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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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)

sample666.0ms (14%)

Memory

-6.9MiB live, 781.3MiB allocated

Samples

460.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 137.0ms

ival-div: 84.0ms (61.1% of total)

ival-sub: 38.0ms (27.7% of total)

exact: 7.0ms (5.1% of total)

ival-true: 6.0ms (4.4% of total)

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

Bogosity

explain202.0ms (4.2%)

Memory

26.6MiB live, 68.2MiB 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

18.0ms

512×

valid

Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions

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

ival-div: 4.0ms (53.8% of total)

ival-sub: 2.0ms (26.9% of total)

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

exact: 0.0ms (0% of total)

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

preprocess19.0ms (0.4%)

Memory

-18.5MiB live, 18.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 5 to 5 computations (0% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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

4.1MiB live, 4.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize385.0ms (8.1%)

Memory

-19.4MiB live, 18.6MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

9.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

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

ival-div: 2.0ms (55.2% of total)

ival-sub: 1.0ms (27.6% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Counts

2 → 12

Calls

Call 1

Inputs
#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)))

simplify14.0ms (0.3%)

Memory

14.7MiB live, 14.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 10

Calls

Call 1

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

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

rewrite533.0ms (11.2%)

Memory

-6.8MiB live, 184.0MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

2 → 313

Calls

Call 1

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

Outputs
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eval63.0ms (1.3%)

Memory: -5.7MiB live, 124.7MiB allocated
Compiler: Compiled 8 097 to 759 computations (90.6% saved)

prune6.0ms (0.1%)

Memory

23.4MiB live, 23.4MiB 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
▶	76.0%	(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))))
▶	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))))
▶	100.0%	(-.f64 x #s(literal 1/3 binary64))
▶	48.9%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 37 to 23 computations (37.8% saved)

simplify8.0ms (0.2%)

Memory

-23.9MiB live, 14.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Rules

40×	`lower-+.f64`
40×	`lower-+.f32`
34×	`lower-fma.f32`
30×	`lower-*.f32`
28×	`lower-*.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	91
0	33	91
1	50	91
2	61	90
3	71	90
4	77	90
0	77	90

Stop Event

1×	iter limit
1×	saturated
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)
(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)
(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)
(fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 x (-.f64 x #s(literal -1/3 binary64))) x (/.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)
(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)

localize127.0ms (2.7%)

Memory

10.8MiB live, 174.5MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.03125	(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
accuracy	0.5800579675335101	(/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	14.307816588790509	(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	14.45502675951705	(/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	0.0078125	(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	0.0078125	(-.f64 x #s(literal -1/3 binary64))
accuracy	0.16796875	(/.f64 x (-.f64 x #s(literal -1/3 binary64)))
accuracy	0.22265625	(/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))
accuracy	0.01171875	(-.f64 x #s(literal 1/3 binary64))
accuracy	32.71097900900519	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Samples

93.0ms	216×	0	valid
13.0ms	27×	1	valid
8.0ms	13×	2	valid

Compiler

Compiled 100 to 25 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

const: 17.0ms (34.6% of total)

ival-div: 10.0ms (20.4% of total)

ival-mult: 10.0ms (20.4% of total)

ival-sub: 5.0ms (10.2% of total)

ival-add: 4.0ms (8.1% of total)

adjust: 2.0ms (4.1% of total)

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

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

exact: 0.0ms (0% of total)

series16.0ms (0.3%)

Memory

-17.2MiB live, 23.8MiB 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 (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 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 (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 (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) (patch (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 3 x) (taylor 0 x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 3 (* -9 x))) (taylor 0 x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 3 (* x (- (* 27 x) 9)))) (taylor 0 x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))) (taylor 0 x) (#s(alt (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 x (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (-.f64 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 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (* -3 x))) 1/3) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (* x (- (* 9 x) 3)))) 1/3) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (patch (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (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 (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>) () ())) ())
#s(alt (- x 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>) () ())) ())
#s(alt (- (* x (+ 1 (* -9 (pow x 2)))) 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>) () ())) ())
#s(alt (- (* x (+ 1 (* (pow x 2) (- (* 27 x) 9)))) 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>) () ())) ())
#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>) () ())) ())
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#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

3.0ms

-inf

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

2.0ms

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

simplify198.0ms (4.2%)

Memory

44.3MiB live, 195.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 344×	`lower-fma.f64`
12 344×	`lower-fma.f32`
3 638×	`lower-+.f64`
3 638×	`lower-+.f32`
3 184×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	195	728
1	580	716
2	1358	698
3	3779	690
0	8304	663

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 122

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

rewrite170.0ms (3.6%)

Memory

-31.1MiB live, 232.6MiB allocated

Rules

5 664×	`lower-/.f32`
5 656×	`lower-/.f64`
3 946×	`lower-*.f32`
3 944×	`lower-*.f64`
3 912×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	78
0	33	78
1	132	77
2	1068	77
0	8483	77

