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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

sample471.0ms (14.2%)

Memory

41.0MiB live, 821.7MiB allocated

Samples

267.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 140.0ms

ival-div: 82.0ms (58.6% of total)

ival-sub: 41.0ms (29.3% of total)

exact: 7.0ms (5% of total)

ival-true: 6.0ms (4.3% of total)

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

Bogosity

explain58.0ms (1.8%)

Memory

-12.7MiB live, 113.7MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

24.0ms

512×

valid

Compiler

Compiled 32 to 19 computations (40.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sub: 5.0ms (48.7% of total)

ival-div: 4.0ms (39% of total)

exact: 1.0ms (9.7% of total)

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

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

preprocess13.0ms (0.4%)

Memory

23.3MiB live, 23.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval4.0ms (0.1%)

Memory: -37.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

2.3MiB live, 2.3MiB 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-+.f64`
4×	`lower-+.f32`
2×	`lift-/.f64`
2×	`1-exp`
2×	`lift--.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize12.0ms (0.4%)

Memory

19.5MiB live, 19.5MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

8.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

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

ival-div: 2.0ms (54.9% of total)

ival-sub: 1.0ms (27.4% 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

1.5MiB live, 1.5MiB allocated

Counts

2 → 12

Calls

Call 1

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

Inputs

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

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

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

Calls

3 calls:

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

simplify21.0ms (0.6%)

Memory

-20.1MiB live, 16.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 10

Calls

Call 1

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

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

rewrite174.0ms (5.3%)

Memory

43.1MiB live, 188.3MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

2 → 313

Calls

Call 1

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

Outputs
#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) (.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #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 x x) (.f64 x x)) (.f64 x x) (fma.f64 (.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 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)))) (+.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 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64))))) (fma.f64 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 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.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 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)) (/.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) (+.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 (-.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) (.f64 x x) (fma.f64 #s(literal 1/9 binary64) (.f64 x x) #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)) (/.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) (.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #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)) (.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 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 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1/729 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (/.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 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x))))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/19683 binary64)) (.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) (fma.f64 (.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 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 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/19683 binary64)) (.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) (fma.f64 (.f64 #s(literal 1/27 binary64) (.f64 x x)) x #s(literal 1/729 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x))))))
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eval41.0ms (1.2%)

Memory: -2.4MiB live, 86.4MiB allocated
Compiler: Compiled 10 409 to 757 computations (92.7% saved)

prune100.0ms (3%)

Memory

-20.0MiB live, 94.9MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Accuracy

100.0%

Counts

324 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	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))
▶	50.6%	#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))

▶

50.6%

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

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify6.0ms (0.2%)

Memory

11.6MiB live, 11.6MiB 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	23	46
1	33	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)

localize72.0ms (2.2%)

Memory

-10.3MiB live, 120.2MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(-.f64 x #s(literal -1/3 binary64))
accuracy	0.03515625	(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
accuracy	0.0546875	(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
accuracy	20.35570949372712	(/.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	0.01171875	(-.f64 x #s(literal 1/3 binary64))
accuracy	31.637982756307512	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Samples

61.0ms

256×

valid

Compiler

Compiled 52 to 19 computations (63.5% saved)

Precisions

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

const: 29.0ms (59.5% of total)

ival-sub: 9.0ms (18.5% of total)

ival-mult: 5.0ms (10.3% of total)

ival-div: 4.0ms (8.2% of total)

ival-add: 2.0ms (4.1% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

13.0MiB live, 13.0MiB 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 (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 (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 1/3) (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 (- x 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 (- x 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 -1/27 (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 (- (pow x 3) 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 (- (pow x 3) 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 (- (pow x 3) 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 (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 (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt 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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt 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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (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 (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (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 (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (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>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

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))

1.0ms

((- 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))

simplify102.0ms (3.1%)

Memory

-15.0MiB live, 101.7MiB allocated

Algorithm

1×	egg-herbie

Rules

5 066×	`lower-fma.f64`
5 066×	`lower-fma.f32`
2 834×	`lower-*.f64`
2 834×	`lower-*.f32`
1 518×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	280
1	109	280
2	283	272
3	849	272
4	2408	272
5	5543	272
0	8114	265

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 76

Calls

Call 1

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

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

rewrite199.0ms (6%)

