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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 7 to 7 computations (0% saved)

sample1.2s (32.4%)

Memory

-223.2MiB live, 650.1MiB allocated

Samples

925.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 553.0ms

ival-div: 492.0ms (89% of total)

ival-add: 45.0ms (8.1% of total)

exact: 7.0ms (1.3% of total)

ival-true: 6.0ms (1.1% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain48.0ms (1.3%)

Memory

11.5MiB live, 89.2MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

19.0ms

512×

valid

Compiler

Compiled 32 to 19 computations (40.6% saved)

Precisions

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

ival-div: 4.0ms (53.7% of total)

ival-add: 2.0ms (26.8% of total)

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

exact: 0.0ms (0% of total)

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

preprocess14.0ms (0.4%)

Memory

19.2MiB live, 19.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`associate--r+`
12×	`sub-neg`
10×	`distribute-lft-neg-in`
10×	`associate-+l-`
10×	`distribute-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB 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 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Memory

4.1MiB live, 4.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize33.0ms (0.9%)

Memory

-24.5MiB live, 19.1MiB 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

28.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

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

ival-div: 21.0ms (88.3% of total)

ival-add: 2.0ms (8.4% 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

1.3MiB live, 1.3MiB allocated

Counts

2 → 12

Calls

Call 1

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

Inputs

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

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

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

Calls

3 calls:

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

simplify5.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`lower-*.f64`
36×	`lower-*.f32`
16×	`lower-/.f32`
16×	`associate-r`
16×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 10

Calls

Call 1

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

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

rewrite208.0ms (5.8%)

Memory

-4.8MiB live, 261.6MiB allocated

Rules

8 708×	`lower-fma.f64`
8 708×	`lower-fma.f32`
5 116×	`lower-*.f64`
5 116×	`lower-*.f32`
3 868×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

2 → 265

Calls

Call 1

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

Outputs
#s(literal 1/3 binary64)
(.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/19683 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) x) x (-.f64 #s(literal 1/729 binary64) (.f64 (.f64 #s(literal 1/27 binary64) (.f64 x x)) x)))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64))))))) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))) (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x (-.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x))))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal 1/3 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) #s(literal -1/2 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 #s(literal 1/3 binary64) x)))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1/729 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (-.f64 #s(literal 1/3 binary64) x)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal 1/3 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1/81 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal 1/3 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1/81 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1/81 binary64)) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1/729 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1/729 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (-.f64 x #s(literal 1/3 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1/729 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1/729 binary64)) (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1/729 binary64)) (.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1/729 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x (-.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x))))))
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(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x x #s(literal -1/9 binary64))) (.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (*.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (.f64 x x)) (.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (neg.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)))))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x (-.f64 #s(literal 1/9 binary64) (.f64 x x))))) (.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 (.f64 x x) (*.f64 x x))))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 (.f64 x x) (.f64 x x))) (.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -1/9 binary64) (.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x (-.f64 #s(literal 1/9 binary64) (*.f64 x x))))))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal -1/9 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (*.f64 x x)))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (.f64 x x)) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal -1/9 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #s(literal 1/27 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (.f64 (.f64 x x) x)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (.f64 (.f64 x x) x)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #s(literal 1/27 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/3 binary64))
(+.f64 (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal 1/3 binary64))) (*.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))))
(+.f64 (.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))
(+.f64 x #s(literal 1/3 binary64))
(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1 binary64)))
(+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1/3 binary64) x)

eval34.0ms (0.9%)

Memory: 5.1MiB live, 87.0MiB allocated
Compiler: Compiled 7 860 to 629 computations (92% saved)

prune66.0ms (1.8%)

Memory

-18.8MiB live, 155.3MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	272	3	275
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	273	3	276

Accuracy

100.0%

Counts

276 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.5%	(/.f64 (fma.f64 (*.f64 x x) x #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))
▶	50.0%	#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64))

Status

Accuracy

Program

▶

67.5%

(/.f64 (fma.f64 (*.f64 x x) x #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))

▶

50.0%

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

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify6.0ms (0.2%)

