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

analyze0.0ms (0%)

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 6 computations (14.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample689.0ms (15.3%)

Results

495.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 165.0ms

ival-div: 91.0ms (55.2% of total)

ival-add: 59.0ms (35.8% of total)

const: 13.0ms (7.9% of total)

backward-pass: 3.0ms (1.8% of total)

Bogosity

preprocess188.0ms (4.2%)

Algorithm

2×	egg-herbie

Rules

80×	`fnmsub-define`
80×	`fmsub-define`
80×	`fnmadd-define`
58×	`fmm-def`
56×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	22	9
2	46	9
3	97	9
4	171	9
5	259	9
6	291	9
7	309	9
8	323	9
9	327	9
0	6	3
1	9	3
0	9	3

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ x (/ 1 3))

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

Call 2

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

Outputs
(+ x (/ 1 3))
(+ x 1/3)
(+ (neg x) (/ 1 3))
(- 1/3 x)
(neg (+ (neg x) (/ 1 3)))
(+ x -1/3)

explain59.0ms (1.3%)

FPErrors

Click to see full error table

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

Results

36.0ms

512×

valid

Compiler

Compiled 32 to 17 computations (46.9% saved)

Precisions

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

ival-div: 5.0ms (59.9% of total)

ival-add: 3.0ms (36% of total)

const: 1.0ms (12% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 4 to 3 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

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

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
1	4	5
0	4	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize22.0ms (0.5%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1/3 binary64))

Results

17.0ms

256×

valid

Compiler

Compiled 7 to 4 computations (42.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

...c/correct-round.rkt:119:19: 4.0ms (70% of total)

ival-add: 2.0ms (35% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (+ x 1/3)>

Outputs
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>

Calls

3 calls:

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

rewrite312.0ms (6.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3890×	`/-lowering-/.f32`
3890×	`/-lowering-/.f64`
3454×	`-lowering-.f32`
3454×	`-lowering-.f64`
2388×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	19	3
2	125	3
3	1011	3
0	8524	3

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 185

Calls

Call 1

Inputs
(+ x 1/3)

Outputs
(+.f64 x #s(literal 1/3 binary64))
(+.f64 #s(literal 1/3 binary64) x)
(+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1 binary64)))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) x)))
(+.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(+.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) x)) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x #s(literal -1/3 binary64))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1/9 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal 1/9 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1/9 binary64))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x #s(literal -1/3 binary64))) (neg.f64 (.f64 (+.f64 x #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))))) (fma.f64 (+.f64 #s(literal -1/3 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (.f64 (+.f64 x #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64))))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x #s(literal -1/3 binary64))) (neg.f64 (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)))))) (fma.f64 (+.f64 (+.f64 #s(literal -1/9 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1/9 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal 1/9 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1/9 binary64))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (neg.f64 (.f64 (+.f64 x #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))))) (fma.f64 (+.f64 #s(literal -1/3 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (.f64 (+.f64 x #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (neg.f64 (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)))))) (fma.f64 (+.f64 (+.f64 #s(literal -1/9 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (*.f64 x x)) #s(literal -1/27 binary64))))))
(+.f64 (fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (+.f64 x #s(literal 1/3 binary64)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1/9 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal 1/9 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1/9 binary64))))
(+.f64 (fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (+.f64 x #s(literal 1/3 binary64)) (neg.f64 (.f64 (+.f64 x #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))))) (fma.f64 (+.f64 #s(literal -1/3 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (.f64 (+.f64 x #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64))))))
(+.f64 (fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (+.f64 x #s(literal 1/3 binary64)) (neg.f64 (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)))))) (fma.f64 (+.f64 (+.f64 #s(literal -1/9 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))))))
(+.f64 (fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1/9 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal 1/9 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1/9 binary64))))
(+.f64 (fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (neg.f64 (.f64 (+.f64 x #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))))) (fma.f64 (+.f64 #s(literal -1/3 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (.f64 (+.f64 x #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))))))
(+.f64 (fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (neg.f64 (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)))))) (fma.f64 (+.f64 (+.f64 #s(literal -1/9 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x (*.f64 x x)) #s(literal -1/27 binary64))))))
(+.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/3 binary64))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) #s(literal 1/27 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) #s(literal 1/27 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (.f64 x (.f64 x x))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (*.f64 x x)))
(+.f64 (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))))))) (.f64 (.f64 x x) (.f64 x x))) (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))))))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (*.f64 x x)))))
(+.f64 (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))))))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 x x)))) (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))))))) (.f64 (.f64 x x) (*.f64 x x))))
(+.f64 (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (.f64 x #s(literal 1/3 binary64))))) (.f64 x x)) (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (.f64 x #s(literal 1/3 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))))))
(+.f64 (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (.f64 x #s(literal 1/3 binary64))))) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (.f64 x #s(literal 1/3 binary64))))) (.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (.f64 x x)) (.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))))
(+.f64 (.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))) (.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (.f64 x x)))
(+.f64 (.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (+.f64 (.f64 x x) #s(literal 1/9 binary64))) (.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (.f64 x #s(literal 1/3 binary64))))
(+.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1/3 binary64))
(+.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal 1 binary64)))
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(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/19683 binary64)) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64)) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x x)) #s(literal -1/27 binary64))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64)) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/81 binary64) (.f64 (*.f64 x x) #s(literal 1/9 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64)) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))))))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 x x)))))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (.f64 x #s(literal 1/3 binary64))))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (*.f64 x #s(literal 1/3 binary64))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (.f64 x #s(literal 1/3 binary64))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (*.f64 x #s(literal 1/3 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal 1/3 binary64)))))))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/81 binary64) (.f64 (*.f64 x x) #s(literal 1/9 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/19683 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x x)) #s(literal -1/27 binary64))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/19683 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 x x)))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/19683 binary64)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (.f64 x #s(literal 1/3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (*.f64 x #s(literal 1/3 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x #s(literal -1/3 binary64))) (*.f64 x x)))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (.f64 x #s(literal 1/3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (.f64 x #s(literal 1/3 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64)) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) #s(literal 1/9 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/3 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64)) (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) #s(literal 1/9 binary64))))) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/81 binary64) (.f64 (*.f64 x x) #s(literal 1/9 binary64))))) (+.f64 x #s(literal -1/3 binary64))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) #s(literal 1/9 binary64))))) (+.f64 #s(literal -1/9 binary64) (neg.f64 (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/3 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64)) (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal 1/9 binary64))) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))) (+.f64 x #s(literal -1/3 binary64))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal 1/9 binary64))) (+.f64 #s(literal -1/9 binary64) (neg.f64 (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/729 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/81 binary64) (.f64 (*.f64 x x) #s(literal 1/9 binary64))))) (-.f64 #s(literal 1/3 binary64) x)))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))) (-.f64 #s(literal 1/3 binary64) x)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/3 binary64))) #s(literal -1/2 binary64)))

