Metrics for sqrt D (should all be same)

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 8 to 6 computations (25% saved)

Precisions

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

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

const: 0.0ms (0% of total)

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

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

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

sample749.0ms (17.6%)

Results

493.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 328.0ms

ival-pow: 181.0ms (55.1% of total)

ival-mult: 73.0ms (22.2% of total)

ival-sqrt: 62.0ms (18.9% of total)

const: 9.0ms (2.7% of total)

backward-pass: 3.0ms (0.9% of total)

Bogosity

preprocess19.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

124×	`fmsub-define`
120×	`fnmsub-define`
120×	`fnmadd-define`
98×	`fma-define`
64×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	20	16
2	44	16
3	128	16
4	243	16
5	362	16
6	488	16
7	531	16
0	5	6
1	7	5
2	12	5
3	13	5
0	13	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (* 2 (pow x 2)))

Outputs
(sqrt (* 2 (pow x 2)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Call 2

Inputs
(sqrt (* 2 (pow x 2)))
(sqrt (* 2 (pow (neg x) 2)))
(neg (sqrt (* 2 (pow (neg x) 2))))

Outputs
(sqrt (* 2 (pow x 2)))
(sqrt (* 2 (square x)))
(sqrt (* 2 (pow (neg x) 2)))
(sqrt (* 2 (square x)))
(neg (sqrt (* 2 (pow (neg x) 2))))
(neg (sqrt (* 2 (square x))))

Symmetry

(abs x)

explain66.0ms (1.5%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
123	-	1	(5.444358836608646e-159)	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`x`
0	-	0	-	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`

Results

47.0ms

512×

valid

Compiler

Compiled 43 to 17 computations (60.5% saved)

Precisions

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

ival-pow: 23.0ms (74.6% of total)

ival-mult: 4.0ms (13% of total)

ival-sqrt: 4.0ms (13% of total)

const: 1.0ms (3.2% of total)

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

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 #s(literal 2 binary64) (.f64 x x))
✓	cost-diff	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
6×	`*-commutative`
2×	`sqrt-lowering-sqrt.f64`
2×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	9	13
2	12	13
0	12	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (* 2 (* x x)))
(* 2 (* x x))
2
(* x x)
x

Outputs
(sqrt (* 2 (* x x)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(* 2 (* x x))
(.f64 #s(literal 2 binary64) (.f64 x x))
2
#s(literal 2 binary64)
(* x x)
(*.f64 x x)
x

localize29.0ms (0.7%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 x x))
✓	accuracy	55.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Results

22.0ms

256×

valid

Compiler

Compiled 18 to 6 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 12.0ms (84.4% of total)

ival-sqrt: 2.0ms (14.1% of total)

const: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (sqrt (* 2 (* x x)))>
#<alt (* 2 (* x x))>
#<alt (* x x)>

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (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 (pow x 2)>

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt (* 2 (* x x)))
1.0ms	x	@	inf	(* 2 (* x x))
0.0ms	x	@	inf	(sqrt (* 2 (* x x)))
0.0ms	x	@	0	(* 2 (* x x))
0.0ms	x	@	inf	(* x x)

rewrite275.0ms (6.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3406×	`-lowering-.f32`
3406×	`-lowering-.f64`
1454×	`+-lowering-+.f64`
1454×	`+-lowering-+.f32`
1444×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	15	11
2	44	10
3	125	10
4	590	10
5	4124	10
0	8112	10

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 216

Calls

Call 1

Inputs
(sqrt (* 2 (* x x)))
(* 2 (* x x))
(* x x)