Memory

11.4MiB live, 11.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

36×	`lower-+.f64`
36×	`lower-+.f32`
26×	`lower-fma.f32`
22×	`lower-fma.f64`
16×	`+-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	46
0	24	46
1	34	44
2	40	44
3	49	44
4	55	44
0	55	44

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

localize46.0ms (1.3%)

Memory

24.3MiB live, 100.5MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
accuracy	0.015625	(-.f64 x #s(literal 1/3 binary64))
accuracy	0.046875	(fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))
accuracy	20.3222582998375	(/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (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	32.03160924390678	#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64))

Samples

37.0ms

256×

valid

Compiler

Compiled 52 to 19 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

const: 11.0ms (39.1% of total)

ival-mult: 6.0ms (21.3% of total)

ival-div: 5.0ms (17.8% of total)

ival-add: 3.0ms (10.7% of total)

ival-sub: 2.0ms (7.1% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

-25.1MiB live, 13.5MiB allocated

Counts

7 → 84

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

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

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify110.0ms (3.1%)

Memory

35.9MiB live, 147.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 758×	`lower-fma.f64`
7 758×	`lower-fma.f32`
2 964×	`lower-*.f64`
2 964×	`lower-*.f32`
1 582×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	280
1	120	280
2	294	272
3	949	272
4	2763	272
5	5105	272
6	7987	272
0	8004	265

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 76

Calls

Call 1

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

rewrite217.0ms (6%)

Memory

19.7MiB live, 320.1MiB allocated

Rules

4 420×	`lower-fma.f32`
4 416×	`lower-fma.f64`
4 086×	`lower-*.f32`
4 084×	`lower-*.f64`
3 430×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
0	24	28
1	91	28
2	581	28
3	7206	28
0	8515	28

Stop Event

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

Counts

7 → 827

Calls

Call 1

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

Outputs
#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (neg.f64 (fma.f64 x x #s(literal -1/9 binary64)))) (neg.f64 (-.f64 x #s(literal -1/3 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (neg.f64 (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) (-.f64 (fma.f64 x x #s(literal -1/9 binary64)) (.f64 #s(literal -1/3 binary64) x)))) (-.f64 (fma.f64 x x #s(literal -1/9 binary64)) (*.f64 #s(literal -1/3 binary64) x)))
(.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64))) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x))) (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)))
(.f64 (/.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1/19683 binary64))) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/27 binary64) #s(literal 1/729 binary64))))
(.f64 (/.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64))) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)))
(.f64 (/.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/19683 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64)) (-.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x))))) (-.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x))))
(.f64 (/.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/19683 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)) (.f64 (.f64 x x) x) (.f64 (.f64 (fma.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x) #s(literal 1/729 binary64)) (fma.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x) #s(literal 1/729 binary64))) (fma.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x) #s(literal 1/729 binary64))))) (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x) (.f64 (.f64 (.f64 (.f64 x x) x) x) x)) x (.f64 (fma.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x) #s(literal 1/729 binary64)) (-.f64 (fma.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x) #s(literal 1/729 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)))))
(.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))))) (-.f64 #s(literal 1/9 binary64) (.f64 (-.f64 x #s(literal 1/3 binary64)) x)))
(.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (neg.f64 (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64)))) (fma.f64 (-.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (neg.f64 (fma.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x)) x #s(literal 1/729 binary64)))) (neg.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (fma.f64 (-.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)))
(.f64 (/.f64 (-.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x)) x #s(literal 1/729 binary64))) (neg.f64 (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64)))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x)) x #s(literal 1/729 binary64)))) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/27 binary64) (.f64 (.f64 x x) x))) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) #s(literal -1/2 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/19683 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (fma.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x)) x #s(literal 1/729 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/19683 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/19683 binary64)) (fma.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x)) x #s(literal 1/729 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/19683 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x)) x #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x)) x #s(literal 1/729 binary64))) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))
(.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x)) x #s(literal 1/729 binary64))) (.f64 (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))))
(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (-.f64 #s(literal -1/27 binary64) (.f64 (*.f64 x x) x)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (fma.f64 x x #s(literal -1/9 binary64)))
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
(*.f64 #s(literal -1 binary64) (neg.f64 (-.f64 x #s(literal -1/3 binary64))))
(.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))))
(.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) (/.f64 (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))))
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
(.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/19683 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/19683 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1/19683 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))))
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(+.f64 (.f64 (.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)))) (.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))))
(+.f64 (*.f64 x #s(literal 1 binary64)) #s(literal -1/3 binary64))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64))) (fma.f64 x x #s(literal 1/9 binary64))) (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64))) (*.f64 #s(literal -1/3 binary64) x)))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64))) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64))) (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64))) (*.f64 x x)))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64))) (.f64 x x)) (.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64))))
(+.f64 (*.f64 #s(literal 1 binary64) x) #s(literal -1/3 binary64))
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))))
(+.f64 (.f64 (.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(+.f64 #s(literal -1/3 binary64) (*.f64 x #s(literal 1 binary64)))
(+.f64 #s(literal -1/3 binary64) (*.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal -1/3 binary64) x)
(+.f64 x #s(literal -1/3 binary64))