Memory

6.3MiB live, 228.8MiB allocated

Rules

4 476×	`lower-fma.f32`
4 472×	`lower-fma.f64`
4 018×	`lower-*.f32`
4 016×	`lower-*.f64`
3 298×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
0	23	28
1	87	28
2	541	28
3	6583	28
0	8054	28

Stop Event

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

Counts

7 → 807

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

eval124.0ms (3.7%)

Memory: 3.6MiB live, 248.5MiB allocated
Compiler: Compiled 28 041 to 1 668 computations (94.1% saved)

prune173.0ms (5.2%)

Memory

4.0MiB live, 162.0MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	882	1	883
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	882	4	886

Accuracy

100.0%

Counts

886 → 4

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)))
▶	51.7%	(/.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))
✓	50.6%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify6.0ms (0.2%)

Memory

11.6MiB live, 11.6MiB 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)

localize59.0ms (1.8%)

Memory

-13.5MiB live, 60.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(-.f64 x #s(literal -1/3 binary64))
accuracy	0.03515625	(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
accuracy	20.35570949372712	(/.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	30.943335710462755	#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))

Samples

50.0ms

256×

valid

Compiler

Compiled 38 to 13 computations (65.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

const: 8.0ms (40.5% of total)

ival-mult: 5.0ms (25.3% of total)

ival-add: 3.0ms (15.2% of total)

ival-div: 2.0ms (10.1% of total)

ival-sub: 1.0ms (5.1% of total)

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

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

series3.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB 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 (- x 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 (- x 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 (- x 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 -1/27 (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 (- (pow x 3) 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 (- (pow x 3) 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 (- (pow x 3) 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 1/9 (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* 1/3 x)) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt 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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (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 (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (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 (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (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>) () ())) ())

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))

simplify127.0ms (3.8%)

Memory

27.9MiB live, 102.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4 890×	`lower-fma.f64`
4 890×	`lower-fma.f32`
2 784×	`lower-*.f64`
2 784×	`lower-*.f32`
1 584×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	184
1	109	184
2	283	176
3	835	176
4	2410	176
5	5488	176
0	8127	169

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 44

Calls

Call 1

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

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

rewrite372.0ms (11.2%)

Memory

-205.4MiB live, 298.6MiB 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))))
(/.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 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 (/.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 (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 (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 -1/9 binary64) (.f64 (-.f64 x #s(literal -1/3 binary64)) x))))) (-.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)) (.f64 #s(literal -1/9 binary64) (.f64 (-.f64 x #s(literal -1/3 binary64)) x))))
(/.f64 (.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 (fma.f64 #s(literal -1/9 binary64) (.f64 (-.f64 x #s(literal -1/3 binary64)) x) #s(literal 1/81 binary64)) (fma.f64 #s(literal -1/9 binary64) (.f64 (-.f64 x #s(literal -1/3 binary64)) x) #s(literal 1/81 binary64))) (fma.f64 #s(literal -1/9 binary64) (.f64 (-.f64 x #s(literal -1/3 binary64)) x) #s(literal 1/81 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 x #s(literal -1/3 binary64)) x) x) (-.f64 x #s(literal -1/3 binary64))) (.f64 (.f64 (.f64 (-.f64 x #s(literal -1/3 binary64)) x) x) (-.f64 x #s(literal -1/3 binary64)))) (.f64 (.f64 (.f64 (-.f64 x #s(literal -1/3 binary64)) x) x) (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 x #s(literal -1/3 binary64)) x) x) (-.f64 x #s(literal -1/3 binary64))) (.f64 (.f64 (-.f64 x #s(literal -1/3 binary64)) (-.f64 x #s(literal -1/3 binary64))) x)) x (.f64 (fma.f64 #s(literal -1/9 binary64) (.f64 (-.f64 x #s(literal -1/3 binary64)) x) #s(literal 1/81 binary64)) (-.f64 (fma.f64 #s(literal -1/9 binary64) (.f64 (-.f64 x #s(literal -1/3 binary64)) x) #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 (.f64 (neg.f64 #s(approx (+ ( (* x x) x) -1/27) #s(literal -1/27 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal -1/9 binary64) (*.f64 (-.f64 x #s(literal -1/3 binary64)) x)))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ ( (* x x) x) -1/27) #s(literal -1/27 binary64)))) (-.f64 #s(literal -1/9 binary64) (*.f64 (-.f64 x #s(literal -1/3 binary64)) x)))
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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))

eval41.0ms (1.2%)