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1/8 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))))) #s(literal 1/8 binary64)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (/.f64 x (.f64 #s(literal 2 binary64) x))))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (log.f64 (/.f64 x (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 x x))))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(/.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)) (log.f64 (/.f64 (.f64 x x) #s(literal 2 binary64))))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 (/.f64 (*.f64 x x) #s(literal 2 binary64))))))
(/.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (log.f64 (/.f64 (.f64 #s(literal 2 binary64) x) x)))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) x) x)))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 1 binary64)))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/16 binary64)) #s(literal 8 binary64))
(pow.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 4 binary64)))) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) (log.f64 (/.f64 (.f64 #s(literal 2 binary64) x) x))))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (.f64 (log.f64 x) (log.f64 (/.f64 x (.f64 #s(literal 2 binary64) x)))))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 (/.f64 (.f64 x x) #s(literal 2 binary64)))))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)) (.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)))))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))) (log.f64 (/.f64 x (.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 x (*.f64 #s(literal 2 binary64) x)))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))) (log.f64 (/.f64 (.f64 x x) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (*.f64 x x) #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))) (log.f64 (/.f64 (.f64 #s(literal 2 binary64) x) x)))) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) x) x))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 3/8 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (.f64 x (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 3/8 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 3/8 binary64))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 3/8 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (pow.f64 (.f64 x (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 3/8 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/16 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/16 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 3/8 binary64))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)))))
(.f64 (pow.f64 (.f64 x (.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 3/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 (.f64 x (.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)))
(.f64 (.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 3/8 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 3/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 3/8 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 3/8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 3/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/16 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/16 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (pow.f64 x #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal 2 binary64) x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(.f64 (sqrt.f64 x) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (*.f64 #s(literal 2 binary64) x)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 7/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 5/4 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 3/8 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 #s(literal 2 binary64) x)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(.f64 (pow.f64 x #s(literal 5/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 7/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 7/4 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) x) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) x) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 5/4 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal 5/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 8 binary64)))
(exp.f64 (*.f64 (log.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 8 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (.f64 (log.f64 x) #s(literal 4 binary64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) (log.f64 x))))
(exp.f64 (.f64 (log.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (log.f64 x))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (log.f64 x)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1 binary64))) (.f64 #s(literal 2 binary64) (log.f64 x))))
(fabs.f64 (*.f64 x x))
(fabs.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(sqrt.f64 (.f64 x (.f64 x (*.f64 x x))))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 x (log.f64 (exp.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 8 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 16 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 4 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 4 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/8 binary64)) #s(literal 8 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 x))
(pow.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1/8 binary64))
(pow.f64 (.f64 (exp.f64 #s(literal 2 binary64)) (exp.f64 #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 8 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (*.f64 (log.f64 x) #s(literal 4 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 x) #s(literal 4 binary64)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 x) #s(literal 4 binary64)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 4 binary64)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 4 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 x) #s(literal 4 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 4 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 4 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(*.f64 x x)
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (sqrt.f64 x) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) x)))
(.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 3 binary64) (log.f64 x))))
(.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 3/4 binary64) (log.f64 x))))
(.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 x) (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (log.f64 x) #s(literal 3/2 binary64))))
(.f64 (sqrt.f64 x) (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 x) (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 #s(literal 3/4 binary64) (log.f64 x))))
(.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 1 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 7/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 7/2 binary64))))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (fabs.f64 (pow.f64 x #s(literal 7/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 7/2 binary64) (log.f64 x))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 #s(literal 7/4 binary64) (log.f64 x))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 #s(literal 7/4 binary64) (log.f64 x))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 7/4 binary64))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 5/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 5/2 binary64))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 5/2 binary64) (log.f64 x))))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (pow.f64 x #s(literal 5/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (pow.f64 x #s(literal 7/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 7/2 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 5/2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 7/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) x)
(.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) (sqrt.f64 x))
(.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 7/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 3 binary64) (log.f64 x))) (sqrt.f64 x))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 7/2 binary64) (log.f64 x))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 5/2 binary64) (log.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 3/4 binary64) (log.f64 x))) (sqrt.f64 x))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 x))
(.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/8 binary64) (log.f64 x))) (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 3/8 binary64) (log.f64 x))))
(.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 3/8 binary64) (log.f64 x))) (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) (log.f64 x))))
(.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (log.f64 x) #s(literal 3/2 binary64))) (sqrt.f64 x))
(.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 x))
(.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 #s(literal 7/4 binary64) (log.f64 x))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) x))) (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) x))))
(.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 #s(literal 3/4 binary64) (log.f64 x))) (sqrt.f64 x))
(.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (sqrt.f64 x))
(.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 #s(literal 7/4 binary64) (log.f64 x))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) x))) (pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) x))))

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

106×	`sum3-define`
98×	`fma-define`
46×	`fma-lowering-fma.f32`
46×	`fma-lowering-fma.f64`
38×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	124
2	33	124
3	38	124
4	42	124
5	64	124
6	96	124
7	108	124
8	139	124
9	232	124
10	235	124
0	235	124

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 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)
(pow x 2)
(pow x 2)

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 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)

eval50.0ms (1.2%)

Compiler: Compiled 3127 to 756 computations (75.8% saved)

prune34.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	247	5	252
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	247	6	253

