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

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-sub: 0.0ms (0% of total)

const: 0.0ms (0% of total)

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

sample520.0ms (11%)

Results

356.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 135.0ms

ival-div: 74.0ms (54.7% of total)

ival-sub: 45.0ms (33.3% of total)

const: 13.0ms (9.6% of total)

backward-pass: 3.0ms (2.2% of total)

Bogosity

preprocess18.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

26×	`sub-neg`
24×	`distribute-lft-neg-in`
16×	`cancel-sign-sub-inv`
12×	`associate-+l-`
12×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	20	12
2	42	9
3	68	9
4	107	9
5	124	9
6	132	9
7	138	9
8	143	9
9	145	9
0	6	3
1	11	3
2	12	3
0	12	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)

explain68.0ms (1.4%)

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

45.0ms

512×

valid

Compiler

Compiled 32 to 27 computations (15.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-div: 8.0ms (63.1% of total)

ival-sub: 3.0ms (23.7% of total)

const: 2.0ms (15.8% of total)

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

eval21.0ms (0.4%)

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)

localize20.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x #s(literal -1/3 binary64))
✓	accuracy	100.0%	(+.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)

Results

8.0ms

256×

valid

Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-add: 2.0ms (91.7% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Counts

1 → 12

Calls

Call 1

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

Outputs
#<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

3 calls:

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

rewrite776.0ms (16.4%)

Algorithm

1×	batch-egg-rewrite

Rules

8708×	`accelerator-lowering-fma.f32`
8708×	`accelerator-lowering-fma.f64`
5116×	`-lowering-.f32`
5116×	`-lowering-.f64`
3868×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	19	3
2	121	3
3	951	3
0	8641	3

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 264

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

simplify26.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

192×	`accelerator-lowering-fma.f32`
192×	`accelerator-lowering-fma.f64`
144×	`-lowering-.f32`
144×	`-lowering-.f64`
96×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

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

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

eval85.0ms (1.8%)

Compiler: Compiled 8476 to 4511 computations (46.8% saved)

prune39.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	273	3	276
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	273	4	277

Accuracy

100.0%

Counts

277 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.3%	(-.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))))
✓	100.0%	(+.f64 x #s(literal -1/3 binary64))
▶	49.2%	x
▶	53.3%	#s(literal -1/3 binary64)

Compiler

Compiled 22 to 16 computations (27.3% saved)

localize101.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x #s(literal 1/3 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 (*.f64 x x) (+.f64 x #s(literal 1/3 binary64)))
✓	cost-diff	0	(-.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))))
✓	accuracy	100.0%	(-.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))))
✓	accuracy	100.0%	(+.f64 x #s(literal 1/3 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal 1/3 binary64)))
✓	accuracy	77.1%	(/.f64 (*.f64 x x) (+.f64 x #s(literal 1/3 binary64)))

Rules

264×	`accelerator-lowering-fma.f32`
264×	`accelerator-lowering-fma.f64`
184×	`-lowering-.f32`
184×	`-lowering-.f64`
128×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	14	35
2	25	35
3	38	35
4	65	35
5	100	35
6	180	35
7	326	35
8	751	35
9	867	35
10	893	35
11	900	35
12	901	35
0	901	34

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

Results

38.0ms

256×

valid

Compiler

Compiled 38 to 23 computations (39.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-add: 12.0ms (47.8% of total)

ival-div: 8.0ms (31.9% of total)

ival-mult: 2.0ms (8% of total)

ival-sub: 1.0ms (4% of total)

const: 1.0ms (4% of total)

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

series11.0ms (0.2%)

Counts

5 → 60

Calls

Call 1

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

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

Calls

15 calls:

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

rewrite546.0ms (11.5%)

Algorithm

1×	batch-egg-rewrite

Rules

6380×	`accelerator-lowering-fma.f32`
6380×	`accelerator-lowering-fma.f64`
4528×	`/-lowering-/.f32`
4528×	`/-lowering-/.f64`
3820×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	60	21
2	637	21
0	8994	21