Stop Event

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

Counts

11 → 469

Calls

Call 1

Inputs
#s(approx (- x (/ 1 3)) #s(literal -1/3 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 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 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))
(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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eval221.0ms (4.7%)

Memory: 5.3MiB live, 196.8MiB allocated
Compiler: Compiled 20 249 to 1 986 computations (90.2% saved)

prune22.0ms (0.5%)

Memory

11.2MiB live, 52.9MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	767	2	769
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	768	5	773

Accuracy

100.0%

Counts

773 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.3%	(fma.f64 (.f64 x x) #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x)) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
✓	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))))
▶	97.5%	(fma.f64 x #s(approx (/ x (- x -1/3)) #s(literal 1 binary64)) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
✓	48.9%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 42 to 33 computations (21.4% saved)

simplify7.0ms (0.1%)

Memory

-28.4MiB live, 10.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

36×	`lower-+.f64`
36×	`lower-+.f32`
34×	`lower-fma.f32`
30×	`lower-*.f32`
28×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	97
0	34	97
1	48	97
2	56	97
3	65	97
4	71	97
0	71	97

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize112.0ms (2.4%)

Memory

6.7MiB live, 117.6MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.03125	(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
accuracy	0.5800579675335101	(/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	14.307816588790509	(fma.f64 (.f64 x x) #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x)) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
accuracy	32.461560767510555	#s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x))
accuracy	0.0078125	(fma.f64 x #s(approx (/ x (- x -1/3)) #s(literal 1 binary64)) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
accuracy	0.0078125	(-.f64 x #s(literal -1/3 binary64))
accuracy	0.22265625	(/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))
accuracy	30.69738137841561	#s(approx (/ x (- x -1/3)) #s(literal 1 binary64))

Samples

37.0ms	216×	0	valid
9.0ms	27×	1	valid
6.0ms	13×	2	valid

Compiler

Compiled 94 to 22 computations (76.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

const: 15.0ms (38.4% of total)

ival-mult: 9.0ms (23% of total)

ival-div: 8.0ms (20.5% of total)

ival-add: 4.0ms (10.2% of total)

adjust: 2.0ms (5.1% of total)

ival-sub: 2.0ms (5.1% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.2%)

Memory

23.2MiB live, 23.2MiB allocated

Counts

10 → 120

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify260.0ms (5.5%)

Memory

-34.4MiB live, 213.8MiB allocated

Algorithm

1×	egg-herbie

Rules

12 344×	`lower-fma.f64`
12 344×	`lower-fma.f32`
3 638×	`lower-+.f64`
3 638×	`lower-+.f32`
3 184×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	195	704
1	580	692
2	1357	674
3	3767	666
0	8290	639

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 114

Calls

Call 1

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

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

rewrite217.0ms (4.6%)

Memory

24.2MiB live, 215.7MiB allocated

Rules

10 620×	`lower-fma.f32`
10 614×	`lower-fma.f64`
6 164×	`lower-*.f32`
6 160×	`lower-*.f64`
3 964×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	85
0	34	85
1	124	85
2	880	85
0	8636	85

Stop Event

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

Counts

10 → 349

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
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#<batchref>
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#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval124.0ms (2.6%)

Memory: -6.5MiB live, 151.1MiB allocated
Compiler: Compiled 13 202 to 1 460 computations (88.9% saved)

prune13.0ms (0.3%)

Memory

-16.3MiB live, 32.4MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	527	2	529
Fresh	0	0	0
Picked	2	0	2
Done	0	3	3
Total	529	5	534

Accuracy

100.0%

Counts

534 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.0%	(fma.f64 (.f64 x x) #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x)) (/.f64 #s(literal -1/27 binary64) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
✓	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))))
▶	57.0%	(fma.f64 x #s(approx (/ x (- x -1/3)) #s(literal 1 binary64)) #s(approx (/ -1/9 (- x -1/3)) (-.f64 x #s(literal 1/3 binary64))))
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
✓	48.9%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 40 to 32 computations (20% saved)

simplify6.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

44×	`lower-+.f64`
44×	`lower-+.f32`
38×	`lower-fma.f32`
34×	`lower-*.f32`
32×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	114
0	35	114
1	52	114
2	61	114
3	70	114
4	76	114
0	76	112

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize100.0ms (2.1%)

Memory

11.4MiB live, 121.5MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.5800579675335101	(/.f64 #s(literal -1/27 binary64) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	14.307816588790509	(fma.f64 (.f64 x x) #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x)) (/.f64 #s(literal -1/27 binary64) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
accuracy	32.461560767510555	#s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x))
accuracy	32.59112977182097	#s(approx (- x -1/3) #s(literal 1/3 binary64))
accuracy	0.0078125	(fma.f64 x #s(approx (/ x (- x -1/3)) #s(literal 1 binary64)) #s(approx (/ -1/9 (- x -1/3)) (-.f64 x #s(literal 1/3 binary64))))
accuracy	0.01171875	(-.f64 x #s(literal 1/3 binary64))
accuracy	30.69738137841561	#s(approx (/ x (- x -1/3)) #s(literal 1 binary64))
accuracy	32.92366721029355	#s(approx (/ -1/9 (- x -1/3)) (-.f64 x #s(literal 1/3 binary64)))