eval232.0ms (6.5%)

Memory: -30.3MiB live, 188.7MiB allocated
Compiler: Compiled 28 461 to 1 727 computations (93.9% saved)

prune165.0ms (4.6%)

Memory

-3.5MiB live, 194.3MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	902	1	903
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	903	3	906

Accuracy

100.0%

Counts

906 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

50.4%

(/.f64 #s(approx (+ (* (* x x) x) 1/27) #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))

✓

50.0%

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

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify6.0ms (0.2%)

Memory

3.2MiB live, 3.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 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	#s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))
cost-diff	0	(/.f64 #s(approx (+ (* (* x x) x) 1/27) #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`
26×	`lower-fma.f32`
24×	`lower-fma.f64`
14×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	38
0	15	38
1	22	34
2	29	34
3	38	34
4	44	34
0	44	34

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize61.0ms (1.7%)

Memory

2.8MiB live, 41.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
accuracy	0.015625	(-.f64 x #s(literal 1/3 binary64))
accuracy	20.3222582998375	(/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	31.827514094565608	#s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))

Samples

26.0ms

256×

valid

Compiler

Compiled 38 to 13 computations (65.8% saved)

Precisions

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

const: 8.0ms (41.3% of total)

ival-mult: 5.0ms (25.8% of total)

ival-div: 2.0ms (10.3% of total)

ival-add: 2.0ms (10.3% of total)

ival-sub: 1.0ms (5.2% of total)

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

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

series3.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

0.0ms

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

simplify141.0ms (3.9%)

Memory

-3.7MiB live, 112.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 778×	`lower-fma.f64`
7 778×	`lower-fma.f32`
3 304×	`lower-*.f64`
3 304×	`lower-*.f32`
1 582×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	184
1	120	184
2	293	176
3	946	176
4	2723	176
5	5041	176
6	7921	176
0	8172	169

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 44

Calls

Call 1

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

rewrite179.0ms (5%)

Memory

-27.9MiB live, 254.8MiB allocated

Rules

4 590×	`lower-fma.f32`
4 588×	`lower-fma.f64`
4 034×	`lower-*.f64`
4 034×	`lower-*.f32`
3 154×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
0	15	30
1	70	30
2	447	30
3	4506	30
0	8708	30

