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

0.5MiB live, 0.5MiB 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)

sample506.0ms (13.3%)

Memory

-11.7MiB live, 912.7MiB allocated

Samples

295.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 141.0ms

ival-div: 84.0ms (59.4% of total)

ival-sub: 42.0ms (29.7% of total)

exact: 7.0ms (5% of total)

ival-true: 5.0ms (3.5% of total)

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

Bogosity

explain55.0ms (1.5%)

Memory

-18.0MiB live, 113.4MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

20.0ms

512×

valid

Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions

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

ival-div: 4.0ms (52.7% of total)

ival-sub: 2.0ms (26.4% of total)

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

exact: 0.0ms (0% of total)

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

preprocess161.0ms (4.2%)

Memory

-2.9MiB live, 34.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 5 to 5 computations (0% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 5 computations (0% saved)

simplify4.0ms (0.1%)

Memory

7.6MiB live, 7.6MiB 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)

localize27.0ms (0.7%)

Memory

-4.3MiB live, 34.7MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

23.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

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

ival-div: 2.0ms (53.8% of total)

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

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Counts

2 → 12

Calls

Call 1

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

Inputs

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

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

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

Calls

3 calls:

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

simplify23.0ms (0.6%)

Memory

-9.6MiB live, 28.4MiB 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))

rewrite214.0ms (5.6%)

Memory

8.5MiB live, 281.5MiB 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 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/81 binary64))) (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/729 binary64))) (pow.f64 (+.f64 (hypot.f64 (.f64 x x) (.f64 #s(literal -1/3 binary64) x)) #s(literal 1/81 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/729 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/27 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/19683 binary64))) (pow.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64)) (+.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #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 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) #s(literal 2 binary64))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) (hypot.f64 (pow.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 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))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (pow.f64 (-.f64 #s(literal -1/3 binary64) x) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(*.f64 (pow.f64 (pow.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/81 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal -1/3 binary64) x)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal -1/3 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 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)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)))) (pow.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/81 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (neg.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/81 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)))) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/81 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/27 binary64))) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (-.f64 x #s(literal 1/3 binary64)))) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/729 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (pow.f64 (+.f64 (hypot.f64 (.f64 x x) (*.f64 #s(literal -1/3 binary64) x)) #s(literal 1/81 binary64)) #s(literal -1 binary64)) (neg.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/729 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)))) (/.f64 (pow.f64 (+.f64 (hypot.f64 (.f64 x x) (*.f64 #s(literal -1/3 binary64) x)) #s(literal 1/81 binary64)) #s(literal -1 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/729 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/27 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/729 binary64)) (hypot.f64 (pow.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/27 binary64)) #s(literal -1 binary64)) (pow.f64 (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))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/19683 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64)) (+.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/19683 binary64)) (hypot.f64 (pow.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (pow.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64)) (+.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (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))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/81 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (-.f64 x #s(literal -1/3 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/729 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (+.f64 (hypot.f64 (.f64 x x) (*.f64 #s(literal -1/3 binary64) x)) #s(literal 1/81 binary64)) #s(literal -1 binary64)) (-.f64 x #s(literal -1/3 binary64))))
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(+.f64 (.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) #s(literal -1/9 binary64)) (.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (*.f64 x x)))
(+.f64 (.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (.f64 x x)) (*.f64 (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) #s(literal -1/9 binary64)))
(+.f64 (.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #s(literal -1 binary64)) #s(literal -1/27 binary64)) (.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))))
(+.f64 (.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #s(literal -1 binary64)) #s(literal -1/27 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) x) #s(literal -1/3 binary64))
(+.f64 (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))))
(+.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(+.f64 (.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(+.f64 #s(literal -1/3 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))

eval42.0ms (1.1%)

Memory: -10.6MiB live, 109.9MiB allocated
Compiler: Compiled 8 049 to 759 computations (90.6% saved)

prune6.0ms (0.1%)

Memory

25.0MiB live, 25.0MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Accuracy

100.0%

Counts

324 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.6%	(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
▶	100.0%	(-.f64 x #s(literal 1/3 binary64))
▶	48.9%	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Status

Accuracy

Program

▶

72.6%

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

▶

100.0%

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

▶

48.9%

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

Compiler

Compiled 25 to 16 computations (36% saved)

simplify7.0ms (0.2%)

Memory

-24.5MiB live, 13.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize85.0ms (2.2%)

Memory

0.9MiB live, 123.2MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
accuracy	0.48321865321703034	(/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	16.337696306597184	(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
accuracy	16.544874095543395	(/.f64 x (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	0.00390625	(-.f64 x #s(literal 1/3 binary64))
accuracy	32.68310577172492	#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