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 303

Calls

Call 1

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

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

simplify520.0ms (11%)

Algorithm

1×	egg-herbie

Rules

9112×	`accelerator-lowering-fma.f32`
9112×	`accelerator-lowering-fma.f64`
2768×	`-lowering-.f32`
2768×	`-lowering-.f64`
2012×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	108	367
1	319	350
2	765	302
3	2218	282
4	6260	282
0	8095	271

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

eval298.0ms (6.3%)

Compiler: Compiled 10888 to 6895 computations (36.7% saved)

prune50.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	421	1	422
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	422	4	426

Accuracy

100.0%

Counts

426 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.6%	(-.f64 (/.f64 (*.f64 x x) #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal 1/3 binary64))))
✓	100.0%	(+.f64 x #s(literal -1/3 binary64))
✓	49.2%	x
✓	53.3%	#s(literal -1/3 binary64)

Compiler

Compiled 20 to 15 computations (25% saved)

localize77.0ms (1.6%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal 1/3 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 (*.f64 x x) #s(literal 1/3 binary64))
✓	cost-diff	0	(-.f64 (/.f64 (*.f64 x x) #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal 1/3 binary64))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 x #s(literal 1/3 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal 1/3 binary64)))
✓	accuracy	99.7%	(/.f64 (*.f64 x x) #s(literal 1/3 binary64))

Rules

248×	`accelerator-lowering-fma.f32`
248×	`accelerator-lowering-fma.f64`
168×	`-lowering-.f32`
168×	`-lowering-.f64`
72×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	13	30
2	24	30
3	38	30
4	65	30
5	100	30
6	172	30
7	265	30
8	375	30
9	415	30
10	442	30
11	452	30
0	452	29

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

Results

28.0ms

256×

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-div: 8.0ms (46.4% of total)

ival-add: 5.0ms (29% of total)

ival-mult: 2.0ms (11.6% of total)

ival-sub: 1.0ms (5.8% of total)

const: 1.0ms (5.8% of total)

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

series6.0ms (0.1%)

Counts

5 → 60

Calls

Call 1

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

Outputs
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt 1/3>
#<alt (+ 1/3 (* -1 x))>
#<alt (+ 1/3 (* x (- (* 3 x) 1)))>
#<alt (+ 1/3 (* x (- (* x (+ 3 (* -9 x))) 1)))>
#<alt (/ 1/9 x)>
#<alt (/ (- 1/9 (* 1/27 (/ 1 x))) x)>
#<alt (/ (- (+ 1/9 (/ 1/81 (pow x 2))) (* 1/27 (/ 1 x))) x)>
#<alt (/ (- (+ 1/9 (/ 1/81 (pow x 2))) (+ (* 1/27 (/ 1 x)) (* 1/243 (/ 1 (pow x 3))))) x)>
#<alt (/ 1/9 x)>
#<alt (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/81 (/ 1 x)) 1/27) x)) 1/9) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/243 (/ 1 x)) 1/81) x)) 1/27) x)) 1/9) x))>
#<alt 1/3>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt (+ 1/3 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/3 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt -1/3>
#<alt (- x 1/3)>
#<alt (- (* x (+ 1 (* 9 (pow x 2)))) 1/3)>
#<alt (- (* x (+ 1 (* (pow x 2) (+ 9 (* -27 x))))) 1/3)>
#<alt (* 3 (pow x 2))>
#<alt (* (pow x 2) (- 3 (* 1/9 (/ 1 (pow x 3)))))>
#<alt (* (pow x 2) (- (+ 3 (/ 1/27 (pow x 4))) (* 1/9 (/ 1 (pow x 3)))))>
#<alt (* (pow x 2) (- (+ 3 (/ 1/27 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 3))) (* 1/81 (/ 1 (pow x 5))))))>
#<alt (* 3 (pow x 2))>
#<alt (* (pow x 2) (- 3 (* 1/9 (/ 1 (pow x 3)))))>
#<alt (* (pow x 2) (+ 3 (* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) (pow x 3)))))>
#<alt (* (pow x 2) (+ 3 (* -1 (/ (+ 1/9 (* -1 (/ (- 1/27 (* 1/81 (/ 1 x))) x))) (pow x 3)))))>