Accuracy

100.0%

Counts

253 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	29.7%	(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64))
▶	99.5%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
▶	99.2%	(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
▶	99.4%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
▶	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	55.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 107 to 75 computations (29.9% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(pow.f64 x #s(literal 3/8 binary64))
✓	cost-diff	64	(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
✓	cost-diff	64	(.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
✓	cost-diff	64	(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
✓	cost-diff	0	(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
✓	cost-diff	0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
✓	cost-diff	6656	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 4 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))
✓	cost-diff	0	(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	64	(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
✓	cost-diff	64	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))

Rules

98×	`-lowering-.f32`
98×	`-lowering-.f64`
36×	`associate-r`
32×	`*-commutative`
18×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	105
1	44	101
2	70	101
3	82	101
4	85	101
5	87	101
0	87	101

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (pow (* 2 x) 1/2) (sqrt x))
(pow (* 2 x) 1/2)
(* 2 x)
2
x
1/2
(sqrt x)
(* (sqrt 2) x)
(sqrt 2)
2
x
(pow (* (* x x) (* (* x x) 4)) 1/4)
(* (* x x) (* (* x x) 4))
(* x x)
x
(* (* x x) 4)
4
1/4
(* (pow 2 1/4) (* x (pow 2 1/4)))
(pow 2 1/4)
2
1/4
(* x (pow 2 1/4))
x
(* (pow x 3/8) (* (pow x 1/8) (pow (* 2 x) 1/2)))
(pow x 3/8)
x
3/8
(* (pow x 1/8) (pow (* 2 x) 1/2))
(pow x 1/8)
1/8
(pow (* 2 x) 1/2)
(* 2 x)
2
1/2

Outputs
(* (pow (* 2 x) 1/2) (sqrt x))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(pow (* 2 x) 1/2)
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x
1/2
#s(literal 1/2 binary64)
(sqrt x)
(sqrt.f64 x)
(* (sqrt 2) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
x
(pow (* (* x x) (* (* x x) 4)) 1/4)
(pow.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 4 binary64)))) #s(literal 1/4 binary64))
(* (* x x) (* (* x x) 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 4 binary64))))
(* x x)
(*.f64 x x)
x
(* (* x x) 4)
(.f64 x (.f64 x #s(literal 4 binary64)))
4
#s(literal 4 binary64)
1/4
#s(literal 1/4 binary64)
(* (pow 2 1/4) (* x (pow 2 1/4)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow 2 1/4)
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
2
#s(literal 2 binary64)
1/4
#s(literal 1/4 binary64)
(* x (pow 2 1/4))
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
x
(* (pow x 3/8) (* (pow x 1/8) (pow (* 2 x) 1/2)))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/8 binary64))))
(pow x 3/8)
(pow.f64 x #s(literal 3/8 binary64))
x
3/8
#s(literal 3/8 binary64)
(* (pow x 1/8) (pow (* 2 x) 1/2))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/8 binary64)))
(pow x 1/8)
(pow.f64 x #s(literal 1/8 binary64))
1/8
#s(literal 1/8 binary64)
(pow (* 2 x) 1/2)
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
1/2
#s(literal 1/2 binary64)

localize144.0ms (3.4%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 x #s(literal 1/8 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	99.5%	(.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
✓	accuracy	99.4%	(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
✓	accuracy	99.7%	(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
✓	accuracy	99.5%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal 4 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.8%	(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))
✓	accuracy	29.7%	(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	accuracy	100.0%	(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.5%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))

Results

110.0ms

256×

valid

Compiler

Compiled 123 to 25 computations (79.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-pow: 49.0ms (61.1% of total)

ival-mult: 26.0ms (32.4% of total)

ival-sqrt: 4.0ms (5% of total)

const: 1.0ms (1.2% of total)

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

series212.0ms (5%)

Counts

17 → 180

Calls

Call 1

Inputs
#<alt (* (pow (* 2 x) 1/2) (sqrt x))>
#<alt (pow (* 2 x) 1/2)>
#<alt (* 2 x)>
#<alt (sqrt x)>
#<alt (* (sqrt 2) x)>
#<alt (sqrt 2)>
#<alt (pow (* (* x x) (* (* x x) 4)) 1/4)>
#<alt (* (* x x) (* (* x x) 4))>
#<alt (* x x)>
#<alt (* (* x x) 4)>
#<alt (* (pow 2 1/4) (* x (pow 2 1/4)))>
#<alt (pow 2 1/4)>
#<alt (* x (pow 2 1/4))>
#<alt (* (pow x 3/8) (* (pow x 1/8) (pow (* 2 x) 1/2)))>
#<alt (* (pow x 1/8) (pow (* 2 x) 1/2))>
#<alt (pow x 3/8)>
#<alt (pow x 1/8)>

