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)

sample785.0ms (22.6%)

Results

611.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 234.0ms

ival-add: 127.0ms (54.2% of total)

ival-div: 90.0ms (38.4% of total)

const: 14.0ms (6% of total)

backward-pass: 3.0ms (1.3% of total)

Bogosity

preprocess30.0ms (0.9%)

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)

explain87.0ms (2.5%)

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

65.0ms

512×

valid

Compiler

Compiled 32 to 17 computations (46.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 5.0ms (57.1% of total)

ival-add: 3.0ms (34.3% of total)

const: 1.0ms (11.4% 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 (0.6%)

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: 8.0ms

...c/correct-round.rkt:119:19: 6.0ms (79.5% of total)

ival-add: 2.0ms (26.5% 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)

rewrite354.0ms (10.2%)

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)))

simplify16.0ms (0.4%)

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)

eval27.0ms (0.8%)

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

prune47.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	194	4	198

Accuracy

100.0%

Counts

198 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.0%	(/.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))))
✓	100.0%	(+.f64 x #s(literal 1/3 binary64))
▶	51.4%	x
▶	50.8%	#s(literal 1/3 binary64)

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 4 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))))

Rules

86×	`fma-define`
86×	`-lowering-.f32`
86×	`-lowering-.f64`
50×	`/-lowering-/.f32`
50×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	23	33
2	49	32
3	110	32
4	159	32
5	194	32
6	208	32
0	208	32

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

localize81.0ms (2.3%)

Localize:

Found 4 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 (*.f64 x x) #s(literal -1/9 binary64))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64)))
✓	accuracy	75.2%	(/.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))))

Results

49.0ms

256×

valid

Compiler

Compiled 44 to 12 computations (72.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

...c/correct-round.rkt:119:19: 10.0ms (45.6% of total)

ival-div: 6.0ms (27.4% of total)

ival-add: 3.0ms (13.7% of total)

ival-mult: 2.0ms (9.1% of total)

const: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Counts

5 → 60

Calls

Call 1

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

Calls

15 calls:

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

rewrite380.0ms (10.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2646×	`fma-lowering-fma.f32`
2646×	`fma-lowering-fma.f64`
2580×	`-lowering-.f32`
2580×	`-lowering-.f64`
2138×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	73	19
2	492	19
3	4671	19
0	8500	19