Calls

15 calls:

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

rewrite504.0ms (10.7%)

Algorithm

1×	batch-egg-rewrite

Rules

4852×	`accelerator-lowering-fma.f32`
4852×	`accelerator-lowering-fma.f64`
4196×	`/-lowering-/.f32`
4196×	`/-lowering-/.f64`
4010×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	62	27
2	603	27
0	8684	26

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 263

Calls

Call 1

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

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

simplify855.0ms (18.1%)

Algorithm

1×	egg-herbie

Rules

11472×	`accelerator-lowering-fma.f32`
11472×	`accelerator-lowering-fma.f64`
2858×	`-lowering-.f32`
2858×	`-lowering-.f64`
2638×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	377
1	309	362
2	802	356
3	2537	340
4	7456	340
0	8313	327

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(* 3 (pow x 2))
(* 3 (pow x 2))
(* 3 (pow x 2))
(* 3 (pow x 2))
(* 3 (pow x 2))
(* 3 (pow x 2))
(* 3 (pow x 2))
(* 3 (pow x 2))
(* 3 (pow x 2))
(* 3 (pow x 2))
(* 3 (pow x 2))
(* 3 (pow x 2))
1/3
(+ 1/3 (* -1 x))
(+ 1/3 (* x (- (* 3 x) 1)))
(+ 1/3 (* x (- (* x (+ 3 (* -9 x))) 1)))
(/ 1/9 x)
(/ (- 1/9 (* 1/27 (/ 1 x))) x)
(/ (- (+ 1/9 (/ 1/81 (pow x 2))) (* 1/27 (/ 1 x))) x)
(/ (- (+ 1/9 (/ 1/81 (pow x 2))) (+ (* 1/27 (/ 1 x)) (* 1/243 (/ 1 (pow x 3))))) x)
(/ 1/9 x)
(* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x))
(* -1 (/ (- (* -1 (/ (- (* 1/81 (/ 1 x)) 1/27) x)) 1/9) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/243 (/ 1 x)) 1/81) x)) 1/27) x)) 1/9) x))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1/3
(- x 1/3)
(- (* x (+ 1 (* 9 (pow x 2)))) 1/3)
(- (* x (+ 1 (* (pow x 2) (+ 9 (* -27 x))))) 1/3)
(* 3 (pow x 2))
(* (pow x 2) (- 3 (* 1/9 (/ 1 (pow x 3)))))
(* (pow x 2) (- (+ 3 (/ 1/27 (pow x 4))) (* 1/9 (/ 1 (pow x 3)))))
(* (pow x 2) (- (+ 3 (/ 1/27 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 3))) (* 1/81 (/ 1 (pow x 5))))))
(* 3 (pow x 2))
(* (pow x 2) (- 3 (* 1/9 (/ 1 (pow x 3)))))
(* (pow x 2) (+ 3 (* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) (pow x 3)))))
(* (pow x 2) (+ 3 (* -1 (/ (+ 1/9 (* -1 (/ (- 1/27 (* 1/81 (/ 1 x))) x))) (pow x 3)))))

