3.0ms

-inf

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

simplify176.0ms (6.9%)

Memory

-2.6MiB live, 149.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	800
1	558	790
2	1415	765
3	4423	754
0	8277	712

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 134

Calls

Call 1

Inputs
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-3
(- (* -9 x) 3)
(- (* x (- (* -27 x) 9)) 3)
(- (* x (- (* x (- (* -81 x) 27)) 9)) 3)
1/9
(+ 1/9 (pow x 2))
(+ 1/9 (pow x 2))
(+ 1/9 (pow x 2))
-1/27
(- (* 1/9 x) 1/27)
(- (* x (+ 1/9 (* -1/3 x))) 1/27)
(- (* x (+ 1/9 (* x (- x 1/3)))) 1/27)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 9 x)
(* x (+ 9 (* -27 x)))
(* x (+ 9 (* x (- (* 243 (pow x 2)) 27))))
(* x (+ 9 (* x (- (* (pow x 2) (+ 243 (* -729 x))) 27))))
1/9
(+ 1/9 (* 1/3 x))
(+ 1/9 (* x (+ 1/3 x)))
(+ 1/9 (* x (+ 1/3 x)))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/3
(- x 1/3)
(- (* x (+ 1 (* -9 (pow x 2)))) 1/3)
(- (* x (+ 1 (* (pow x 2) (- (* 27 x) 9)))) 1/3)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(/ 1 x)
(/ (+ 1 (* 1/3 (/ 1 x))) x)
(/ (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))) x)
(/ (+ 1 (+ (/ 1/9 (pow x 2)) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3)))))) x)
(pow x 2)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(pow x 3)
(* (pow x 3) (- 1 (* 1/3 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/27 (pow x 3))) (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/27 (pow x 3))) (+ (* 1/3 (/ 1 x)) (* 1/81 (/ 1 (pow x 4))))) x)
(pow x 2)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(/ -1/27 (pow x 2))
(/ (- (* 1/81 (/ 1 x)) 1/27) (pow x 2))
(/ (- (* 1/81 (/ 1 x)) (+ 1/27 (/ 1/729 (pow x 3)))) (pow x 2))
(/ (- (+ (* 1/81 (/ 1 x)) (* 1/2187 (/ 1 (pow x 4)))) (+ 1/27 (/ 1/729 (pow x 3)))) (pow x 2))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(/ 1 x)
(/ (+ 1 (* 1/3 (/ 1 x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/3 (* 1/9 (/ 1 x))) x)) 1) x))
(* -1 (/ (- (* -1 (/ (+ 1/3 (+ (/ 1/27 (pow x 2)) (* 1/9 (/ 1 x)))) x)) 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)))))
(pow x 3)
(* -1 (* (pow x 3) (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 (pow x 2))) 1/3) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 (pow x 2))) (+ 1/3 (/ 1/81 (pow x 3)))) x)) 1) x))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(/ -1/27 (pow x 2))
(/ (- (* 1/81 (/ 1 x)) 1/27) (pow x 2))
(/ (- (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) 1/81) x)) 1/27) (pow x 2))
(/ (- (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) (+ 1/81 (/ 1/2187 (pow x 3)))) x)) 1/27) (pow x 2))