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

36×	`-lowering-.f32`
36×	`-lowering-.f64`
28×	`fma-define`
24×	`fma-lowering-fma.f32`
24×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	23	30
2	43	30
3	93	30
4	93	30
5	96	30
6	98	30
7	98	30
0	98	30

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

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

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

eval24.0ms (0.5%)

Compiler: Compiled 6446 to 536 computations (91.7% saved)

prune40.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	191	6	197
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	191	7	198

Accuracy

100.0%

Counts

198 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.8%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64))))
	68.2%	(/.f64 (-.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))
▶	75.9%	(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x))
✓	100.0%	(+.f64 x #s(literal 1/3 binary64))
▶	75.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))
▶	52.8%	x
▶	48.5%	#s(literal 1/3 binary64)

Compiler

Compiled 116 to 83 computations (28.4% saved)

simplify90.0ms (2%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64)))
✓	cost-diff	0	(+.f64 x #s(literal -1/3 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64)))
✓	cost-diff	256	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64))))
✓	cost-diff	0	(+.f64 (*.f64 x x) #s(literal -1/9 binary64))
✓	cost-diff	0	(+.f64 x #s(literal -1/3 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64)))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))
✓	cost-diff	0	(-.f64 #s(literal 1/3 binary64) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x))

Rules

1056×	`fnmadd-define`
882×	`fma-define`
652×	`fmsub-define`
644×	`fnmsub-define`
622×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	77
1	46	77
2	100	77
3	203	77
4	346	77
5	582	77
6	1265	77
7	2210	77
8	3185	77
9	3609	77
10	3646	77
11	3654	77
0	3654	77

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize127.0ms (2.8%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64)))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/3 binary64))
✓	accuracy	99.3%	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64)))
✓	accuracy	76.6%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64))))
✓	accuracy	100.0%	(+.f64 (*.f64 x x) #s(literal -1/9 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64)))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/3 binary64))
✓	accuracy	75.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
✓	accuracy	100.0%	(-.f64 #s(literal 1/3 binary64) x)
✓	accuracy	75.9%	(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x))

Results

96.0ms

256×

valid

Compiler

Compiled 98 to 17 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 25.0ms (47.3% of total)

...c/correct-round.rkt:119:19: 13.0ms (24.6% of total)

ival-div: 8.0ms (15.1% of total)

ival-sub: 3.0ms (5.7% of total)

ival-add: 3.0ms (5.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series5.0ms (0.1%)

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (/ (- 1/9 (* x x)) (- 1/3 x))>
#<alt (- 1/9 (* x x))>
#<alt (* x x)>
#<alt (- 1/3 x)>
#<alt (* (/ 1 (+ x -1/3)) (+ (* x x) -1/9))>
#<alt (/ 1 (+ x -1/3))>
#<alt (+ x -1/3)>
#<alt (+ (* x x) -1/9)>
#<alt (/ (/ 1 (+ x -1/3)) (/ 1 (+ (* x x) -1/9)))>
#<alt (/ 1 (+ (* x x) -1/9))>

Outputs
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt 1/9>
#<alt (+ 1/9 (* -1 (pow x 2)))>
#<alt (+ 1/9 (* -1 (pow x 2)))>
#<alt (+ 1/9 (* -1 (pow x 2)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/3>
#<alt (+ 1/3 (* -1 x))>
#<alt (+ 1/3 (* -1 x))>
#<alt (+ 1/3 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/3 (/ 1 x)) 1))>
#<alt (* x (- (* 1/3 (/ 1 x)) 1))>
#<alt (* x (- (* 1/3 (/ 1 x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* x (- 1 (* 1/3 (/ 1 x)))))>
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt -3>
#<alt (- (* -9 x) 3)>
#<alt (- (* x (- (* -27 x) 9)) 3)>
#<alt (- (* x (- (* x (- (* -81 x) 27)) 9)) 3)>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* 1/3 (/ 1 x))) x)>
#<alt (/ (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))) x)>
#<alt (/ (+ 1 (+ (/ 1/9 (pow x 2)) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3)))))) x)>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* 1/3 (/ 1 x))) x)>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/3 (* 1/9 (/ 1 x))) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/3 (+ (/ 1/27 (pow x 2)) (* 1/9 (/ 1 x)))) x)) 1) x))>
#<alt -1/3>
#<alt (- x 1/3)>
#<alt (- x 1/3)>
#<alt (- x 1/3)>
#<alt x>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt -1/9>
#<alt (- (pow x 2) 1/9)>
#<alt (- (pow x 2) 1/9)>
#<alt (- (pow x 2) 1/9)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))>
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt -9>
#<alt (- (* -81 (pow x 2)) 9)>
#<alt (- (* (pow x 2) (- (* -729 (pow x 2)) 81)) 9)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -6561 (pow x 2)) 729)) 81)) 9)>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1/81 (pow x 4)) (* 1/9 (/ 1 (pow x 2))))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1/81 (pow x 4)) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6)))))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1/81 (pow x 4)) (* 1/9 (/ 1 (pow x 2))))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1/81 (pow x 4)) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6)))))) (pow x 2))>