Outputs
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* -1 x))
(-.f64 #s(literal 1/3 binary64) x)
(+ 1/3 (* x (- (* 3 x) 1)))
(+.f64 #s(literal 1/3 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 3 binary64) x))))
(+ 1/3 (* x (- (* x (+ 3 (* -9 x))) 1)))
(+.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)
(/ (- 1/9 (* 1/27 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 1/9 binary64) (/.f64 #s(literal 1/27 binary64) x)) x)
(/ (- (+ 1/9 (/ 1/81 (pow x 2))) (* 1/27 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/9 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal -1/27 binary64)) x)) x)
(/ (- (+ 1/9 (/ 1/81 (pow x 2))) (+ (* 1/27 (/ 1 x)) (* 1/243 (/ 1 (pow x 3))))) x)
(/.f64 (+.f64 #s(literal 1/9 binary64) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1/243 binary64) x)) x) #s(literal -1/27 binary64)) x)) x)
(/ 1/9 x)
(/.f64 #s(literal 1/9 binary64) x)
(* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x))
(/.f64 (-.f64 #s(literal 1/9 binary64) (/.f64 #s(literal 1/27 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 1/81 (/ 1 x)) 1/27) x)) 1/9) x))
(/.f64 (+.f64 #s(literal 1/9 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/81 binary64) x) #s(literal -1/27 binary64)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/243 (/ 1 x)) 1/81) x)) 1/27) x)) 1/9) x))
(/.f64 (+.f64 #s(literal 1/9 binary64) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/81 binary64) (/.f64 #s(literal 1/243 binary64) x)) x) #s(literal -1/27 binary64)) x)) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 x #s(literal 1/3 binary64))
(+ 1/3 x)
(+.f64 x #s(literal 1/3 binary64))
(+ 1/3 x)
(+.f64 x #s(literal 1/3 binary64))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal 1/3 binary64))
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal 1/3 binary64))
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal 1/3 binary64))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal 1/3 binary64))
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal 1/3 binary64))
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 x #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(+.f64 x #s(literal -1/3 binary64))
(- (* x (+ 1 (* 9 (pow x 2)))) 1/3)
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 9 binary64)))) #s(literal -1/3 binary64))
(- (* x (+ 1 (* (pow x 2) (+ 9 (* -27 x))))) 1/3)
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 9 binary64) (.f64 x #s(literal -27 binary64)))))) #s(literal -1/3 binary64))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* (pow x 2) (- 3 (* 1/9 (/ 1 (pow x 3)))))
(+.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) (/.f64 #s(literal -1/9 binary64) x))
(* (pow x 2) (- (+ 3 (/ 1/27 (pow x 4))) (* 1/9 (/ 1 (pow x 3)))))
(-.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) (/.f64 (-.f64 #s(literal 1/9 binary64) (/.f64 #s(literal 1/27 binary64) x)) x))
(* (pow x 2) (- (+ 3 (/ 1/27 (pow x 4))) (+ (* 1/9 (/ 1 (pow x 3))) (* 1/81 (/ 1 (pow x 5))))))
(+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal -1/9 binary64)) x) (.f64 (-.f64 #s(literal 3 binary64) (/.f64 #s(literal 1/81 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 x x)))
(* 3 (pow x 2))
(.f64 #s(literal 3 binary64) (.f64 x x))
(* (pow x 2) (- 3 (* 1/9 (/ 1 (pow x 3)))))
(+.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) (/.f64 #s(literal -1/9 binary64) x))
(* (pow x 2) (+ 3 (* -1 (/ (- 1/9 (* 1/27 (/ 1 x))) (pow x 3)))))
(-.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) (/.f64 (-.f64 #s(literal 1/9 binary64) (/.f64 #s(literal 1/27 binary64) x)) x))
(* (pow x 2) (+ 3 (* -1 (/ (+ 1/9 (* -1 (/ (- 1/27 (* 1/81 (/ 1 x))) x))) (pow x 3)))))
(+.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/27 binary64) (/.f64 #s(literal -1/81 binary64) x)) x) #s(literal -1/9 binary64)) x))

eval87.0ms (1.8%)

Compiler: Compiled 7438 to 4762 computations (36% saved)

prune38.0ms (0.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	323	4	327

Accuracy

100.0%

Counts

327 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.6%	(-.f64 (/.f64 (*.f64 x x) #s(literal 1/3 binary64)) (/.f64 #s(literal 1/9 binary64) (+.f64 x #s(literal 1/3 binary64))))
✓	100.0%	(+.f64 x #s(literal -1/3 binary64))
✓	49.2%	x
✓	53.3%	#s(literal -1/3 binary64)

