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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

sample939.0ms (29%)

Memory

-15.2MiB live, 1 148.9MiB allocated

Samples

557.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 228.0ms

ival-div: 138.0ms (60.4% of total)

ival-sub: 74.0ms (32.4% of total)

exact: 7.0ms (3.1% of total)

ival-true: 5.0ms (2.2% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

explain163.0ms (5%)

Memory

8.1MiB live, 87.2MiB 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

83.0ms

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 (54.3% of total)

ival-sub: 2.0ms (27.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess13.0ms (0.4%)

Memory

24.3MiB live, 24.3MiB 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)

simplify21.0ms (0.6%)

Memory

-33.0MiB live, 6.3MiB 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)

localize13.0ms (0.4%)

Memory

22.3MiB live, 22.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
accuracy	0.00390625	(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Samples

8.0ms

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 (56.7% of total)

ival-sub: 1.0ms (28.4% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.0MiB live, 2.0MiB 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)))

simplify29.0ms (0.9%)

Memory

-18.9MiB live, 22.3MiB 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))

rewrite203.0ms (6.3%)

Memory

12.2MiB live, 204.7MiB 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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eval42.0ms (1.3%)

Memory: 9.3MiB live, 81.2MiB allocated
Compiler: Compiled 8 097 to 759 computations (90.6% saved)

prune5.0ms (0.2%)

Memory

19.0MiB live, 19.0MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Accuracy

100.0%

Counts

324 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.6%	(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%	(-.f64 x #s(literal 1/3 binary64))
▶	46.4%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Status

Accuracy

Program

▶

72.6%

(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%

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

▶

46.4%

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

Compiler

Compiled 25 to 16 computations (36% saved)

simplify11.0ms (0.3%)

Memory

-41.0MiB live, 7.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 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 x #s(literal 1/3 binary64))
cost-diff	0	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	63
0	25	63
1	39	63
2	50	62
3	60	62
4	66	62
0	66	62

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 (*.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 (*.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)

localize59.0ms (1.8%)

Memory

7.6MiB live, 80.8MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 x #s(literal -1/3 binary64))
accuracy	0.32749183350931843	(/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	16.30469391107203	(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	16.43482054660281	(/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	0.00390625	(-.f64 x #s(literal 1/3 binary64))
accuracy	34.318560062960444	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Samples

40.0ms	247×	0	valid
2.0ms	6×	1	valid
1.0ms	3×	2	valid

Compiler

Compiled 71 to 20 computations (71.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

const: 11.0ms (33% of total)

ival-sub: 9.0ms (27% of total)

ival-div: 5.0ms (15% of total)

ival-mult: 5.0ms (15% of total)

ival-add: 2.0ms (6% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.2%)

Memory

19.7MiB live, 19.7MiB allocated

Counts

8 → 96

Calls

Call 1

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

Outputs
#s(alt -1/3 (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 9 x) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 9 (* -27 x))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 9 (* x (- (* 243 (pow x 2)) 27)))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 9 (* x (- (* (pow x 2) (+ 243 (* -729 x))) 27)))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/9 (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* 1/3 x)) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#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>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (* 1/3 (/ 1 x))) x) (taylor inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1/27 (pow x 3))) (* 1/3 (/ 1 x))) x) (taylor inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1/27 (pow x 3))) (+ (* 1/3 (/ 1 x)) (* 1/81 (/ 1 (pow x 4))))) x) (taylor inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 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 (* x (- 1 (* 1/3 (/ 1 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 (* x (- 1 (* 1/3 (/ 1 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 (/ -1/27 (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 (/ (- (* 1/81 (/ 1 x)) (+ 1/27 (/ 1/729 (pow x 3)))) (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)) (* 1/2187 (/ 1 (pow x 4)))) (+ 1/27 (/ 1/729 (pow x 3)))) (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 x (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 (pow x 2))) 1/3) x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 (pow x 2))) (+ 1/3 (/ 1/81 (pow x 3)))) x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (patch (fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ -1/27 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 1/81 (/ 1 x)) 1/27) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) 1/81) x)) 1/27) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (- (* 1/729 (/ 1 (pow x 2))) (+ 1/81 (/ 1/2187 (pow x 3)))) x)) 1/27) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

2.0ms

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

simplify132.0ms (4.1%)

Memory

9.8MiB live, 165.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10 196×	`lower-fma.f64`
10 196×	`lower-fma.f32`
3 368×	`lower-*.f64`
3 368×	`lower-*.f32`
1 996×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	122	482
1	346	478
2	846	470
3	2476	466
4	6522	466
0	8425	450