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/ 1 (+ (* x x) -1/9))
0.0ms	x	@	inf	(/ (- 1/9 (* x x)) (- 1/3 x))
0.0ms	x	@	0	(/ (- 1/9 (* x x)) (- 1/3 x))
0.0ms	x	@	-inf	(* (/ 1 (+ x -1/3)) (+ (* x x) -1/9))
0.0ms	x	@	0	(* (/ 1 (+ x -1/3)) (+ (* x x) -1/9))

rewrite369.0ms (8.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4684×	`-lowering-.f32`
4684×	`-lowering-.f64`
3842×	`/-lowering-/.f32`
3842×	`/-lowering-/.f64`
1712×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	124	34
2	1002	34
0	9160	34

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 1450

Calls

Call 1

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

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

simplify207.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

2300×	`-lowering-.f32`
2300×	`-lowering-.f64`
1588×	`fnmadd-define`
1390×	`fma-lowering-fma.f32`
1390×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	113	560
1	287	472
2	676	472
3	1737	472
4	4393	470
0	8318	470

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
1/9
(+ 1/9 (* -1 (pow x 2)))
(+ 1/9 (* -1 (pow x 2)))
(+ 1/9 (* -1 (pow x 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/3
(+ 1/3 (* -1 x))
(+ 1/3 (* -1 x))
(+ 1/3 (* -1 x))
(* -1 x)
(* x (- (* 1/3 (/ 1 x)) 1))
(* x (- (* 1/3 (/ 1 x)) 1))
(* x (- (* 1/3 (/ 1 x)) 1))
(* -1 x)
(* -1 (* x (- 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (- 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (- 1 (* 1/3 (/ 1 x)))))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
-3
(- (* -9 x) 3)
(- (* x (- (* -27 x) 9)) 3)
(- (* x (- (* x (- (* -81 x) 27)) 9)) 3)
(/ 1 x)
(/ (+ 1 (* 1/3 (/ 1 x))) x)
(/ (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))) x)
(/ (+ 1 (+ (/ 1/9 (pow x 2)) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3)))))) x)
(/ 1 x)
(/ (+ 1 (* 1/3 (/ 1 x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/3 (* 1/9 (/ 1 x))) x)) 1) x))
(* -1 (/ (- (* -1 (/ (+ 1/3 (+ (/ 1/27 (pow x 2)) (* 1/9 (/ 1 x)))) x)) 1) x))
-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)))
-1/9
(- (pow x 2) 1/9)
(- (pow x 2) 1/9)
(- (pow x 2) 1/9)
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
-9
(- (* -81 (pow x 2)) 9)
(- (* (pow x 2) (- (* -729 (pow x 2)) 81)) 9)
(- (* (pow x 2) (- (* (pow x 2) (- (* -6561 (pow x 2)) 729)) 81)) 9)
(/ 1 (pow x 2))
(/ (+ 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 1 (+ (/ 1/81 (pow x 4)) (* 1/9 (/ 1 (pow x 2))))) (pow x 2))
(/ (+ 1 (+ (/ 1/81 (pow x 4)) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6)))))) (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 1 (+ (/ 1/81 (pow x 4)) (* 1/9 (/ 1 (pow x 2))))) (pow x 2))
(/ (+ 1 (+ (/ 1/81 (pow x 4)) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6)))))) (pow x 2))

Outputs
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #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 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* -1 (pow x 2)))
(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
(+ 1/9 (* -1 (pow x 2)))
(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
(+ 1/9 (* -1 (pow x 2)))
(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/9 (/ 1 (pow x 2))) 1))
(-.f64 #s(literal 1/9 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* -1 x))
(-.f64 #s(literal 1/3 binary64) x)
(+ 1/3 (* -1 x))
(-.f64 #s(literal 1/3 binary64) x)
(+ 1/3 (* -1 x))
(-.f64 #s(literal 1/3 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (* 1/3 (/ 1 x)) 1))
(-.f64 #s(literal 1/3 binary64) x)
(* x (- (* 1/3 (/ 1 x)) 1))
(-.f64 #s(literal 1/3 binary64) x)
(* x (- (* 1/3 (/ 1 x)) 1))
(-.f64 #s(literal 1/3 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (- 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal 1/3 binary64) x)
(* -1 (* x (- 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal 1/3 binary64) x)
(* -1 (* x (- 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal 1/3 binary64) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
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 #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)
-3
#s(literal -3 binary64)
(- (* -9 x) 3)
(+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64))
(- (* x (- (* -27 x) 9)) 3)
(+.f64 (.f64 x (+.f64 #s(literal -9 binary64) (.f64 x #s(literal -27 binary64)))) #s(literal -3 binary64))
(- (* x (- (* x (- (* -81 x) 27)) 9)) 3)
(+.f64 (.f64 x (+.f64 #s(literal -9 binary64) (.f64 x (+.f64 #s(literal -27 binary64) (*.f64 x #s(literal -81 binary64)))))) #s(literal -3 binary64))
(/ 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 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x)) x)
(/ (+ 1 (+ (/ 1/9 (pow x 2)) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3)))))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/27 binary64) (*.f64 x x)))) 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 (/ (+ 1/3 (* 1/9 (/ 1 x))) x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x)) x)
(* -1 (/ (- (* -1 (/ (+ 1/3 (+ (/ 1/27 (pow x 2)) (* 1/9 (/ 1 x)))) x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/27 binary64) (*.f64 x x)))) x)) 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))
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))
-1/9
#s(literal -1/9 binary64)
(- (pow x 2) 1/9)
(+.f64 (*.f64 x x) #s(literal -1/9 binary64))
(- (pow x 2) 1/9)
(+.f64 (*.f64 x x) #s(literal -1/9 binary64))
(- (pow x 2) 1/9)
(+.f64 (*.f64 x x) #s(literal -1/9 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(+.f64 (*.f64 x x) #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(+.f64 (*.f64 x x) #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(+.f64 (*.f64 x x) #s(literal -1/9 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(+.f64 (*.f64 x x) #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(+.f64 (*.f64 x x) #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(+.f64 (*.f64 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)
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 #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)
-9
#s(literal -9 binary64)
(- (* -81 (pow x 2)) 9)
(+.f64 #s(literal -9 binary64) (.f64 (.f64 x x) #s(literal -81 binary64)))
(- (* (pow x 2) (- (* -729 (pow x 2)) 81)) 9)
(+.f64 #s(literal -9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -81 binary64) (.f64 (.f64 x x) #s(literal -729 binary64)))))
(- (* (pow x 2) (- (* (pow x 2) (- (* -6561 (pow x 2)) 729)) 81)) 9)
(+.f64 #s(literal -9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -81 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -729 binary64) (.f64 (.f64 x x) #s(literal -6561 binary64)))))))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/9 binary64) (*.f64 x x))) x) x)
(/ (+ 1 (+ (/ 1/81 (pow x 4)) (* 1/9 (/ 1 (pow x 2))))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1/9 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/81 binary64) (.f64 x (.f64 x (.f64 x x)))))) (*.f64 x x))
(/ (+ 1 (+ (/ 1/81 (pow x 4)) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6)))))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1/9 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/81 binary64) (.f64 x (.f64 x (.f64 x x))))))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* 1/9 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/9 binary64) (*.f64 x x))) x) x)
(/ (+ 1 (+ (/ 1/81 (pow x 4)) (* 1/9 (/ 1 (pow x 2))))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1/9 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/81 binary64) (.f64 x (.f64 x (.f64 x x)))))) (*.f64 x x))
(/ (+ 1 (+ (/ 1/81 (pow x 4)) (+ (* 1/9 (/ 1 (pow x 2))) (* 1/729 (/ 1 (pow x 6)))))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1/9 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/81 binary64) (.f64 x (.f64 x (.f64 x x))))))) (*.f64 x x))