Outputs
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-3
#s(literal -3 binary64)
(- (* -9 x) 3)
(fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))
(- (* x (- (* -27 x) 9)) 3)
(fma.f64 (fma.f64 #s(literal -27 binary64) x #s(literal -9 binary64)) x #s(literal -3 binary64))
(- (* x (- (* x (- (* -81 x) 27)) 9)) 3)
(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))
1/9
#s(literal 1/9 binary64)
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
(+ 1/9 (pow x 2))
(fma.f64 x x #s(literal 1/9 binary64))
-1/27
#s(literal -1/27 binary64)
(- (* 1/9 x) 1/27)
(fma.f64 #s(literal 1/9 binary64) x #s(literal -1/27 binary64))
(- (* x (+ 1/9 (* -1/3 x))) 1/27)
(fma.f64 (fma.f64 x #s(literal -1/3 binary64) #s(literal 1/9 binary64)) x #s(literal -1/27 binary64))
(- (* x (+ 1/9 (* x (- x 1/3)))) 1/27)
(fma.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) x #s(literal -1/27 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 9 x)
(*.f64 #s(literal 9 binary64) x)
(* x (+ 9 (* -27 x)))
(*.f64 (fma.f64 #s(literal -27 binary64) x #s(literal 9 binary64)) x)
(* x (+ 9 (* x (- (* 243 (pow x 2)) 27))))
(.f64 (fma.f64 (fma.f64 #s(literal 243 binary64) (.f64 x x) #s(literal -27 binary64)) x #s(literal 9 binary64)) x)
(* x (+ 9 (* x (- (* (pow x 2) (+ 243 (* -729 x))) 27))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -729 binary64) x #s(literal 243 binary64)) (.f64 x x) #s(literal -27 binary64)) x #s(literal 9 binary64)) x)
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* 1/3 x))
(fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))
(+ 1/9 (* x (+ 1/3 x)))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
(+ 1/9 (* x (+ 1/3 x)))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- (* x (+ 1 (* -9 (pow x 2)))) 1/3)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -9 binary64) (-.f64 x #s(literal 1/3 binary64)))
(- (* x (+ 1 (* (pow x 2) (- (* 27 x) 9)))) 1/3)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 27 binary64) x #s(literal -9 binary64)) (-.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))
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 (/.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64)) 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 (fma.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 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 3)
(pow.f64 x #s(literal 3 binary64))
(* (pow x 3) (- 1 (* 1/3 (/ 1 x))))
(.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x)
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))
(*.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) x)
(* (pow x 3) (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))))
(fma.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) x (*.f64 (/.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)
(/ (- (+ 1 (/ 1/27 (pow x 3))) (* 1/3 (/ 1 x))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/27 binary64) x) x) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) x)
(/ (- (+ 1 (/ 1/27 (pow x 3))) (+ (* 1/3 (/ 1 x)) (* 1/81 (/ 1 (pow x 4))))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/27 binary64) x) x) #s(literal 1/3 binary64)) x) (-.f64 (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(*.f64 (+.f64 #s(literal 1/3 binary64) x) x)
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(/ -1/27 (pow x 2))
(/.f64 #s(literal -1/27 binary64) (*.f64 x x))
(/ (- (* 1/81 (/ 1 x)) 1/27) (pow x 2))
(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal 1/27 binary64)) x) x)
(/ (- (* 1/81 (/ 1 x)) (+ 1/27 (/ 1/729 (pow x 3)))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal 1/27 binary64)) (/.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 x x))
(/ (- (+ (* 1/81 (/ 1 x)) (* 1/2187 (/ 1 (pow x 4)))) (+ 1/27 (/ 1/729 (pow x 3)))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/2187 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/27 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/729 binary64) (.f64 x x)) #s(literal 1/81 binary64)) x)) (.f64 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))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/3 (/ 1 x))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/3 (* 1/9 (/ 1 x))) 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 (/ (+ 1/3 (+ (/ 1/27 (pow x 2)) (* 1/9 (/ 1 x)))) x)) 1) x))
(/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (* 1/9 (/ 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 3)
(pow.f64 x #s(literal 3 binary64))
(* -1 (* (pow x 3) (- (* 1/3 (/ 1 x)) 1)))
(.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1)))
(*.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) x)
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1)))
(*.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)) (pow.f64 x #s(literal 3 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 (pow x 2))) 1/3) x)) 1) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/27 binary64) x) x) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 (pow x 2))) (+ 1/3 (/ 1/81 (pow x 3)))) x)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal 1/27 binary64)) x) x) #s(literal 1/3 binary64)) x)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(*.f64 (+.f64 #s(literal 1/3 binary64) x) x)
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(/ -1/27 (pow x 2))
(/.f64 #s(literal -1/27 binary64) (*.f64 x x))
(/ (- (* 1/81 (/ 1 x)) 1/27) (pow x 2))
(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal 1/27 binary64)) x) x)
(/ (- (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) 1/81) x)) 1/27) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal 1/27 binary64)) (/.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 x x))
(/ (- (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) (+ 1/81 (/ 1/2187 (pow x 3)))) x)) 1/27) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1/729 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (-.f64 #s(literal -1/81 binary64) (/.f64 #s(literal 1/2187 binary64) (pow.f64 x #s(literal 3 binary64)))) x)) #s(literal 1/27 binary64)) (*.f64 x x))

rewrite178.0ms (7%)