Samples

62.0ms	241×	0	valid
5.0ms	8×	2	valid
2.0ms	7×	1	valid

Compiler

Compiled 71 to 20 computations (71.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

const: 33.0ms (55.8% of total)

ival-mult: 13.0ms (22% of total)

ival-div: 6.0ms (10.1% of total)

ival-sub: 4.0ms (6.8% of total)

ival-add: 2.0ms (3.4% of total)

adjust: 1.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.2%)

Memory

15.6MiB live, 15.6MiB allocated

Counts

8 → 96

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

2.0ms

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

simplify356.0ms (9.4%)

Memory

21.8MiB live, 243.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 88

Calls

Call 1

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

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

rewrite433.0ms (11.4%)

Memory

-29.6MiB live, 391.0MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

8 → 673

Calls

Call 1

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

Outputs
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/27 binary64)))) (fma.f64 x x (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1/9 binary64))) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #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 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))))
(*.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(*.f64 (fma.f64 x (neg.f64 x) #s(literal 1/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1 binary64) x #s(literal -1/3 binary64))))
(*.f64 (neg.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/729 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1/27 binary64)) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))))
(.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -3 binary64)) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -2 binary64)) (/.f64 (-.f64 #s(literal 1/729 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/27 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64)))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (neg.f64 x) (-.f64 x #s(literal -1/3 binary64)) #s(literal -1/9 binary64)) (.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64)))))
(.f64 (fma.f64 (pow.f64 x #s(literal 3 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)) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64))))
(.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -27 binary64)) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64)) #s(literal -27 binary64))))
(.f64 (fma.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) (.f64 (fma.f64 (neg.f64 x) (-.f64 x #s(literal -1/3 binary64)) #s(literal -1/9 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64)))))
(.f64 (fma.f64 #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)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64))))
(.f64 (+.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) (.f64 (.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -27 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -27 binary64)) (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)) (pow.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) (+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal -1/3 binary64)) x) #s(literal 2 binary64)) #s(literal 1/81 binary64))) (/.f64 #s(literal -1/27 binary64) (-.f64 (pow.f64 (*.f64 (-.f64 x #s(literal -1/3 binary64)) x) #s(literal 2 binary64)) #s(literal 1/81 binary64)))))
(.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) (+.f64 (/.f64 #s(literal -1/27 binary64) (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal -1/3 binary64)) x) #s(literal 2 binary64)) #s(literal 1/81 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 (*.f64 (-.f64 x #s(literal -1/3 binary64)) x) #s(literal 2 binary64)) #s(literal 1/81 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/729 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64))) (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #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 (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/27 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -1 binary64)))
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eval746.0ms (19.6%)

Memory: 27.7MiB live, 138.9MiB allocated
Compiler: Compiled 29 206 to 2 012 computations (93.1% saved)

prune376.0ms (9.9%)

Memory

10.0MiB live, 46.0MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Accuracy

100.0%

Counts

956 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

51.6%

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

✓

100.0%

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

✓

48.9%

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

Compiler

Compiled 21 to 18 computations (14.3% saved)

simplify9.0ms (0.2%)

Memory

-29.9MiB live, 9.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize48.0ms (1.3%)

Memory

23.2MiB live, 106.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
accuracy	0.48321865321703034	(/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy	16.337696306597184	(fma.f64 (.f64 x x) #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x)) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
accuracy	32.58179927255314	#s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x))

Samples

31.0ms	241×	0	valid
6.0ms	8×	2	valid
2.0ms	7×	1	valid

Compiler

Compiled 64 to 16 computations (75% saved)

Precisions

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

const: 10.0ms (33.8% of total)

ival-mult: 9.0ms (30.4% of total)

ival-div: 4.0ms (13.5% of total)

ival-sub: 4.0ms (13.5% of total)

ival-add: 3.0ms (10.1% of total)

adjust: 1.0ms (3.4% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.2%)

Memory

-23.1MiB live, 14.6MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify147.0ms (3.9%)

Memory

26.7MiB live, 260.6MiB allocated

Algorithm

1×	egg-herbie

Rules

10 444×	`lower-fma.f64`
10 444×	`lower-fma.f32`
3 058×	`lower-*.f64`
3 058×	`lower-*.f32`
2 528×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	121	460
1	340	456
2	833	456
3	2487	428
4	6793	428
0	8165	412

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 70

Calls

Call 1

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

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

rewrite224.0ms (5.9%)

Memory

-3.0MiB live, 248.5MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	56
0	24	56
1	88	56
2	591	56
3	6576	56
0	8126	56