eval275.0ms (6.1%)

Compiler: Compiled 51386 to 2955 computations (94.2% saved)

prune281.0ms (6.2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	1965	1	1966
Fresh	0	1	1
Picked	2	3	5
Done	0	1	1
Total	1967	6	1973

Accuracy

100.0%

Counts

1973 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.3%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -9 binary64))
▶	68.2%	(/.f64 (-.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))
✓	75.9%	(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x))
✓	100.0%	(+.f64 x #s(literal 1/3 binary64))
✓	52.8%	x
✓	48.5%	#s(literal 1/3 binary64)

Compiler

Compiled 42 to 31 computations (26.2% saved)

simplify180.0ms (4%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x #s(literal -1/3 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64)))
✓	cost-diff	128	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -9 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(-.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64))
✓	cost-diff	0	(/.f64 (-.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))

Rules

1968×	`fnmadd-define`
1374×	`fmsub-define`
1298×	`fnmsub-define`
1168×	`fma-define`
1102×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	39	56
2	76	56
3	106	56
4	141	56
5	224	56
6	430	56
7	858	56
8	1672	56
9	4099	56
10	5332	56
11	5674	56
12	6035	56
13	6746	56
14	6866	56
15	6908	56
16	6970	56
17	6994	56
0	6994	56

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize123.0ms (2.7%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64)))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/3 binary64))
✓	accuracy	99.8%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -9 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64))))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.7%	(*.f64 x (+.f64 x #s(literal -1/3 binary64)))
✓	accuracy	68.8%	(/.f64 (-.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))

Results

103.0ms

256×

valid

Compiler

Compiled 70 to 16 computations (77.1% saved)

Precisions

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

...c/correct-round.rkt:119:19: 15.0ms (48.9% of total)

ival-mult: 6.0ms (19.6% of total)

ival-div: 5.0ms (16.3% of total)

ival-add: 3.0ms (9.8% of total)

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

const: 1.0ms (3.3% of total)

backward-pass: 0.0ms (0% of total)

series6.0ms (0.1%)

Counts

9 → 108

Calls

Call 1

Inputs
#<alt (/ (- (* x (* x x)) -1/27) (+ 1/9 (* x (+ x -1/3))))>
#<alt (- (* x (* x x)) -1/27)>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (/ (/ 1 (+ x -1/3)) -9)>
#<alt (/ 1 (+ x -1/3))>
#<alt (+ x -1/3)>
#<alt (* x (+ x -1/3))>
#<alt (+ 1/9 (* x (+ x -1/3)))>