Samples

40.0ms	216×	0	valid
12.0ms	27×	1	valid
7.0ms	13×	2	valid

Compiler

Compiled 93 to 24 computations (74.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

const: 17.0ms (38.2% of total)

ival-div: 10.0ms (22.5% of total)

ival-mult: 8.0ms (18% of total)

ival-add: 4.0ms (9% of total)

ival-sub: 3.0ms (6.7% of total)

adjust: 2.0ms (4.5% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.2%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

10 → 120

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify242.0ms (5.1%)

Memory

5.5MiB live, 212.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12 164×	`lower-fma.f64`
12 164×	`lower-fma.f32`
3 700×	`lower-+.f64`
3 700×	`lower-+.f32`
2 940×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	187	662
1	551	650
2	1280	640
3	3484	632
0	8241	612

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 112

Calls

Call 1

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

rewrite193.0ms (4.1%)

Memory

-22.5MiB live, 246.0MiB allocated

Rules

10 636×	`lower-fma.f32`
10 630×	`lower-fma.f64`
5 986×	`lower-*.f32`
5 982×	`lower-*.f64`
3 508×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	98
0	35	98
1	147	98
2	1014	98
0	8741	96

Stop Event

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

Counts

10 → 212

Calls

Call 1

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

Outputs
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eval273.0ms (5.7%)

Memory: 9.9MiB live, 94.2MiB allocated
Compiler: Compiled 7 954 to 849 computations (89.3% saved)

prune33.0ms (0.7%)

Memory

-7.7MiB live, 30.4MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	324	0	324
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	324	5	329

Accuracy

100.0%

Counts

329 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.0%	(fma.f64 (.f64 x x) #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x)) (/.f64 #s(literal -1/27 binary64) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
✓	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))))
✓	57.0%	(fma.f64 x #s(approx (/ x (- x -1/3)) #s(literal 1 binary64)) #s(approx (/ -1/9 (- x -1/3)) (-.f64 x #s(literal 1/3 binary64))))
✓	100.0%	(-.f64 x #s(literal 1/3 binary64))
✓	48.9%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 130 to 65 computations (50% saved)

regimes7.0ms (0.1%)

Memory

19.0MiB live, 19.0MiB 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))
(fma.f64 x #s(approx (/ x (- x -1/3)) #s(literal 1 binary64)) #s(approx (/ -1/9 (- x -1/3)) (-.f64 x #s(literal 1/3 binary64))))
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
(fma.f64 x #s(approx (/ x (- x -1/3)) #s(literal 1 binary64)) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
(fma.f64 (.f64 x x) #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x)) (/.f64 #s(literal -1/27 binary64) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 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))))
(fma.f64 (.f64 x x) #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x)) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(fma.f64 (*.f64 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
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)

regimes3.0ms (0.1%)

Memory

8.6MiB live, 8.6MiB 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:

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

Results

Accuracy	Segments	Branch
48.9%	1	`x`
48.9%	1	`(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`

Compiler

Compiled 6 to 6 computations (0% saved)

simplify63.0ms (1.3%)

Memory

-2.2MiB live, 119.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness408.0ms (8.6%)

Memory

-39.7MiB live, 87.0MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 14 to 14 computations (0% saved)

preprocess23.0ms (0.5%)

Memory: 16.7MiB live, 54.4MiB 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%)

sample666.0ms (14%)

explain202.0ms (4.2%)

preprocess19.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize385.0ms (8.1%)

series1.0ms (0%)

simplify14.0ms (0.3%)

rewrite533.0ms (11.2%)

eval63.0ms (1.3%)

prune6.0ms (0.1%)

simplify8.0ms (0.2%)

localize127.0ms (2.7%)

series16.0ms (0.3%)

simplify198.0ms (4.2%)

rewrite170.0ms (3.6%)

eval221.0ms (4.7%)

prune22.0ms (0.5%)

simplify7.0ms (0.1%)

localize112.0ms (2.4%)

series8.0ms (0.2%)

simplify260.0ms (5.5%)

rewrite217.0ms (4.6%)

eval124.0ms (2.6%)

prune13.0ms (0.3%)

simplify6.0ms (0.1%)

localize100.0ms (2.1%)

series8.0ms (0.2%)

simplify242.0ms (5.1%)

rewrite193.0ms (4.1%)

eval273.0ms (5.7%)

prune33.0ms (0.7%)

regimes7.0ms (0.1%)

regimes3.0ms (0.1%)

simplify63.0ms (1.3%)

soundness408.0ms (8.6%)

preprocess23.0ms (0.5%)

end0.0ms (0%)

Profiling