Stop Event

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

Counts

6 → 249

Calls

Call 1

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

Outputs
(.f64 (/.f64 (fma.f64 (pow.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/729 binary64) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64)))) (fma.f64 (pow.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal 1/19683 binary64) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -3 binary64))))) (fma.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) #s(literal 2 binary64))))
(.f64 (/.f64 (fma.f64 (pow.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x))) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) #s(literal 2 binary64)))) (fma.f64 (pow.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (-.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x))))))
(.f64 (/.f64 (fma.f64 (pow.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 3 binary64))) (hypot.f64 (pow.f64 (.f64 (-.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x))) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) #s(literal 3/2 binary64)) (pow.f64 (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (-.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x))) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (-.f64 (.f64 (-.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x))) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) #s(literal 2 binary64))) (pow.f64 (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (pow.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/729 binary64) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64)))) (fma.f64 (pow.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/729 binary64) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64))))) (fma.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))))
(.f64 (fma.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal -2 binary64)) #s(literal 1/729 binary64) (.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)))))
(.f64 (pow.f64 (fma.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) #s(literal -1 binary64)) (fma.f64 (pow.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/729 binary64) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 (fma.f64 (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 2 binary64))) #s(literal -1 binary64)) (fma.f64 (pow.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (*.f64 #s(literal 9 binary64) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 3 binary64))))
(.f64 (neg.f64 (fma.f64 (pow.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/729 binary64) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))))))
(.f64 (neg.f64 (fma.f64 (pow.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 2 binary64))))))
(.f64 (fma.f64 (pow.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/729 binary64) (pow.f64 (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))))
(.f64 (fma.f64 (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 2 binary64))) (/.f64 (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (fma.f64 (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 2 binary64)))))
(.f64 (fma.f64 (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 2 binary64))) (.f64 (fma.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (fma.f64 (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (fma.f64 (pow.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 3 binary64))) (pow.f64 (fma.f64 (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (/.f64 (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))))
(.f64 (fma.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (.f64 (fma.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) (pow.f64 (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) #s(literal -1 binary64))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) #s(literal 4 binary64)) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) #s(literal -1 binary64))) (hypot.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) #s(literal 6 binary64)) (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 6 binary64))) (pow.f64 (fma.f64 #s(approx (/ x (+ (* x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x) (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) #s(literal -1 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 2 binary64)) (hypot.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x))) (pow.f64 (.f64 #s(approx (/ x (+ ( x (- x -1/3)) 1/9)) (.f64 #s(literal 9 binary64) x)) (.f64 x x)) #s(literal 4 binary64))))
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eval56.0ms (1.5%)

Memory: -23.5MiB live, 96.1MiB allocated
Compiler: Compiled 10 547 to 927 computations (91.2% saved)

prune7.0ms (0.2%)

Memory

23.4MiB live, 23.4MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	319	0	319
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	319	3	322

Accuracy

100.0%

Counts

322 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

51.6%

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

✓

100.0%

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

✓

48.9%

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

Compiler

Compiled 67 to 39 computations (41.8% saved)

regimes38.0ms (1%)

Memory

-24.5MiB live, 14.7MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

35.0ms	(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
2.0ms	x

Results

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

Compiler

Compiled 6 to 6 computations (0% saved)

regimes3.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 6 to 6 computations (0% saved)

simplify29.0ms (0.8%)

Memory

-8.9MiB live, 67.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness120.0ms (3.2%)

Memory

-0.9MiB live, 156.8MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 14 to 14 computations (0% saved)

preprocess62.0ms (1.6%)

Memory: 16.4MiB live, 106.3MiB allocated
Compiler: Compiled 20 to 20 computations (0% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample506.0ms (13.3%)

explain55.0ms (1.5%)

preprocess161.0ms (4.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize27.0ms (0.7%)

series1.0ms (0%)

simplify23.0ms (0.6%)

rewrite214.0ms (5.6%)

eval42.0ms (1.1%)

prune6.0ms (0.1%)

simplify7.0ms (0.2%)

localize85.0ms (2.2%)

series8.0ms (0.2%)

simplify356.0ms (9.4%)

rewrite433.0ms (11.4%)

eval746.0ms (19.6%)

prune376.0ms (9.9%)

simplify9.0ms (0.2%)

localize48.0ms (1.3%)

series7.0ms (0.2%)

simplify147.0ms (3.9%)

rewrite224.0ms (5.9%)

eval56.0ms (1.5%)

prune7.0ms (0.2%)

regimes38.0ms (1%)

regimes3.0ms (0.1%)

simplify29.0ms (0.8%)

soundness120.0ms (3.2%)

preprocess62.0ms (1.6%)

end0.0ms (0%)

Profiling