Outputs
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt 1/27>
#<alt (+ 1/27 (pow x 3))>
#<alt (+ 1/27 (pow x 3))>
#<alt (+ 1/27 (pow x 3))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 1 (* 1/27 (/ 1 (pow x 3)))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 (* x (+ 1 (* 3 x))))>
#<alt (+ 1/3 (* x (+ 1 (* x (+ 3 (* 9 x))))))>
#<alt (/ -1/9 x)>
#<alt (* -1 (/ (+ 1/9 (* 1/27 (/ 1 x))) x))>
#<alt (/ (- (* -1 (/ (+ 1/27 (* 1/81 (/ 1 x))) x)) 1/9) x)>
#<alt (/ (- (* -1 (/ (+ 1/81 (* 1/243 (/ 1 x))) (pow x 2))) (+ 1/9 (* 1/27 (/ 1 x)))) x)>
#<alt (/ -1/9 x)>
#<alt (* -1 (/ (+ 1/9 (* 1/27 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 1/9 (+ (/ 1/81 (pow x 2)) (* 1/27 (/ 1 x)))) x))>
#<alt (* -1 (/ (+ 1/9 (* -1 (/ (- (* -1 (/ (+ 1/81 (* 1/243 (/ 1 x))) x)) 1/27) x))) x))>
#<alt -3>
#<alt (- (* -9 x) 3)>
#<alt (- (* x (- (* -27 x) 9)) 3)>
#<alt (- (* x (- (* x (- (* -81 x) 27)) 9)) 3)>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* 1/3 (/ 1 x))) x)>
#<alt (/ (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))) x)>
#<alt (/ (+ 1 (+ (/ 1/9 (pow x 2)) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3)))))) x)>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* 1/3 (/ 1 x))) x)>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/3 (* 1/9 (/ 1 x))) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/3 (+ (/ 1/27 (pow x 2)) (* 1/9 (/ 1 x)))) x)) 1) x))>
#<alt -1/3>
#<alt (- x 1/3)>
#<alt (- x 1/3)>
#<alt (- x 1/3)>
#<alt x>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt (* x (- 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1)))>
#<alt (* -1/3 x)>
#<alt (* x (- x 1/3))>
#<alt (* x (- x 1/3))>
#<alt (* x (- x 1/3))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 1/3 (/ 1 x))))>
#<alt (* (pow x 2) (- 1 (* 1/3 (/ 1 x))))>
#<alt (* (pow x 2) (- 1 (* 1/3 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 1/3 (/ 1 x))))>
#<alt (* (pow x 2) (- 1 (* 1/3 (/ 1 x))))>
#<alt (* (pow x 2) (- 1 (* 1/3 (/ 1 x))))>
#<alt 1/9>
#<alt (+ 1/9 (* -1/3 x))>
#<alt (+ 1/9 (* x (- x 1/3)))>
#<alt (+ 1/9 (* x (- x 1/3)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 1/3 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 1/3 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x))))>

Calls

27 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(- (* x (* x x)) -1/27)
1.0ms	x	@	0	(/ (- (* x (* x x)) -1/27) (+ 1/9 (* x (+ x -1/3))))
1.0ms	x	@	inf	(/ (- (* x (* x x)) -1/27) (+ 1/9 (* x (+ x -1/3))))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	-inf	(/ (- (* x (* x x)) -1/27) (+ 1/9 (* x (+ x -1/3))))

rewrite375.0ms (8.3%)

Algorithm

1×	batch-egg-rewrite

Rules

5454×	`-lowering-.f32`
5454×	`-lowering-.f64`
4414×	`/-lowering-/.f32`
4414×	`/-lowering-/.f64`
1562×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	100	45
2	708	37
0	8483	37

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 579

Calls

Call 1

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

Outputs
(+.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/3 binary64) x)) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) #s(literal -1/27 binary64) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))
(+.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (/.f64 #s(literal -1/27 binary64) (-.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))))
(+.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/27 binary64) (-.f64 #s(literal -1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))))
(+.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64))))) #s(literal 1/27 binary64)))
(+.f64 (/.f64 #s(literal -1/27 binary64) (-.f64 #s(literal -1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))))
(+.f64 (fma.f64 x (/.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (neg.f64 (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64))))))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))))))
(+.f64 (fma.f64 x (/.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (neg.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x)))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (neg.f64 (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64))))))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (neg.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x)))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))))))
(+.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (neg.f64 (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64))))))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))))))))
(+.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (neg.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x)))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (*.f64 x (-.f64 #s(literal 1/3 binary64) x))))))))
(+.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (neg.f64 (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64))))))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))))))
(+.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (neg.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x)))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))))))
(+.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))) (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (neg.f64 (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64))))))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))))))
(+.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))) (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (neg.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x)))))))) (fma.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) #s(literal 1/27 binary64)) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64))))))
(+.f64 (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) #s(literal 1/81 binary64)) (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (*.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))))
(+.f64 (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))) (.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) #s(literal 1/81 binary64)))
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(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))))) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (*.f64 x (+.f64 x #s(literal -1/3 binary64))))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64))))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (*.f64 x (-.f64 #s(literal 1/3 binary64) x)))))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64)))) #s(literal -1/81 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x)))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x))))) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64))))))) (+.f64 #s(literal 1/531441 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64))))))))) (+.f64 #s(literal 1/6561 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))) (-.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))) #s(literal 1/81 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64))))))) (-.f64 #s(literal 1/6561 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)) (.f64 (+.f64 x #s(literal -1/3 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))))))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (-.f64 #s(literal 1/3 binary64) x)) (+.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (.f64 x (-.f64 #s(literal 1/3 binary64) x)))) (-.f64 #s(literal 1/729 binary64) (.f64 (.f64 (+.f64 x #s(literal -1/3 binary64)) (+.f64 x #s(literal -1/3 binary64))) (.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (+.f64 x #s(literal -1/3 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 x (+.f64 x #s(literal -1/3 binary64)))))))

simplify232.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

2244×	`-lowering-.f32`
2244×	`-lowering-.f64`
1756×	`fma-define`
1682×	`fma-lowering-fma.f32`
1682×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	546
1	361	496
2	946	490
3	2713	476
4	7480	472
0	8239	472

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

eval132.0ms (2.9%)

Compiler: Compiled 24695 to 2090 computations (91.5% saved)

prune94.0ms (2.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	771	1	772
Fresh	0	0	0
Picked	1	1	2
Done	1	3	4
Total	773	5	778

Accuracy

100.0%

Counts

778 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.2%	(/.f64 (-.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))
▶	99.9%	(/.f64 (+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)) #s(literal -9 binary64))
✓	100.0%	(+.f64 x #s(literal 1/3 binary64))
✓	52.8%	x
✓	48.5%	#s(literal 1/3 binary64)

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x #s(literal -9 binary64))
✓	cost-diff	(+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64))
✓	cost-diff	(/.f64 (+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)) #s(literal -9 binary64))