Compiler

Compiled 55 to 39 computations (29.1% saved)

regimes4.0ms (0.1%)

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

regimes4.0ms (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:

3.0ms

Results

Accuracy	Segments	Branch
98.8%	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:

0.0ms

Results

Accuracy	Segments	Branch
53.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch24.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	5.3120756705431217e-11	9.378220345140293e+22
10.0ms	-40.82526496323151	-5.645364922096082e-8

Results

12.0ms

320×

valid

Compiler

Compiled 130 to 108 computations (16.9% saved)

Precisions

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

ival-div: 3.0ms (60.8% of total)

ival-sub: 2.0ms (40.5% of total)

const: 1.0ms (20.3% of total)

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

soundness1.0ms (0%)

Stop Event

1×

done

Compiler

Compiled 16 to 11 computations (31.3% saved)

preprocess24.0ms (0.5%)

Compiler: Compiled 44 to 32 computations (27.3% saved)

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

analyze0.0ms (0%)

sample520.0ms (11%)

preprocess18.0ms (0.4%)

explain68.0ms (1.4%)

eval21.0ms (0.4%)

prune1.0ms (0%)

localize20.0ms (0.4%)

series5.0ms (0.1%)

rewrite776.0ms (16.4%)

simplify26.0ms (0.5%)

eval85.0ms (1.8%)

prune39.0ms (0.8%)

localize101.0ms (2.1%)

series11.0ms (0.2%)

rewrite546.0ms (11.5%)

simplify520.0ms (11%)

eval298.0ms (6.3%)

prune50.0ms (1.1%)

localize77.0ms (1.6%)

series6.0ms (0.1%)

rewrite504.0ms (10.7%)

simplify855.0ms (18.1%)

eval87.0ms (1.8%)

prune38.0ms (0.8%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

regimes1.0ms (0%)

bsearch24.0ms (0.5%)

soundness1.0ms (0%)

preprocess24.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	9	12
1	20	12
2	42	9
3	68	9
4	107	9
5	124	9
6	132	9
7	138	9
8	143	9
9	145	9
0	6	3
1	11	3
2	12	3
0	12	3

Iter	Nodes	Cost
0	9	35
1	14	35
2	25	35
3	38	35
4	65	35
5	100	35
6	180	35
7	326	35
8	751	35
9	867	35
10	893	35
11	900	35
12	901	35
0	901	34

Iter	Nodes	Cost
0	8	30
1	13	30
2	24	30
3	38	30
4	65	30
5	100	30
6	172	30
7	265	30
8	375	30
9	415	30
10	442	30
11	452	30
0	452	29

Iter	Nodes	Cost
0	9	12
1	20	12
2	42	9
3	68	9
4	107	9
5	124	9
6	132	9
7	138	9
8	143	9
9	145	9
0	6	3
1	11	3
2	12	3
0	12	3

Iter	Nodes	Cost
0	9	35
1	14	35
2	25	35
3	38	35
4	65	35
5	100	35
6	180	35
7	326	35
8	751	35
9	867	35
10	893	35
11	900	35
12	901	35
0	901	34

Iter	Nodes	Cost
0	8	30
1	13	30
2	24	30
3	38	30
4	65	30
5	100	30
6	172	30
7	265	30
8	375	30
9	415	30
10	442	30
11	452	30
0	452	29

Iter	Nodes	Cost
0	9	12
1	20	12
2	42	9
3	68	9
4	107	9
5	124	9
6	132	9
7	138	9
8	143	9
9	145	9
0	6	3
1	11	3
2	12	3
0	12	3

Iter	Nodes	Cost
0	9	35
1	14	35
2	25	35
3	38	35
4	65	35
5	100	35
6	180	35
7	326	35
8	751	35
9	867	35
10	893	35
11	900	35
12	901	35
0	901	34

Iter	Nodes	Cost
0	8	30
1	13	30
2	24	30
3	38	30
4	65	30
5	100	30
6	172	30
7	265	30
8	375	30
9	415	30
10	442	30
11	452	30
0	452	29