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 672

Calls

Call 1

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

Outputs
(+.f64 x #s(literal 1/3 binary64))
(+.f64 #s(literal 1/3 binary64) x)
(+.f64 (/.f64 (*.f64 x x) (+.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 x x) (+.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 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(+.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/3 binary64))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal 1/9 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (-.f64 #s(literal 0 binary64) (.f64 x x))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal 1/9 binary64)))
(+.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1/3 binary64))
(+.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/3 binary64)))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (.f64 #s(literal -1 binary64) (log.f64 (+.f64 x #s(literal -1/3 binary64)))) (.f64 #s(literal -1 binary64) (log.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 -1/3 binary64) x))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal -1/9 binary64)))
(-.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (.f64 #s(literal -1/9 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(-.f64 (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (.f64 x x)))
(-.f64 (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 x x) #s(literal 1/9 binary64))) (+.f64 x #s(literal -1/3 binary64))) (/.f64 (/.f64 #s(literal 1/81 binary64) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))) (+.f64 x #s(literal -1/3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/3 binary64) x)) (-.f64 #s(literal -1/3 binary64) x))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x)))) (-.f64 #s(literal -1/3 binary64) x))
(-.f64 (/.f64 x #s(literal 1 binary64)) #s(literal -1/3 binary64))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/27 binary64) (+.f64 (+.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 x #s(literal -1/3 binary64)))))
(fma.f64 #s(literal 1 binary64) x #s(literal 1/3 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(fma.f64 x #s(literal 1 binary64) #s(literal 1/3 binary64))
(fma.f64 x (*.f64 x (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 x (*.f64 x (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64)))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (*.f64 x x) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (*.f64 x x) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -1/9 binary64) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 #s(literal -1/9 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 #s(literal -1/9 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (.f64 (+.f64 x #s(literal 1/3 binary64)) (*.f64 x x)) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (.f64 (+.f64 x #s(literal 1/3 binary64)) (*.f64 x x)) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (.f64 (+.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) (.f64 (+.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(fma.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (.f64 x x)) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (.f64 x x)) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal -1/9 binary64)) (/.f64 (.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal -1/9 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(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 #s(literal 1/3 binary64) x)) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal 1/9 binary64)))
(fma.f64 #s(literal 1/9 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 #s(literal 1/9 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) (.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) (.f64 x x)) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) (.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) (.f64 x x)) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) (.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) #s(literal -1/9 binary64)) (/.f64 (.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) (.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) #s(literal -1/9 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.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 x x)) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.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 x x)) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.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)))) #s(literal -1/9 binary64)) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.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)))) #s(literal -1/9 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1/3 binary64))
(fma.f64 (.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) x) (.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) x) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) x) (.f64 (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) x) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (.f64 x (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64))) (.f64 x (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (.f64 x (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64))) (.f64 x (pow.f64 (+.f64 x #s(literal -1/3 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64)))) (+.f64 x #s(literal 1/3 binary64)) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64)))) (+.f64 x #s(literal 1/3 binary64)) (neg.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal -1/3 binary64)))))
(fma.f64 (.f64 #s(literal -1/9 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))) (+.f64 x #s(literal 1/3 binary64)) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1/3 binary64))))
(fma.f64 (.f64 #s(literal -1/9 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))) (+.f64 x #s(literal 1/3 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
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(fma.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.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)))) (/.f64 #s(literal -1/9 binary64) (+.f64 x #s(literal -1/3 binary64))))
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(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) #s(literal -1/387420489 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1/9 binary64)))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/531441 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/729 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/531441 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1/9 binary64)))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/729 binary64)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/531441 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal 1/9 binary64)))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1/6561 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/81 binary64))))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/6561 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal 1/9 binary64)))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/81 binary64)))
(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))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))
(.f64 (+.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 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x x)) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/729 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))))))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/729 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))))) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/729 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1/9 binary64))))) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal 1/9 binary64))) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 1/9 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1/9 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1/9 binary64))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))) #s(literal -1/729 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal 1/9 binary64))) (+.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/81 binary64)))
(.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/9 binary64) (*.f64 x x))))
(.f64 (pow.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/729 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))))) #s(literal 1 binary64)))
(.f64 (pow.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 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)))
(.f64 (pow.f64 (pow.f64 (+.f64 (.f64 x x) #s(literal -1/9 binary64)) #s(literal -1/2 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 -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/729 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 1/9 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 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 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 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1/9 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1/9 binary64))) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1/9 binary64))))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 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 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64))) (+.f64 (.f64 x x) #s(literal -1/9 binary64)))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/729 binary64)) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) #s(literal 1/9 binary64))) (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) #s(literal 1/9 binary64))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) #s(literal 1/9 binary64))))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) #s(literal 1/9 binary64))) (-.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) #s(literal 1/9 binary64))) (.f64 (.f64 x x) (.f64 x x))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/729 binary64)) (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1/9 binary64)))) (+.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/81 binary64)) (.f64 (.f64 x x) #s(literal -1/9 binary64))))) (+.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) #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 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/729 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) #s(literal -1/9 binary64)))))

simplify243.0ms (7%)

Algorithm

1×	egg-herbie

Rules

2822×	`-lowering-.f32`
2822×	`-lowering-.f64`
1742×	`+-lowering-+.f64`
1742×	`+-lowering-+.f32`
1386×	`fnmadd-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	360
1	268	313
2	622	313
3	1590	313
4	3938	311
0	8334	311

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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)
(- (* 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)))
-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))
-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)))))

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))
(- (* 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))
-9
#s(literal -9 binary64)
(- (* -81 (pow x 2)) 9)
(+.f64 #s(literal -9 binary64) (.f64 #s(literal -81 binary64) (.f64 x x)))
(- (* (pow x 2) (- (* -729 (pow x 2)) 81)) 9)
(+.f64 #s(literal -9 binary64) (.f64 x (.f64 x (+.f64 #s(literal -81 binary64) (.f64 x (.f64 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 x (.f64 x (+.f64 #s(literal -729 binary64) (.f64 x (.f64 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 #s(literal 1 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 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 (/.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 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.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 #s(literal 1 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 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 (/.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 #s(literal 1/729 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x))
-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))

eval116.0ms (3.3%)

Compiler: Compiled 19529 to 2054 computations (89.5% saved)

prune86.0ms (2.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	731	1	732
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	732	4	736