Rules

4×	`fma-lowering-fma.f32`
4×	`fma-define`
4×	`+-lowering-+.f64`
4×	`-lowering-.f32`
4×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	9	16
2	10	16
0	10	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize31.0ms (0.7%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x #s(literal -9 binary64))
✓	accuracy	99.9%	(+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64))
✓	accuracy	99.9%	(/.f64 (+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)) #s(literal -9 binary64))

Results

21.0ms	245×	0	valid
2.0ms	7×	2	valid
1.0ms	4×	1	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

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

ival-mult: 3.0ms (41.5% of total)

ival-div: 2.0ms (27.6% of total)

ival-add: 2.0ms (27.6% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (/ (+ (* x -9) -3) -9)>
#<alt (+ (* x -9) -3)>
#<alt (* x -9)>

Outputs
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt -3>
#<alt (- (* -9 x) 3)>
#<alt (- (* -9 x) 3)>
#<alt (- (* -9 x) 3)>
#<alt (* -9 x)>
#<alt (* -1 (* x (+ 9 (* 3 (/ 1 x)))))>
#<alt (* -1 (* x (+ 9 (* 3 (/ 1 x)))))>
#<alt (* -1 (* x (+ 9 (* 3 (/ 1 x)))))>
#<alt (* -9 x)>
#<alt (* -1 (* x (+ 9 (* 3 (/ 1 x)))))>
#<alt (* -1 (* x (+ 9 (* 3 (/ 1 x)))))>
#<alt (* -1 (* x (+ 9 (* 3 (/ 1 x)))))>
#<alt (* -9 x)>
#<alt (* -9 x)>
#<alt (* -9 x)>
#<alt (* -9 x)>
#<alt (* -9 x)>
#<alt (* -9 x)>
#<alt (* -9 x)>
#<alt (* -9 x)>
#<alt (* -9 x)>
#<alt (* -9 x)>
#<alt (* -9 x)>
#<alt (* -9 x)>

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ (+ (* x -9) -3) -9)
0.0ms	x	@	0	(/ (+ (* x -9) -3) -9)
0.0ms	x	@	-inf	(* x -9)
0.0ms	x	@	inf	(* x -9)
0.0ms	x	@	-inf	(/ (+ (* x -9) -3) -9)

rewrite360.0ms (8%)

Algorithm

1×	batch-egg-rewrite

Rules

4606×	`/-lowering-/.f32`
4606×	`/-lowering-/.f64`
4150×	`-lowering-.f32`
4150×	`-lowering-.f64`
1772×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	33	13
2	206	13
3	1870	13
0	9040	13