Memory

9.9MiB live, 211.3MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	96
0	34	84
1	137	75
2	1053	75
0	8446	75

Stop Event

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

Counts

12 → 692

Calls

Call 1

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

Outputs
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eval174.0ms (6.8%)

Memory: 20.6MiB live, 290.3MiB allocated
Compiler: Compiled 27 796 to 2 876 computations (89.7% saved)

prune24.0ms (0.9%)

Memory

-10.3MiB live, 66.1MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1 104	1	1 105
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	1 106	3	1 109

Accuracy

100.0%

Counts

1 109 → 3

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))))
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
✓	47.0%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify58.0ms (2.3%)

Memory

-10.0MiB live, 36.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 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))))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	29
0	13	29
1	24	29
2	38	27
3	66	27
4	119	27
5	164	27
6	212	27
7	302	27
8	428	27
9	650	27
10	1169	27
11	1356	27
12	1365	27
13	1411	27
14	1427	27
0	1427	27

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.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) (/.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)

localize32.0ms (1.2%)

Memory

13.3MiB live, 51.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x #s(literal -1/9 binary64))
accuracy	0.01953125	(-.f64 x #s(literal -1/3 binary64))
accuracy	0.1171875	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal -1/9 binary64))))
accuracy	14.961300334652442	(/.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal -1/9 binary64)))

Samples

26.0ms

256×

valid

Compiler

Compiled 34 to 11 computations (67.6% saved)

Precisions

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

ival-div: 8.0ms (42.3% of total)

const: 6.0ms (31.7% of total)

ival-mult: 2.0ms (10.6% of total)

ival-sub: 1.0ms (5.3% of total)

ival-add: 1.0ms (5.3% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

4 → 48

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

simplify253.0ms (9.8%)

Memory

-25.1MiB live, 127.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	224
1	170	224
2	367	224
3	925	216
4	2220	216
5	4589	216
6	7906	216
0	8565	199

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 44

Calls

Call 1

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

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

rewrite221.0ms (8.6%)

Memory

-7.3MiB live, 146.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	25
0	13	25
1	69	15
2	467	15
3	7079	15
0	9673	15

Stop Event

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

Counts

4 → 807

Calls

Call 1

Inputs
(/.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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eval156.0ms (6.1%)

Memory: -9.2MiB live, 220.3MiB allocated
Compiler: Compiled 19 111 to 2 632 computations (86.2% saved)

prune16.0ms (0.6%)

Memory

19.0MiB live, 56.6MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	851	0	851
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	851	3	854

Accuracy

100.0%

Counts

854 → 3

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))))
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
✓	47.0%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 70 to 39 computations (44.3% saved)

regimes5.0ms (0.2%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 6 to 6 computations (0% saved)

regimes8.0ms (0.3%)

Memory

-36.6MiB live, 7.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
47.0%	1	`x`
47.0%	1	`(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`

Compiler

Compiled 6 to 6 computations (0% saved)

simplify24.0ms (0.9%)

Memory

17.3MiB live, 54.7MiB 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))

soundness130.0ms (5.1%)

Memory

0.2MiB live, 153.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 14 to 14 computations (0% saved)

preprocess55.0ms (2.2%)

Memory: 18.9MiB live, 57.1MiB 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%)

sample504.0ms (19.6%)

explain52.0ms (2%)

preprocess16.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize16.0ms (0.6%)

series1.0ms (0%)

simplify16.0ms (0.6%)

rewrite148.0ms (5.8%)

eval57.0ms (2.2%)

prune6.0ms (0.2%)

simplify142.0ms (5.5%)

localize73.0ms (2.8%)

series16.0ms (0.6%)

simplify176.0ms (6.9%)

rewrite178.0ms (7%)

eval174.0ms (6.8%)

prune24.0ms (0.9%)

simplify58.0ms (2.3%)

localize32.0ms (1.2%)

series4.0ms (0.1%)

simplify253.0ms (9.8%)

rewrite221.0ms (8.6%)

eval156.0ms (6.1%)

prune16.0ms (0.6%)

regimes5.0ms (0.2%)

regimes8.0ms (0.3%)

simplify24.0ms (0.9%)

soundness130.0ms (5.1%)

preprocess55.0ms (2.2%)

end0.0ms (0%)

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