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* -1 (* (pow 4 1/4) x))>
#<alt (* -1 (* (pow 4 1/4) x))>
#<alt (* -1 (* (pow 4 1/4) x))>
#<alt (* -1 (* (pow 4 1/4) x))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<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 (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* (pow 2 1/4) x)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* (pow -1 1/4) (* x (sqrt -2))))>
#<alt (* -1 (* (pow -1 1/4) (* x (sqrt -2))))>
#<alt (* -1 (* (pow -1 1/4) (* x (sqrt -2))))>
#<alt (* -1 (* (pow -1 1/4) (* x (sqrt -2))))>
#<alt (* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))>
#<alt (* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))>
#<alt (* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))>
#<alt (* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))>
#<alt (* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))>
#<alt (pow (* 1 (pow x 3)) 1/8)>
#<alt (pow (* 1 (pow x 3)) 1/8)>
#<alt (pow (* 1 (pow x 3)) 1/8)>
#<alt (pow (* 1 (pow x 3)) 1/8)>
#<alt (pow (* 1 (pow x 3)) 1/8)>
#<alt (pow (* 1 (pow x 3)) 1/8)>
#<alt (pow (* 1 (pow x 3)) 1/8)>
#<alt (pow (* 1 (pow x 3)) 1/8)>
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (pow (* 1 x) 1/8)>
#<alt (pow (* 1 x) 1/8)>
#<alt (pow (* 1 x) 1/8)>
#<alt (pow (* 1 x) 1/8)>
#<alt (pow (* 1 x) 1/8)>
#<alt (pow (* 1 x) 1/8)>
#<alt (pow (* 1 x) 1/8)>
#<alt (pow (* 1 x) 1/8)>
#<alt (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))>
#<alt (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))>
#<alt (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))>
#<alt (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))>

Calls

45 calls:

Time	Variable		Point	Expression
49.0ms	x	@	0	(* (pow x 3/8) (* (pow x 1/8) (pow (* 2 x) 1/2)))
43.0ms	x	@	0	(pow (* (* x x) (* (* x x) 4)) 1/4)
17.0ms	x	@	0	(* x (pow 2 1/4))
14.0ms	x	@	-inf	(* (pow x 3/8) (* (pow x 1/8) (pow (* 2 x) 1/2)))
14.0ms	x	@	0	(pow x 3/8)

rewrite588.0ms (13.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3510×	`-lowering-.f32`
3510×	`-lowering-.f64`
2068×	`+-lowering-+.f64`
2068×	`+-lowering-+.f32`
1364×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	81
1	82	74
2	277	62
3	1406	62
4	6266	62
0	8883	62

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 760

Calls

Call 1

Inputs
(* (pow (* 2 x) 1/2) (sqrt x))
(pow (* 2 x) 1/2)
(* 2 x)
(sqrt x)
(* (sqrt 2) x)
(sqrt 2)
(pow (* (* x x) (* (* x x) 4)) 1/4)
(* (* x x) (* (* x x) 4))
(* x x)
(* (* x x) 4)
(* (pow 2 1/4) (* x (pow 2 1/4)))
(pow 2 1/4)
(* x (pow 2 1/4))
(* (pow x 3/8) (* (pow x 1/8) (pow (* 2 x) 1/2)))
(* (pow x 1/8) (pow (* 2 x) 1/2))
(pow x 3/8)
(pow x 1/8)