Stop Event

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

Counts

4 → 250

Calls

Call 1

Inputs
(/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
#s(approx (+ (* (* x x) x) 1/27) #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
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))))) (-.f64 #s(literal 1/9 binary64) (.f64 (-.f64 x #s(literal 1/3 binary64)) x)))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (neg.f64 (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64)))) (neg.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) (-.f64 x #s(literal 1/3 binary64))) x #s(literal 1/729 binary64)))) (neg.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))
(.f64 (/.f64 (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (neg.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))))
(.f64 (/.f64 (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) (fma.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) (-.f64 x #s(literal 1/3 binary64))) x #s(literal 1/729 binary64))) (neg.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64)))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) (-.f64 x #s(literal 1/3 binary64))) x #s(literal 1/729 binary64)))) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) (-.f64 x #s(literal 1/3 binary64))) x #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) (-.f64 x #s(literal 1/3 binary64))) x #s(literal 1/729 binary64))) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) (-.f64 x #s(literal 1/3 binary64))) x #s(literal 1/729 binary64))) (.f64 (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) (-.f64 x #s(literal 1/3 binary64))) x #s(literal 1/729 binary64))))
(.f64 (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 1 binary64))
(.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(pow.f64 (exp.f64 (log.f64 (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))))) #s(literal -1 binary64))
(pow.f64 (.f64 (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 1 binary64))
(/.f64 (/.f64 (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))
(/.f64 (.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (fma.f64 (.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) (.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal -1/729 binary64))) (fma.f64 (.f64 (.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal 1/9 binary64) #s(literal 1/81 binary64))))
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(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)))
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x #s(literal -1/3 binary64)))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))))
(*.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64)))
(.f64 (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) x)))))
(.f64 (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/3 binary64) x))) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1 binary64))
(/.f64 (.f64 (fma.f64 (.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64)))) (fma.f64 x x #s(literal 1/9 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64)))) (fma.f64 (.f64 (.f64 x x) x) x (fma.f64 #s(literal 1/9 binary64) (.f64 x x) #s(literal 1/81 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1/19683 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x (fma.f64 #s(literal 1/27 binary64) (.f64 (.f64 x x) x) #s(literal 1/729 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64)))
(/.f64 (-.f64 (.f64 (.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))))) (.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))) (fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))) (.f64 (.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))) (.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))) (fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal -1/3 binary64) x))
(/.f64 (-.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x) (.f64 (.f64 (-.f64 x #s(literal -1/3 binary64)) (-.f64 x #s(literal -1/3 binary64))) (-.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal 1/729 binary64) (.f64 (.f64 (-.f64 x #s(literal -1/3 binary64)) (-.f64 x #s(literal -1/3 binary64))) (-.f64 x #s(literal -1/3 binary64))))) (fma.f64 (.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (fma.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))))))
(/.f64 (-.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))) (/.f64 #s(literal 1/19683 binary64) (.f64 (.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))) (fma.f64 (.f64 (.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))) (.f64 (.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))) (fma.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (.f64 (.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))) (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1/9 binary64)))) (neg.f64 (neg.f64 (-.f64 x #s(literal -1/3 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal 1 binary64)) (-.f64 x #s(literal -1/3 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal -1/81 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1/19683 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x (fma.f64 #s(literal 1/27 binary64) (.f64 (*.f64 x x) x) #s(literal 1/729 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) x) x (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))) (-.f64 x #s(literal -1/3 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x #s(literal -1/3 binary64))) (.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (.f64 (-.f64 x #s(literal -1/3 binary64)) (-.f64 x #s(literal -1/3 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) x) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) #s(literal 1/27 binary64))) (*.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal -1/81 binary64)) (*.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1/19683 binary64)) (.f64 (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/3 binary64) x))) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x (fma.f64 #s(literal 1/27 binary64) (.f64 (*.f64 x x) x) #s(literal 1/729 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1/19683 binary64)) (.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x (fma.f64 #s(literal 1/27 binary64) (.f64 (.f64 x x) x) #s(literal 1/729 binary64)))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1/9 binary64))) (neg.f64 (-.f64 x #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/3 binary64) x)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64)))))
(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 (.f64 (.f64 x x) x) x (fma.f64 #s(literal 1/9 binary64) (.f64 x x) #s(literal 1/81 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (.f64 (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/3 binary64) x))) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1/729 binary64)) (.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/3 binary64) x))) (fma.f64 (.f64 x x) x #s(literal -1/27 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))))
(/.f64 (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (-.f64 (.f64 x x) (*.f64 #s(literal -1/3 binary64) x))))
(/.f64 (fma.f64 (.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/3 binary64) x))))
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x #s(literal -1/9 binary64))) (-.f64 x #s(literal -1/3 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (neg.f64 (-.f64 x #s(literal -1/3 binary64)))))
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 x x) x) (.f64 (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (-.f64 (fma.f64 x x #s(literal -1/9 binary64)) (.f64 #s(literal 1/3 binary64) x)))) (-.f64 (fma.f64 x x #s(literal -1/9 binary64)) (*.f64 #s(literal 1/3 binary64) x)) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x))) (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (-.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 x x #s(literal -1/9 binary64))) (-.f64 x #s(literal 1/3 binary64)) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 x x) x #s(literal 1/27 binary64))) (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/3 binary64) x))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal -1/3 binary64))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(fma.f64 (.f64 (.f64 x x) x) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(fma.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/3 binary64) x)))) (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/3 binary64) x)))))
(-.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
(-.f64 (.f64 (.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))) (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))))
(-.f64 x #s(literal 1/3 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64)))) #s(literal -1 binary64)))
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))))
(+.f64 (.f64 (.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))))
(+.f64 #s(literal -1/3 binary64) x)
(+.f64 x #s(literal -1/3 binary64))