Accuracy

100.0%

Counts

736 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.3%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -9 binary64))
✓	100.0%	(+.f64 x #s(literal 1/3 binary64))
✓	51.4%	x
✓	50.8%	#s(literal 1/3 binary64)

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 3 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))

Rules

8×	`+-lowering-+.f64`
8×	`/-lowering-/.f32`
8×	`/-lowering-/.f64`
8×	`-lowering-.f32`
8×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	13	16
2	27	16
3	29	16
0	29	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize36.0ms (1%)

Localize:

Found 3 expressions of interest:

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

Results

27.0ms

256×

valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-div: 5.0ms (44.1% of total)

...c/correct-round.rkt:119:19: 4.0ms (35.3% of total)

ival-add: 2.0ms (17.6% of total)

const: 1.0ms (8.8% of total)

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

series1.0ms (0%)

Counts

3 → 36

Calls

Call 1

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

Outputs
#<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)))>

Calls

9 calls:

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

rewrite416.0ms (12%)

Algorithm

1×	batch-egg-rewrite

Rules

3956×	`/-lowering-/.f32`
3956×	`/-lowering-/.f64`
3230×	`-lowering-.f32`
3230×	`-lowering-.f64`
1542×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	45	12
2	243	12
3	1795	12
0	8336	12

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 524

Calls

Call 1

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

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

simplify174.0ms (5%)

Algorithm

1×	egg-herbie

Rules

1948×	`fma-lowering-fma.f32`
1948×	`-lowering-.f32`
1948×	`-lowering-.f64`
1948×	`fma-lowering-fma.f64`
1436×	`fmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	242
1	301	223
2	742	217
3	1889	217
4	5093	215
0	8058	215

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
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)))

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

eval372.0ms (10.7%)

Compiler: Compiled 16239 to 2087 computations (87.1% saved)

prune87.0ms (2.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	560	0	560
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	560	4	564

Accuracy

100.0%

Counts

564 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.3%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/3 binary64))) #s(literal -9 binary64))
✓	100.0%	(+.f64 x #s(literal 1/3 binary64))
✓	51.4%	x
✓	50.8%	#s(literal 1/3 binary64)

Compiler

Compiled 47 to 30 computations (36.2% saved)

regimes8.0ms (0.2%)

Counts

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0.1%)

Counts

2 → 3

Calls

Call 1

Inputs
#s(literal 1/3 binary64)
x

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
98.7%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (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
50.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch28.0ms (0.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
15.0ms	5.553070242342735e-8	943.0873923284815
11.0ms	-1139.4333277093995	-4.2103990395837493e-7

Results

16.0ms

304×

valid

Compiler

Compiled 124 to 103 computations (16.9% saved)

Precisions

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

ival-div: 3.0ms (59.5% of total)

ival-add: 2.0ms (39.7% of total)

const: 1.0ms (19.8% of total)

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

simplify8.0ms (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 6124895493223875/18014398509481984 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 6124895493223875/18014398509481984 binary64)) #s(literal 1/3 binary64) x))

#s(literal 1/3 binary64)

soundness16.0ms (0.5%)

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
0	6	3
1	9	3
0	9	3

Stop Event

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

Compiler

Compiled 38 to 26 computations (31.6% saved)

preprocess29.0ms (0.8%)

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

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

analyze0.0ms (0%)

sample785.0ms (22.6%)

preprocess30.0ms (0.9%)

explain87.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize22.0ms (0.6%)

series1.0ms (0%)

rewrite354.0ms (10.2%)

simplify16.0ms (0.4%)

eval27.0ms (0.8%)

prune47.0ms (1.4%)

simplify10.0ms (0.3%)

localize81.0ms (2.3%)

series3.0ms (0.1%)

rewrite380.0ms (10.9%)

simplify243.0ms (7%)

eval116.0ms (3.3%)

prune86.0ms (2.5%)

simplify5.0ms (0.2%)

localize36.0ms (1%)

series1.0ms (0%)

rewrite416.0ms (12%)

simplify174.0ms (5%)

eval372.0ms (10.7%)

prune87.0ms (2.5%)

regimes8.0ms (0.2%)

regimes2.0ms (0.1%)

regimes1.0ms (0%)

bsearch28.0ms (0.8%)

simplify8.0ms (0.2%)

soundness16.0ms (0.5%)

preprocess29.0ms (0.8%)

end0.0ms (0%)

Profiling