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/4 binary64))) (log.f64 (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64)))))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(pow.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 16 binary64))) #s(literal 1/8 binary64))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))))
(pow.f64 (.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64)))) #s(literal 2 binary64))
(pow.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/16 binary64)))) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) (.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 16 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (*.f64 x x) #s(literal 16 binary64)))) #s(literal 1/16 binary64))
(pow.f64 (.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/16 binary64))) (pow.f64 x #s(literal 1/16 binary64))) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) x) (.f64 x x)) (*.f64 #s(literal 2 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64))))))) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 #s(literal 4 binary64) (log.f64 x))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/8 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 (.f64 x (.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x x))) #s(literal 1/4 binary64)))
(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) x) #s(literal 1/8 binary64)))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) (*.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/8 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64)))) #s(literal 1/8 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (.f64 (pow.f64 x #s(literal 1/16 binary64)) (pow.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal 1/8 binary64))) #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 1/16 binary64)) (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/8 binary64))) (.f64 (pow.f64 x #s(literal 1/16 binary64)) (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/8 binary64)))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 7/16 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 1/16 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/8 binary64)))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 3/8 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 9/16 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x x))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/8 binary64)) (pow.f64 (.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64))))) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x x)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64)))) #s(literal 3/16 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64))) (.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 x #s(literal 7/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 9/16 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 9/16 binary64))) (pow.f64 x #s(literal 7/16 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 16 binary64) x) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 7/8 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64))) (pow.f64 x #s(literal 3/16 binary64)))
(.f64 (pow.f64 x #s(literal 5/16 binary64)) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/16 binary64))))
(.f64 (pow.f64 x #s(literal 5/8 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/8 binary64))))
(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 7/8 binary64)) (pow.f64 (.f64 #s(literal 16 binary64) x) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64)))) (.f64 (pow.f64 x #s(literal 3/16 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) x) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 5/8 binary64)))
(.f64 (pow.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))) #s(literal 1/8 binary64)) (pow.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/16 binary64))) (pow.f64 x #s(literal 5/16 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 7/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/16 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/8 binary64)))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))) (pow.f64 x #s(literal 3/32 binary64)))
(.f64 (pow.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64)))) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (pow.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) #s(literal 3/16 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/8 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 9/16 binary64)))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64))))
(.f64 (pow.f64 (.f64 x (.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x x))) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x x))) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) (.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 x)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))))
(.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 x)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 #s(literal 4 binary64) (log.f64 x))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 #s(literal 3 binary64) (log.f64 x))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 (*.f64 x #s(literal 4 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) (.f64 x (.f64 x x))) #s(literal 1/8 binary64)) (pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/16 binary64)))) (.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/16 binary64)))))
(.f64 (.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/16 binary64))) (pow.f64 x #s(literal 1/16 binary64))) (.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/16 binary64))) (pow.f64 x #s(literal 1/16 binary64))))
(.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (/.f64 (log.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (/.f64 (log.f64 (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64))))) #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) (.f64 x x)) #s(literal 1/8 binary64))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x x)) #s(literal 1/8 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64))))) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64))))))
(.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 7/32 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/32 binary64)))) (.f64 (pow.f64 x #s(literal 7/32 binary64)) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/32 binary64)))))
(.f64 (.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/32 binary64))) (pow.f64 x #s(literal 7/32 binary64))) (.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/32 binary64))) (pow.f64 x #s(literal 7/32 binary64))))
(.f64 (.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64)))) (pow.f64 x #s(literal 3/32 binary64))) (.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/16 binary64)))) (pow.f64 x #s(literal 3/32 binary64))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) x))))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 16 binary64)))) #s(literal 1/8 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) x))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 #s(literal 2 binary64) (log.f64 (.f64 #s(literal 2 binary64) x))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (.f64 #s(literal 16 binary64) x) #s(literal 1/8 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/8 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
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(*.f64 (pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 5/8 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 5/8 binary64)) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 7/8 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/16 binary64)) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 13/16 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 7/16 binary64)) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 9/16 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 7/8 binary64)) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 11/16 binary64)) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 5/16 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 15/16 binary64)) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 1/16 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (pow.f64 x #s(literal 1/64 binary64))) (*.f64 (pow.f64 x #s(literal 3/64 binary64)) (pow.f64 x #s(literal 1/64 binary64))))

simplify245.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1856×	`-lowering-.f32`
1856×	`-lowering-.f64`
1348×	`fma-lowering-fma.f32`
1348×	`fma-lowering-fma.f64`
1346×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	65	892
1	144	860
2	380	840
3	694	840
4	984	832
5	1596	832
6	3200	832
7	5226	832
0	8074	832