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 402

Calls

Call 1

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

Outputs
(+.f64 (.f64 #s(literal -1/9 binary64) (.f64 x #s(literal -9 binary64))) #s(literal 1/3 binary64))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/9 binary64) (.f64 x #s(literal -9 binary64))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x #s(literal -9 binary64)) #s(literal -1/9 binary64)))
(+.f64 (.f64 (.f64 x #s(literal -9 binary64)) #s(literal -1/9 binary64)) #s(literal 1/3 binary64))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal -9 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/3 binary64) (/.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -9 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 81 binary64))) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64))) #s(literal -9 binary64)) (/.f64 (/.f64 #s(literal 9 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64))) #s(literal -9 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 81 binary64))) (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))) (/.f64 #s(literal 9 binary64) (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))
(-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 x #s(literal -9 binary64)) #s(literal 9 binary64)))
(-.f64 (/.f64 (/.f64 #s(literal 9 binary64) (-.f64 #s(literal -3 binary64) (.f64 x #s(literal -9 binary64)))) #s(literal -9 binary64)) (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 81 binary64))) (-.f64 #s(literal -3 binary64) (.f64 x #s(literal -9 binary64)))) #s(literal -9 binary64)))
(-.f64 (/.f64 (*.f64 x #s(literal 9 binary64)) #s(literal 9 binary64)) #s(literal -1/3 binary64))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 81 binary64))) (+.f64 (.f64 x #s(literal 9 binary64)) #s(literal -3 binary64))) #s(literal 9 binary64)) (/.f64 (/.f64 #s(literal -9 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64))) #s(literal 9 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal 27 binary64))) (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))) (/.f64 (/.f64 #s(literal 729 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal 27 binary64))) (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal 27 binary64))) (.f64 #s(literal 9 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))) (/.f64 (/.f64 #s(literal 729 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal 27 binary64))) (.f64 #s(literal 9 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x))))) (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))) (/.f64 (/.f64 #s(literal 729 binary64) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x))))) (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))) (/.f64 (/.f64 #s(literal 81 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))) (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)) (neg.f64 (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 #s(literal 9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))) (-.f64 #s(literal -1/3 binary64) (/.f64 (.f64 x #s(literal -9 binary64)) #s(literal -9 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 #s(literal -9 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))) (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)) (.f64 #s(literal -9 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (neg.f64 (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 #s(literal 9 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -9 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 #s(literal -9 binary64) (+.f64 (.f64 x #s(literal 9 binary64)) #s(literal -3 binary64)))) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (.f64 #s(literal -9 binary64) (+.f64 (.f64 x #s(literal 9 binary64)) #s(literal -3 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) (.f64 (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal 27 binary64)))) (/.f64 #s(literal 729 binary64) (.f64 (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal 27 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) (.f64 (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x)))))) (/.f64 #s(literal 729 binary64) (.f64 (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x)))))))
(-.f64 (/.f64 #s(literal 9 binary64) (.f64 #s(literal -9 binary64) (-.f64 #s(literal -3 binary64) (.f64 x #s(literal -9 binary64))))) (/.f64 (.f64 x (.f64 x #s(literal 81 binary64))) (.f64 #s(literal -9 binary64) (-.f64 #s(literal -3 binary64) (.f64 x #s(literal -9 binary64))))))
(-.f64 (/.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))))) (/.f64 #s(literal 81 binary64) (.f64 (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))))))
(fma.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -1/9 binary64) #s(literal 1/3 binary64))
(fma.f64 #s(literal -1/9 binary64) (*.f64 x #s(literal -9 binary64)) #s(literal 1/3 binary64))
(neg.f64 (-.f64 #s(literal -1/3 binary64) (/.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -9 binary64))))
(neg.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/3 binary64) (/.f64 (.f64 x #s(literal -9 binary64)) #s(literal -9 binary64)))))
(/.f64 (+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)) #s(literal -9 binary64))
(/.f64 (-.f64 #s(literal 3 binary64) (*.f64 x #s(literal -9 binary64))) #s(literal 9 binary64))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)) (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)) (.f64 #s(literal 9 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -9 binary64) (+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))) (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)) #s(literal -1/9 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64)) (.f64 #s(literal -1/9 binary64) (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))))))
(/.f64 #s(literal -1/9 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64))))
(/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 (*.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -9 binary64) (-.f64 #s(literal 3 binary64) (*.f64 x #s(literal -9 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))) (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)) #s(literal -1/9 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64)) (.f64 #s(literal -1/9 binary64) (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))))))
(/.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64))) (neg.f64 (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))))
(/.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64))) (.f64 #s(literal 9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))
(/.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64))) (.f64 #s(literal -9 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))))
(/.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64))) (neg.f64 (.f64 #s(literal 9 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))))
(/.f64 (+.f64 (neg.f64 (.f64 x (.f64 x #s(literal 81 binary64)))) #s(literal 9 binary64)) (neg.f64 (+.f64 (*.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))
(/.f64 (+.f64 (neg.f64 (.f64 x (.f64 x #s(literal 81 binary64)))) #s(literal 9 binary64)) (.f64 #s(literal 9 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64))))
(/.f64 (+.f64 (neg.f64 (.f64 x (.f64 x #s(literal 81 binary64)))) #s(literal 9 binary64)) (.f64 #s(literal -9 binary64) (+.f64 (.f64 x #s(literal 9 binary64)) #s(literal -3 binary64))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -387420489 binary64)) #s(literal -19683 binary64)) (.f64 (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) (+.f64 #s(literal 729 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -19683 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) #s(literal -729 binary64)) (.f64 (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))) (+.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal -729 binary64)) #s(literal 27 binary64))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) #s(literal -729 binary64)) (.f64 (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x))))))
(/.f64 #s(literal 1/9 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)))))
(/.f64 (+.f64 #s(literal 9 binary64) (.f64 #s(literal -81 binary64) (.f64 x x))) (.f64 #s(literal -9 binary64) (-.f64 #s(literal -3 binary64) (.f64 x #s(literal -9 binary64)))))
(/.f64 (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -81 binary64)) (.f64 (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)) #s(literal -1/9 binary64)) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))
(/.f64 (.f64 #s(literal -1/9 binary64) (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64)))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)) #s(literal -1/9 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))
(/.f64 (neg.f64 (.f64 #s(literal -1/9 binary64) (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))))) (+.f64 (.f64 x #s(literal 9 binary64)) #s(literal -3 binary64)))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) #s(literal -729 binary64))) (neg.f64 (.f64 (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))) (+.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal -729 binary64)) #s(literal 27 binary64)))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) #s(literal -729 binary64))) (neg.f64 (.f64 (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x)))))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -81 binary64))) (neg.f64 (.f64 (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))))))
(/.f64 (neg.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64)))) (neg.f64 (.f64 #s(literal 9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))))
(/.f64 (neg.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64)))) (neg.f64 (neg.f64 (.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))))
(/.f64 (neg.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64)))) (neg.f64 (.f64 #s(literal -9 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))))
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(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) #s(literal -729 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x))))) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) #s(literal -729 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x))))) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) #s(literal -729 binary64)) (-.f64 (/.f64 (.f64 x (.f64 x #s(literal 81 binary64))) #s(literal 1 binary64)) #s(literal 9 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) #s(literal -729 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) #s(literal -729 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 (neg.f64 (.f64 x (.f64 x #s(literal 81 binary64)))) #s(literal 9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x))))) (+.f64 (.f64 x #s(literal 9 binary64)) #s(literal -3 binary64))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 531441 binary64))) #s(literal -729 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal 9 binary64) (.f64 #s(literal -81 binary64) (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 81 binary64) (.f64 #s(literal 729 binary64) (.f64 x x))))) (-.f64 #s(literal -3 binary64) (.f64 x #s(literal -9 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -81 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal 27 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 81 binary64))) (+.f64 #s(literal 9 binary64) (*.f64 x #s(literal 27 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -81 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -81 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -81 binary64)) (-.f64 (/.f64 (.f64 x (.f64 x #s(literal 81 binary64))) #s(literal 1 binary64)) #s(literal 9 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -81 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -81 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 (neg.f64 (.f64 x (.f64 x #s(literal 81 binary64)))) #s(literal 9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (+.f64 (.f64 x #s(literal 9 binary64)) #s(literal -3 binary64))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 6561 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -81 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal 9 binary64) (.f64 #s(literal -81 binary64) (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (-.f64 #s(literal -3 binary64) (.f64 x #s(literal -9 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal -9 binary64))) #s(literal 1 binary64)) (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64))))) (/.f64 #s(literal -9 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal -9 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal 27 binary64))) (/.f64 #s(literal -9 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 81 binary64))) (+.f64 #s(literal 9 binary64) (*.f64 x #s(literal 27 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal -9 binary64))) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)))) (/.f64 #s(literal -9 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal -9 binary64))) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))))) (/.f64 #s(literal -9 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal -9 binary64))) #s(literal 1 binary64)) (-.f64 (/.f64 (.f64 x (.f64 x #s(literal 81 binary64))) #s(literal 1 binary64)) #s(literal 9 binary64))) (/.f64 #s(literal -9 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal -9 binary64))) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64))))) (/.f64 #s(literal -9 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal -9 binary64))) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 (neg.f64 (.f64 x (.f64 x #s(literal 81 binary64)))) #s(literal 9 binary64)))) (/.f64 #s(literal 9 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal -9 binary64))) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal 9 binary64) (.f64 #s(literal -81 binary64) (.f64 x x))))) (/.f64 #s(literal -9 binary64) (-.f64 #s(literal -3 binary64) (.f64 x #s(literal -9 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -729 binary64)) #s(literal -27 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64))))))
(.f64 (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal 3 binary64))))
(.f64 (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (-.f64 (/.f64 (.f64 x (.f64 x #s(literal 81 binary64))) #s(literal 1 binary64)) #s(literal 9 binary64))) (+.f64 (.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)))
(.f64 (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 729 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (+.f64 (.f64 x #s(literal 81 binary64)) #s(literal -27 binary64)))))))
(.f64 (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 (neg.f64 (.f64 x (.f64 x #s(literal 81 binary64)))) #s(literal 9 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 9 binary64)) #s(literal -3 binary64))))
(.f64 (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (/.f64 (+.f64 #s(literal -9 binary64) (.f64 x (.f64 x #s(literal 81 binary64)))) (+.f64 #s(literal 9 binary64) (.f64 #s(literal -81 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -3 binary64) (.f64 x #s(literal -9 binary64)))))
(exp.f64 (log.f64 (*.f64 x #s(literal -9 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal -9 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 x #s(literal -9 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal -9 binary64))
(*.f64 #s(literal -9 binary64) x)
(*.f64 #s(literal -9 binary64) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) #s(literal -9 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 #s(literal -9 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal -9 binary64))) (exp.f64 (log.f64 x)))