Memory: -12.7MiB live, 107.0MiB allocated
Compiler: Compiled 8 293 to 855 computations (89.7% saved)

prune34.0ms (1%)

Memory

13.2MiB live, 88.1MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	293	1	294
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	294	4	298

Accuracy

100.0%

Counts

298 → 4

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)))
▶	50.8%	(/.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))
✓	50.6%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify5.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB 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)

localize44.0ms (1.3%)

Memory

0.8MiB live, 83.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.03515625	(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
accuracy	20.35570949372712	(/.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	30.943335710462755	#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
accuracy	31.511845212737352	#s(approx (- x -1/3) #s(literal 1/3 binary64))

Samples

37.0ms

256×

valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

const: 16.0ms (53.5% of total)

ival-add: 5.0ms (16.7% of total)

ival-mult: 5.0ms (16.7% of total)

ival-div: 2.0ms (6.7% of total)

ival-sub: 1.0ms (3.3% of total)

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

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

series3.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB 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 (- x 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 (- x 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 (- x 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 -1/27 (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 (- (pow x 3) 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 (- (pow x 3) 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 (- (pow x 3) 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 1/9 (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 (+ 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 (+ 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 1/3 (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 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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (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 (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (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 (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (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>) () ())) ())

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))

simplify114.0ms (3.4%)

Memory

-24.0MiB live, 88.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4 890×	`lower-fma.f64`
4 890×	`lower-fma.f32`
2 784×	`lower-*.f64`
2 784×	`lower-*.f32`
1 584×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	184
1	109	184
2	283	176
3	835	176
4	2410	176
5	5488	176
0	8127	169

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 44

Calls

Call 1

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

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

rewrite451.0ms (13.6%)

Memory

3.2MiB live, 216.4MiB 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))
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(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) (.f64 (.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x)) (.f64 (.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x)) (.f64 (.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 (.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x)) (.f64 (.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x)) #s(literal 1/387420489 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)) (fma.f64 (.f64 (.f64 (.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) (.f64 (.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) 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) (.f64 (.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x)) (-.f64 #s(literal 1/531441 binary64) (.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 (.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal 1/729 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))) (*.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)))))
(/.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)) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))
(/.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))

eval38.0ms (1.1%)

Memory: 4.5MiB live, 76.8MiB allocated
Compiler: Compiled 6 787 to 647 computations (90.5% saved)

prune37.0ms (1.1%)

Memory

22.6MiB live, 59.5MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	250	4	254

Accuracy

100.0%

Counts

254 → 4

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)))
✓	50.8%	(/.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))
✓	50.6%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Compiler

Compiled 71 to 38 computations (46.5% saved)

regimes212.0ms (6.4%)

Memory

-33.2MiB live, 15.0MiB 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:

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

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0.1%)

Memory

7.1MiB live, 7.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
50.6%	1	`x`
50.6%	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

13.3MiB live, 13.3MiB 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))

soundness160.0ms (4.8%)

Memory

-16.9MiB live, 144.1MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

preprocess21.0ms (0.6%)

Memory: 17.7MiB live, 55.7MiB 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%)

sample471.0ms (14.2%)

explain58.0ms (1.8%)

preprocess13.0ms (0.4%)

eval4.0ms (0.1%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize12.0ms (0.4%)

series1.0ms (0%)

simplify21.0ms (0.6%)

rewrite174.0ms (5.3%)

eval41.0ms (1.2%)

prune100.0ms (3%)

simplify6.0ms (0.2%)

localize72.0ms (2.2%)

series6.0ms (0.2%)

simplify102.0ms (3.1%)

rewrite199.0ms (6%)

eval124.0ms (3.7%)

prune173.0ms (5.2%)

simplify6.0ms (0.2%)

localize59.0ms (1.8%)

series3.0ms (0.1%)

simplify127.0ms (3.8%)

rewrite372.0ms (11.2%)

eval41.0ms (1.2%)

prune34.0ms (1%)

simplify5.0ms (0.1%)

localize44.0ms (1.3%)

series3.0ms (0.1%)

simplify114.0ms (3.4%)

rewrite451.0ms (13.6%)

eval38.0ms (1.1%)

prune37.0ms (1.1%)

regimes212.0ms (6.4%)

regimes3.0ms (0.1%)

simplify6.0ms (0.2%)

soundness160.0ms (4.8%)

preprocess21.0ms (0.6%)

end0.0ms (0%)

Profiling