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(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)
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* (pow 2 1/4) x)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* (pow -1 1/4) (* x (sqrt -2))))
(* -1 (* (pow -1 1/4) (* x (sqrt -2))))
(* -1 (* (pow -1 1/4) (* x (sqrt -2))))
(* -1 (* (pow -1 1/4) (* x (sqrt -2))))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))
(* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))
(* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))
(* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))
(pow (* 1 (pow x 3)) 1/8)
(pow (* 1 (pow x 3)) 1/8)
(pow (* 1 (pow x 3)) 1/8)
(pow (* 1 (pow x 3)) 1/8)
(pow (* 1 (pow x 3)) 1/8)
(pow (* 1 (pow x 3)) 1/8)
(pow (* 1 (pow x 3)) 1/8)
(pow (* 1 (pow x 3)) 1/8)
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(pow (* 1 x) 1/8)
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) x)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) x)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) x)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) x)))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* -1 (* (pow 4 1/4) x))
(-.f64 #s(literal 0 binary64) (*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))))
(* -1 (* (pow 4 1/4) x))
(-.f64 #s(literal 0 binary64) (*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))))
(* -1 (* (pow 4 1/4) x))
(-.f64 #s(literal 0 binary64) (*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))))
(* -1 (* (pow 4 1/4) x))
(-.f64 #s(literal 0 binary64) (*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 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)
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* (pow 2 1/4) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow -1 1/4) (* x (sqrt -2))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64))))
(* -1 (* (pow -1 1/4) (* x (sqrt -2))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64))))
(* -1 (* (pow -1 1/4) (* x (sqrt -2))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64))))
(* -1 (* (pow -1 1/4) (* x (sqrt -2))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64))))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64)))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64)))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64)))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64)))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64)))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64)))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64)))
(* (pow (* 1 (pow x 5)) 1/8) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64)))
(* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -5 binary64))) #s(literal 1/8 binary64)))
(* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -5 binary64))) #s(literal 1/8 binary64)))
(* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -5 binary64))) #s(literal 1/8 binary64)))
(* (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (sqrt -2))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -5 binary64))) #s(literal 1/8 binary64)))
(pow (* 1 (pow x 3)) 1/8)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 3)) 1/8)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 3)) 1/8)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 3)) 1/8)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 3)) 1/8)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 3)) 1/8)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 3)) 1/8)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 3)) 1/8)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3/8 binary64)))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3/8 binary64)))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3/8 binary64)))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3/8 binary64)))
(pow (* 1 x) 1/8)
(pow.f64 x #s(literal 1/8 binary64))
(pow (* 1 x) 1/8)
(pow.f64 x #s(literal 1/8 binary64))
(pow (* 1 x) 1/8)
(pow.f64 x #s(literal 1/8 binary64))
(pow (* 1 x) 1/8)
(pow.f64 x #s(literal 1/8 binary64))
(pow (* 1 x) 1/8)
(pow.f64 x #s(literal 1/8 binary64))
(pow (* 1 x) 1/8)
(pow.f64 x #s(literal 1/8 binary64))
(pow (* 1 x) 1/8)
(pow.f64 x #s(literal 1/8 binary64))
(pow (* 1 x) 1/8)
(pow.f64 x #s(literal 1/8 binary64))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/8 binary64))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/8 binary64))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/8 binary64))
(exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/8 binary64))

eval118.0ms (2.8%)

Compiler: Compiled 15012 to 1249 computations (91.7% saved)

prune89.0ms (2.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	1058	2	1060
Fresh	0	0	0
Picked	2	3	5
Done	0	1	1
Total	1060	6	1066

Accuracy

100.0%

Counts

1066 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	29.7%	(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64))
▶	99.1%	(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)
✓	99.4%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
▶	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	55.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 50 to 34 computations (32% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
✓	cost-diff	6528	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	cost-diff	6528	(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))

Rules

22×	`-lowering-.f32`
22×	`-lowering-.f64`
12×	`*-commutative`
6×	`sqrt-lowering-sqrt.f64`
6×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	14	32
2	22	30
3	25	30
0	25	30

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (sqrt (* 2 x)) (sqrt x))
(sqrt (* 2 x))
(* 2 x)
2
x
(sqrt x)
(* (pow (pow 2 1/4) 2) x)
(pow (pow 2 1/4) 2)
(pow 2 1/4)
2
1/4
x

Outputs
(* (sqrt (* 2 x)) (sqrt x))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(sqrt (* 2 x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x
(sqrt x)
(sqrt.f64 x)
(* (pow (pow 2 1/4) 2) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow (pow 2 1/4) 2)
(sqrt.f64 #s(literal 2 binary64))
(pow 2 1/4)
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
2
#s(literal 2 binary64)
1/4
#s(literal 1/4 binary64)
x

localize46.0ms (1.1%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
✓	accuracy	99.4%	(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)
✓	accuracy	98.4%	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))