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 88

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

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

rewrite191.0ms (5.9%)

Memory

-17.9MiB live, 348.5MiB allocated

Rules

8 592×	`lower-fma.f32`
8 588×	`lower-fma.f64`
5 618×	`lower-*.f32`
5 616×	`lower-*.f64`
3 818×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	56
0	25	39
1	98	39
2	724	39
0	8930	39

Stop Event

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

Counts

8 → 673

Calls

Call 1

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

Outputs
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eval124.0ms (3.8%)

Memory: 0.3MiB live, 310.1MiB allocated
Compiler: Compiled 29 206 to 2 012 computations (93.1% saved)

prune18.0ms (0.6%)

Memory

9.3MiB live, 56.0MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	952	1	953
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	953	3	956

Accuracy

100.0%

Counts

956 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

48.5%

(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%

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

✓

46.4%

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

Compiler

Compiled 21 to 18 computations (14.3% saved)

simplify5.0ms (0.2%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 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))))

Rules

32×	`lower-+.f64`
32×	`lower-+.f32`
30×	`lower-fma.f32`
26×	`lower-fma.f64`
26×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	64
0	24	64
1	34	64
2	42	64
3	51	64
4	57	64
0	57	64

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(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 (.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)

localize44.0ms (1.4%)

Memory

-17.2MiB live, 57.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 x #s(literal -1/3 binary64))
accuracy	0.32749183350931843	(/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	16.30469391107203	(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	34.04931918856098	#s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x))

Samples

30.0ms	247×	0	valid
1.0ms	6×	1	valid
1.0ms	3×	2	valid

Compiler

Compiled 64 to 16 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

const: 9.0ms (37.2% of total)

ival-mult: 7.0ms (28.9% of total)

ival-div: 4.0ms (16.5% of total)

ival-add: 2.0ms (8.3% of total)

ival-sub: 1.0ms (4.1% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

6 → 72

Calls

Call 1

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

Outputs
#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 1/3 (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 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>) () ())) ())
#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>) () ())) ())
#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>) () ())) ())
#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))) 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 (/ 1/27 (pow x 3))) (* 1/3 (/ 1 x))) 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 (/ 1/27 (pow x 3))) (+ (* 1/3 (/ 1 x)) (* 1/81 (/ 1 (pow x 4))))) 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 (/ -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 (/ (- (* 1/81 (/ 1 x)) (+ 1/27 (/ 1/729 (pow x 3)))) (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)) (* 1/2187 (/ 1 (pow x 4)))) (+ 1/27 (/ 1/729 (pow x 3)))) (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 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 (* -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 (* -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>) () ())) ())
#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 (/ -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>) () ())) ())
#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>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify152.0ms (4.7%)

Memory

0.4MiB live, 155.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 306×	`lower-fma.f64`
11 306×	`lower-fma.f32`
3 488×	`lower-*.f64`
3 488×	`lower-*.f32`
1 718×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	386
1	314	382
2	763	382
3	2214	378
4	6741	378
0	8114	369

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 68

Calls

Call 1

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

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

rewrite198.0ms (6.1%)

Memory

11.8MiB live, 254.9MiB allocated

Rules

7 612×	`lower-fma.f32`
7 608×	`lower-fma.f64`
4 594×	`lower-*.f32`
4 590×	`lower-*.f64`
3 156×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	53
0	24	53
1	88	53
2	591	53
3	6576	53
0	8126	53

Stop Event

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

Counts

6 → 231

Calls

Call 1

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

Outputs
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eval71.0ms (2.2%)

Memory: -6.7MiB live, 68.8MiB allocated
Compiler: Compiled 9 846 to 941 computations (90.4% saved)

prune5.0ms (0.2%)

Memory

18.6MiB live, 18.6MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	299	3	302

Accuracy

100.0%

Counts

302 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

48.5%

(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%

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

✓

46.4%

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

Compiler

Compiled 20 to 18 computations (10% saved)

simplify8.0ms (0.2%)

Memory

-28.7MiB live, 8.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 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))))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	74
0	24	74
1	35	74
2	43	74
3	52	74
4	58	74
0	58	72

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(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 (.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)

localize48.0ms (1.5%)

Memory

30.4MiB live, 70.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.32749183350931843	(/.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	16.30469391107203	(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	34.04931918856098	#s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x))
accuracy	34.11723812524532	#s(approx (- x -1/3) #s(literal 1/3 binary64))