eval36.0ms (1%)

Memory: 25.9MiB live, 103.2MiB allocated
Compiler: Compiled 8 293 to 855 computations (89.7% saved)

prune71.0ms (2%)

Memory

-6.6MiB live, 75.0MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	293	1	294
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	294	3	297

Accuracy

100.0%

Counts

297 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

49.8%

(/.f64 #s(approx (+ (* (* x x) x) 1/27) #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))

✓

50.0%

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

Compiler

Compiled 16 to 11 computations (31.3% saved)

simplify5.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

12×	`lower-+.f64`
12×	`lower-+.f32`
10×	`lower-*.f64`
10×	`lower-*.f32`
8×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	44
0	16	44
1	22	40
2	25	40
0	25	40

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize40.0ms (1.1%)

Memory

-19.7MiB live, 56.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 x #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
accuracy	20.3222582998375	(/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 x #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	31.827514094565608	#s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))
accuracy	32.04278354006126	#s(approx (- x 1/3) #s(literal -1/3 binary64))

Samples

30.0ms

256×

valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

const: 11.0ms (51.2% of total)

ival-mult: 5.0ms (23.3% of total)

ival-add: 2.0ms (9.3% of total)

ival-sub: 1.0ms (4.7% of total)

ival-div: 1.0ms (4.7% of total)

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

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

series3.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

0.0ms

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

simplify145.0ms (4%)

Memory

31.6MiB live, 109.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 778×	`lower-fma.f64`
7 778×	`lower-fma.f32`
3 304×	`lower-*.f64`
3 304×	`lower-*.f32`
1 582×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	184
1	120	184
2	293	176
3	946	176
4	2723	176
5	5041	176
6	7921	176
0	8172	169

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 44

Calls

Call 1

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

rewrite255.0ms (7.1%)

Memory

-18.6MiB live, 245.3MiB allocated

Rules

5 024×	`lower-fma.f32`
5 022×	`lower-fma.f64`
4 780×	`lower-*.f64`
4 780×	`lower-*.f32`
2 732×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
0	16	36
1	70	36
2	436	36
3	3798	36
0	8521	36

Stop Event

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

Counts

4 → 206

Calls

Call 1

Inputs
(/.f64 #s(approx (+ (* (* x x) x) 1/27) #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 x) x) 1/27) #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))