Results

33.0ms

256×

valid

Compiler

Compiled 38 to 11 computations (71.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-pow: 9.0ms (47.4% of total)

ival-mult: 6.0ms (31.6% of total)

ival-sqrt: 4.0ms (21.1% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

7 → 60

Calls

Call 1

Inputs
#<alt (* (sqrt (* 2 x)) (sqrt x))>
#<alt (sqrt (* 2 x))>
#<alt (* 2 x)>
#<alt (sqrt x)>
#<alt (* (pow (pow 2 1/4) 2) x)>
#<alt (pow (pow 2 1/4) 2)>
#<alt (pow 2 1/4)>

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(sqrt (* 2 x))
0.0ms	x	@	0	(sqrt (* 2 x))
0.0ms	x	@	0	(* (sqrt (* 2 x)) (sqrt x))
0.0ms	x	@	inf	(sqrt (* 2 x))
0.0ms	x	@	inf	(* (sqrt (* 2 x)) (sqrt x))

rewrite94.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

486×	`-lowering-.f32`
486×	`-lowering-.f64`
334×	`associate-r`
290×	`associate-l`
274×	`prod-exp`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	37	25
2	115	21
3	402	17
0	2643	17

Stop Event

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

Counts

7 → 127

Calls

Call 1

Inputs
(* (sqrt (* 2 x)) (sqrt x))
(sqrt (* 2 x))
(* 2 x)
(sqrt x)
(* (pow (pow 2 1/4) 2) x)
(pow (pow 2 1/4) 2)
(pow 2 1/4)

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))))
(exp.f64 (+.f64 (log.f64 x) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (log.f64 x)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 1 binary64)))
(sqrt.f64 (.f64 #s(literal 1 binary64) (.f64 x x)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 x x)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 x x) (.f64 #s(literal 4 binary64) (.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1 binary64))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1 binary64) x)
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))))
(.f64 (.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64)))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 4 binary64) (*.f64 x x))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) (.f64 #s(literal 1/4 binary64) (log.f64 (*.f64 #s(literal 2 binary64) x)))))
(exp.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (log.f64 (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 1/4 binary64) (log.f64 (.f64 #s(literal 2 binary64) x)))))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(exp.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (log.f64 (.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 1/4 binary64) (log.f64 x))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(sqrt.f64 (*.f64 x #s(literal 1 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) (.f64 #s(literal 1/4 binary64) (log.f64 x))))
(fabs.f64 (sqrt.f64 x))
(sqrt.f64 x)
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))))
(exp.f64 (+.f64 (log.f64 x) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (log.f64 x)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 1 binary64)))
(sqrt.f64 (.f64 #s(literal 1 binary64) (.f64 x x)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 x x)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 x x) (.f64 #s(literal 4 binary64) (.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1 binary64))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1 binary64) x)
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))))
(.f64 (.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64)))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/8 binary64)))
#s(literal 1 binary64)
#s(literal 1 binary64)

simplify184.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

3744×	`fnmadd-define`
2176×	`fma-define`
2092×	`sum3-define`
1044×	`fma-lowering-fma.f32`
1044×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	248
1	42	248
2	117	248
3	239	248
4	472	248
5	903	248
6	2123	248
7	2841	248
8	3255	248
9	3420	248
10	3614	248
11	4179	248
12	5859	248
13	5895	248
14	5971	248
15	5987	248
16	5987	248
17	6017	248
18	6121	248
19	7031	248
0	8099	248

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))

eval19.0ms (0.4%)

Compiler: Compiled 1702 to 252 computations (85.2% saved)

prune19.0ms (0.4%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	186	7	193

Accuracy

100.0%

Counts

193 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	29.7%	(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64))
✓	99.1%	(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)
✓	99.4%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
✓	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	20.3%	(*.f64 x #s(literal 1 binary64))
✓	55.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 54 to 37 computations (31.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(*.f64 x #s(literal 1 binary64))

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`
2×	`*-rgt-identity`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	6	3
2	7	3
0	7	3

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x 1)
x
1

Outputs
(* x 1)
x
x
1
#s(literal 1 binary64)

localize15.0ms (0.3%)

Localize:

Found 1 expressions of interest:

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

Results

8.0ms

256×

valid

Compiler

Compiled 7 to 4 computations (42.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (74.7% of total)

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (* x 1)>

Outputs
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>

Calls

3 calls:

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

rewrite9.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`
2×	`*-rgt-identity`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	1
1	6	1
2	7	1
0	7	1

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 3

Calls

Call 1

Inputs
(* x 1)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12
0	1	12

Stop Event

1×	saturated
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x

Outputs
x
x
x
x
x
x
x
x
x
x
x
x

eval1.0ms (0%)