Samples

31.0ms	247×	0	valid
7.0ms	3×	2	valid
1.0ms	6×	1	valid

Compiler

Compiled 64 to 17 computations (73.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

const: 12.0ms (38.2% of total)

ival-div: 9.0ms (28.7% of total)

ival-mult: 6.0ms (19.1% of total)

ival-add: 2.0ms (6.4% of total)

ival-sub: 1.0ms (3.2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.3%)

Memory

-24.5MiB live, 11.1MiB allocated

Counts

6 → 72

Calls

Call 1

Inputs
#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 (.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>) () ())) ())
#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>) () ())) ())
#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>) () ())) ())
#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 #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 #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 (- x 1/3) (taylor 0 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 (- (* x (+ 1 (* -9 (pow x 2)))) 1/3) (taylor 0 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 (- (* x (+ 1 (* (pow x 2) (- (* 27 x) 9)))) 1/3) (taylor 0 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 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 (* 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 #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 (* 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 #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 (* 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 #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))) 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 (/ 1/27 (pow x 3))) (* 1/3 (/ 1 x))) 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 (/ 1/27 (pow x 3))) (+ (* 1/3 (/ 1 x)) (* 1/81 (/ 1 (pow x 4))))) 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 (/ (- (* 1/81 (/ 1 x)) (+ 1/27 (/ 1/729 (pow x 3)))) (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)) (* 1/2187 (/ 1 (pow x 4)))) (+ 1/27 (/ 1/729 (pow x 3)))) (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 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 (+ (* 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 (+ (* 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 (+ (* 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)))

simplify162.0ms (5%)

Memory

-12.5MiB live, 164.9MiB allocated

Algorithm

1×	egg-herbie

Rules

11 306×	`lower-fma.f64`
11 306×	`lower-fma.f32`
3 488×	`lower-*.f64`
3 488×	`lower-*.f32`
1 718×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	386
1	314	382
2	762	382
3	2209	378
4	6754	378
0	8127	369

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 68

Calls

Call 1

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

rewrite281.0ms (8.7%)

Memory

31.4MiB live, 188.1MiB allocated

Rules

9 086×	`lower-fma.f32`
9 082×	`lower-fma.f64`
5 514×	`lower-*.f32`
5 510×	`lower-*.f64`
3 798×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	61
0	24	61
1	101	61
2	727	61
3	7883	61
0	8736	59

Stop Event

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

Counts

6 → 161

Calls

Call 1

Inputs
(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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eval40.0ms (1.2%)

Memory: 1.3MiB live, 39.7MiB allocated
Compiler: Compiled 7 187 to 540 computations (92.5% saved)

prune23.0ms (0.7%)

Memory

-22.6MiB live, 15.7MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	229	3	232

Accuracy

100.0%

Counts

232 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

48.5%

(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%

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

✓

46.4%

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

Compiler

Compiled 81 to 43 computations (46.9% saved)

regimes5.0ms (0.2%)

Memory

10.5MiB live, 10.5MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Results

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

Compiler

Compiled 6 to 6 computations (0% saved)

regimes3.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB 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
46.4%	1	`x`
46.4%	1	`(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`

Compiler

Compiled 6 to 6 computations (0% saved)

simplify26.0ms (0.8%)

Memory

-9.4MiB live, 37.3MiB 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))

soundness154.0ms (4.8%)

Memory

-12.6MiB live, 140.0MiB 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)

preprocess21.0ms (0.7%)

Memory: 23.4MiB live, 60.0MiB 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%)

sample939.0ms (29%)

explain163.0ms (5%)

preprocess13.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify21.0ms (0.6%)

localize13.0ms (0.4%)

series1.0ms (0%)

simplify29.0ms (0.9%)

rewrite203.0ms (6.3%)

eval42.0ms (1.3%)

prune5.0ms (0.2%)

simplify11.0ms (0.3%)

localize59.0ms (1.8%)

series8.0ms (0.2%)

simplify132.0ms (4.1%)

rewrite191.0ms (5.9%)

eval124.0ms (3.8%)

prune18.0ms (0.6%)

simplify5.0ms (0.2%)

localize44.0ms (1.4%)

series5.0ms (0.2%)

simplify152.0ms (4.7%)

rewrite198.0ms (6.1%)

eval71.0ms (2.2%)

prune5.0ms (0.2%)

simplify8.0ms (0.2%)

localize48.0ms (1.5%)

series8.0ms (0.3%)

simplify162.0ms (5%)

rewrite281.0ms (8.7%)

eval40.0ms (1.2%)

prune23.0ms (0.7%)

regimes5.0ms (0.2%)

regimes3.0ms (0.1%)

simplify26.0ms (0.8%)

soundness154.0ms (4.8%)

preprocess21.0ms (0.7%)

end0.0ms (0%)

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