Outputs
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (neg.f64 (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64)))) (neg.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (neg.f64 x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(literal -1/729 binary64))) (neg.f64 (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))
(.f64 (/.f64 (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (neg.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))))
(.f64 (/.f64 (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64))) (neg.f64 (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64)))) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64)))) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64))) (.f64 (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64))) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64))))
(.f64 (neg.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(.f64 (/.f64 #s(approx (+ ( (* x x) x) 1/27) #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 binary64))
(.f64 #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(pow.f64 (exp.f64 (log.f64 (/.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))))) #s(literal -1 binary64))
(pow.f64 (.f64 (/.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ ( (* x x) x) 1/27) #s(literal 1/27 binary64))) (/.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1 binary64))
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(/.f64 (neg.f64 (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (neg.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))))
(/.f64 (fma.f64 (.f64 (neg.f64 x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(literal -1/729 binary64)) (.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))))
(/.f64 (fma.f64 (.f64 (neg.f64 x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(literal -1/729 binary64)) (neg.f64 (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(/.f64 (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64)) (*.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))))
(/.f64 (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64)) (neg.f64 (neg.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64)) (.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64)) (neg.f64 (neg.f64 (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x #s(literal 1/729 binary64)) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))
(/.f64 (-.f64 #s(literal -1/9 binary64) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) #s(literal -1 binary64))
(/.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 1 binary64))
(neg.f64 (-.f64 #s(literal -1/9 binary64) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)))
(fma.f64 (exp.f64 (log.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)))) x #s(literal 1/9 binary64))
(fma.f64 (pow.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x #s(literal 1/9 binary64))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (fma.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/729 binary64))) (fma.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64)) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal 1/9 binary64) #s(literal 1/81 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) (/.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x) (/.f64 x (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (/.f64 (.f64 x x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (.f64 (.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (/.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) (/.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))
(fma.f64 (.f64 x x) (/.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 x (exp.f64 (log.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)))) #s(literal 1/9 binary64))
(fma.f64 x (pow.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(literal 1 binary64)) #s(literal 1/9 binary64))
(fma.f64 x (/.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64))) x) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 x #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(-.f64 (/.f64 #s(literal 1/81 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x))) (/.f64 (.f64 (.f64 (.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/9 binary64) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal -1 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) #s(literal -1 binary64)))
(+.f64 (neg.f64 (*.f64 (neg.f64 x) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) #s(literal 1/9 binary64))
(+.f64 (/.f64 (.f64 (.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))))
(+.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal 1/9 binary64))
(+.f64 #s(literal 1/9 binary64) (neg.f64 (*.f64 (neg.f64 x) #s(approx (- x 1/3) #s(literal -1/3 binary64)))))
(+.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x))
#s(approx (- x 1/3) #s(literal -1/3 binary64))

eval34.0ms (1%)

Memory: -4.9MiB live, 81.9MiB allocated
Compiler: Compiled 6 787 to 647 computations (90.5% saved)

prune34.0ms (0.9%)

Memory

29.7MiB live, 105.5MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	250	3	253

Accuracy

100.0%

Counts

253 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

49.8%

(/.f64 #s(approx (+ (* (* x x) x) 1/27) #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))

✓

50.0%

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

Compiler

Compiled 57 to 29 computations (49.1% saved)

regimes9.0ms (0.3%)

Memory

-29.3MiB live, 15.2MiB allocated

Counts

6 → 1

Calls

Call 1

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

6.0ms	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 8 to 6 computations (25% saved)

regimes3.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
50.0%	1	`x`
50.0%	1	`(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`

Compiler

Compiled 8 to 6 computations (25% saved)

simplify6.0ms (0.2%)

Memory

18.5MiB live, 18.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

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))

soundness129.0ms (3.6%)

Memory

-15.6MiB live, 94.9MiB allocated

Rules

8 708×	`lower-fma.f64`
8 708×	`lower-fma.f32`
5 116×	`lower-*.f64`
5 116×	`lower-*.f32`
3 868×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

preprocess64.0ms (1.8%)

Memory: -6.7MiB live, 115.3MiB allocated
Compiler: Compiled 24 to 18 computations (25% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.2s (32.4%)

explain48.0ms (1.3%)

preprocess14.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize33.0ms (0.9%)

series1.0ms (0%)

simplify5.0ms (0.1%)

rewrite208.0ms (5.8%)

eval34.0ms (0.9%)

prune66.0ms (1.8%)

simplify6.0ms (0.2%)

localize46.0ms (1.3%)

series8.0ms (0.2%)

simplify110.0ms (3.1%)

rewrite217.0ms (6%)

eval232.0ms (6.5%)

prune165.0ms (4.6%)

simplify6.0ms (0.2%)

localize61.0ms (1.7%)

series3.0ms (0.1%)

simplify141.0ms (3.9%)

rewrite179.0ms (5%)

eval36.0ms (1%)

prune71.0ms (2%)

simplify5.0ms (0.1%)

localize40.0ms (1.1%)

series3.0ms (0.1%)

simplify145.0ms (4%)

rewrite255.0ms (7.1%)

eval34.0ms (1%)

prune34.0ms (0.9%)

regimes9.0ms (0.3%)

regimes3.0ms (0.1%)

simplify6.0ms (0.2%)

soundness129.0ms (3.6%)

preprocess64.0ms (1.8%)

end0.0ms (0%)

Profiling