Compiler: Compiled 20 to 4 computations (80% saved)

prune4.0ms (0.1%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	14	1	15
Fresh	0	0	0
Picked	1	0	1
Done	0	6	6
Total	15	7	22

Accuracy

100.0%

Counts

22 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	29.7%	(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64))
✓	99.1%	(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)
✓	99.4%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
✓	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	55.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
	20.3%	x

Compiler

Compiled 128 to 70 computations (45.3% saved)

regimes16.0ms (0.4%)

Counts

11 → 1

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))

Outputs
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))

Calls

4 calls:

5.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
4.0ms	x
3.0ms	(pow.f64 x #s(literal 2 binary64))
3.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
99.5%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
99.5%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes17.0ms (0.4%)

Counts

6 → 1

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/4 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Outputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Calls

4 calls:

9.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
3.0ms	x
2.0ms	(pow.f64 x #s(literal 2 binary64))
2.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
99.4%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
99.4%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 1 binary64))

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
20.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	11	12

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
x

Outputs
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x

soundness1.1s (26.6%)

Rules

3510×	`-lowering-.f32`
3510×	`-lowering-.f64`
3406×	`-lowering-.f32`
3406×	`-lowering-.f64`
2068×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	1
1	6	1
2	7	1
0	7	1
0	24	81
1	82	74
2	277	62
3	1406	62
4	6266	62
0	8883	62
0	5	11
1	15	11
2	44	10
3	125	10
4	590	10
5	4124	10
0	8112	10
0	5	6
1	7	5
2	12	5
3	13	5
0	13	5
0	10	27
1	37	25
2	115	21
3	402	17
0	2643	17

Stop Event

1×	fuel
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	saturated

Compiler

Compiled 75 to 54 computations (28% saved)

preprocess34.0ms (0.8%)

Compiler: Compiled 72 to 50 computations (30.6% saved)

Iter	Nodes	Cost
0	10	20
1	20	16
2	44	16
3	128	16
4	243	16
5	362	16
6	488	16
7	531	16
0	5	6
1	7	5
2	12	5
3	13	5
0	13	5

Iter	Nodes	Cost
0	8	148
1	15	124
2	33	124
3	38	124
4	42	124
5	64	124
6	96	124
7	108	124
8	139	124
9	232	124
10	235	124
0	235	124

Iter	Nodes	Cost
0	10	20
1	20	16
2	44	16
3	128	16
4	243	16
5	362	16
6	488	16
7	531	16
0	5	6
1	7	5
2	12	5
3	13	5
0	13	5

Iter	Nodes	Cost
0	8	148
1	15	124
2	33	124
3	38	124
4	42	124
5	64	124
6	96	124
7	108	124
8	139	124
9	232	124
10	235	124
0	235	124

analyze0.0ms (0%)

sample749.0ms (17.6%)

preprocess19.0ms (0.4%)

explain66.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize29.0ms (0.7%)

series3.0ms (0.1%)

rewrite275.0ms (6.5%)

simplify13.0ms (0.3%)

eval50.0ms (1.2%)

prune34.0ms (0.8%)

simplify7.0ms (0.2%)

localize144.0ms (3.4%)

series212.0ms (5%)

rewrite588.0ms (13.8%)

simplify245.0ms (5.7%)

eval118.0ms (2.8%)

prune89.0ms (2.1%)

simplify6.0ms (0.1%)

localize46.0ms (1.1%)

series2.0ms (0%)

rewrite94.0ms (2.2%)

simplify184.0ms (4.3%)

eval19.0ms (0.4%)

prune19.0ms (0.4%)

simplify3.0ms (0.1%)

localize15.0ms (0.3%)

series0.0ms (0%)

rewrite9.0ms (0.2%)

simplify6.0ms (0.1%)

eval1.0ms (0%)

prune4.0ms (0.1%)

regimes16.0ms (0.4%)

regimes17.0ms (0.4%)

regimes2.0ms (0%)

simplify7.0ms (0.2%)

soundness1.1s (26.6%)

preprocess34.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	20
1	20	16
2	44	16
3	128	16
4	243	16
5	362	16
6	488	16
7	531	16
0	5	6
1	7	5
2	12	5
3	13	5
0	13	5

Iter	Nodes	Cost
0	8	148
1	15	124
2	33	124
3	38	124
4	42	124
5	64	124
6	96	124
7	108	124
8	139	124
9	232	124
10	235	124
0	235	124