simplify37.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

276×	`fma-define`
256×	`fma-lowering-fma.f32`
256×	`fma-lowering-fma.f64`
224×	`sum3-define`
196×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	109
1	54	109
2	134	109
3	341	109
4	412	109
5	501	109
6	609	109
7	711	109
8	805	109
9	986	109
10	1021	109
11	1030	109
12	1031	109
0	1031	109

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

eval100.0ms (2.2%)

Compiler: Compiled 12119 to 1219 computations (89.9% saved)

prune49.0ms (1.1%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	438	0	438
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	438	5	443

Accuracy

100.0%

Counts

443 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.2%	(/.f64 (-.f64 (.f64 x (.f64 x x)) #s(literal -1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (*.f64 x (+.f64 x #s(literal -1/3 binary64)))))
✓	99.9%	(/.f64 (+.f64 (*.f64 x #s(literal -9 binary64)) #s(literal -3 binary64)) #s(literal -9 binary64))
✓	100.0%	(+.f64 x #s(literal 1/3 binary64))
✓	52.8%	x
✓	48.5%	#s(literal 1/3 binary64)

Compiler

Compiled 105 to 55 computations (47.6% saved)

regimes8.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	x
3.0ms	(+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Counts

2 → 3

Calls

Call 1

Inputs
#s(literal 1/3 binary64)
x

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
97.5%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/3 binary64)

Outputs
#s(literal 1/3 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
48.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch22.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.30518365890838833	645.9410449569538
10.0ms	-19.912070981437754	-0.015598077727842581

Results

12.0ms

256×

valid

Compiler

Compiled 106 to 88 computations (17% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 3.0ms (64.2% of total)

ival-add: 1.0ms (21.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`if-if-or-not_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	13	15

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 x #s(literal -5944751508129055/18014398509481984 binary64)) x (if (<=.f64 x #s(literal 5944751508129055/18014398509481984 binary64)) #s(literal 1/3 binary64) x))

#s(literal 1/3 binary64)

Outputs

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

(if (<=.f64 x #s(literal -5944751508129055/18014398509481984 binary64)) x (if (<=.f64 x #s(literal 5944751508129055/18014398509481984 binary64)) #s(literal 1/3 binary64) x))

#s(literal 1/3 binary64)

soundness13.0ms (0.3%)

Rules

36×	`-lowering-.f32`
36×	`-lowering-.f64`
28×	`fma-define`
24×	`fma-lowering-fma.f32`
24×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	3
1	9	3
0	9	3
0	8	30
1	23	30
2	43	30
3	93	30
4	93	30
5	96	30
6	98	30
7	98	30
0	98	30

Stop Event

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

Compiler

Compiled 38 to 26 computations (31.6% saved)

preprocess24.0ms (0.5%)

Compiler: Compiled 44 to 28 computations (36.4% saved)

analyze0.0ms (0%)

sample689.0ms (15.3%)

preprocess188.0ms (4.2%)

explain59.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize22.0ms (0.5%)

series1.0ms (0%)

rewrite312.0ms (6.9%)

simplify7.0ms (0.2%)

eval24.0ms (0.5%)

prune40.0ms (0.9%)

simplify90.0ms (2%)

localize127.0ms (2.8%)

series5.0ms (0.1%)

rewrite369.0ms (8.2%)

simplify207.0ms (4.6%)

eval275.0ms (6.1%)

prune281.0ms (6.2%)

simplify180.0ms (4%)

localize123.0ms (2.7%)

series6.0ms (0.1%)

rewrite375.0ms (8.3%)

simplify232.0ms (5.2%)

eval132.0ms (2.9%)

prune94.0ms (2.1%)

simplify7.0ms (0.1%)

localize31.0ms (0.7%)

series3.0ms (0.1%)

rewrite360.0ms (8%)

simplify37.0ms (0.8%)

eval100.0ms (2.2%)

prune49.0ms (1.1%)

regimes8.0ms (0.2%)

regimes2.0ms (0%)

regimes2.0ms (0%)

bsearch22.0ms (0.5%)

simplify7.0ms (0.2%)

soundness13.0ms (0.3%)

preprocess24.0ms (0.5%)

end0.0ms (0%)

Profiling