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)

sample886.0ms (19.7%)

Results

595.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 280.0ms

ival-pow: 116.0ms (41.5% of total)

ival-sqrt: 76.0ms (27.2% of total)

ival-mult: 72.0ms (25.7% of total)

const: 10.0ms (3.6% of total)

backward-pass: 5.0ms (1.8% of total)

Bogosity

preprocess18.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

124×	`fmsub-define`
120×	`fnmsub-define`
120×	`fnmadd-define`
90×	`fma-define`
52×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	20	16
2	41	16
3	113	16
4	205	16
5	330	16
6	465	16
7	508	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)

explain75.0ms (1.7%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
115	-	4	(1.017673314806113e-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

55.0ms

512×

valid

Compiler

Compiled 43 to 17 computations (60.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-pow: 8.0ms (48.6% of total)

ival-mult: 4.0ms (24.3% of total)

ival-sqrt: 4.0ms (24.3% of total)

const: 1.0ms (6.1% 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
▶	58.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify5.0ms (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

localize27.0ms (0.6%)

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	58.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Results

20.0ms

256×

valid

Compiler

Compiled 18 to 6 computations (66.7% saved)

Precisions

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

ival-mult: 5.0ms (64.7% of total)

ival-sqrt: 2.0ms (25.9% 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)

rewrite240.0ms (5.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2622×	`-lowering-.f32`
2622×	`-lowering-.f64`
1850×	`fma-define`
1570×	`fma-lowering-fma.f32`
1570×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	15	11
2	39	10
3	79	10
4	242	10
5	796	10
6	3966	10
0	8155	10

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 171

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

simplify24.0ms (0.5%)

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)

eval23.0ms (0.5%)

Compiler: Compiled 2248 to 561 computations (75% saved)

prune28.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	198	9	207
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	198	10	208

Accuracy

100.0%

Counts

208 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
▶	99.4%	(.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))))
	75.2%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
▶	67.7%	(.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64)))))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
	58.5%	(sqrt.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 x))))
▶	58.3%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
✓	58.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
	29.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (.f64 x (.f64 x x))))))

Compiler

Compiled 189 to 149 computations (21.2% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
✓	cost-diff	64	(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
✓	cost-diff	64	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64)))
✓	cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))))
✓	cost-diff	0	(pow.f64 x #s(literal 1/8 binary64))
✓	cost-diff	0	(.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64)))))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
✓	cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 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	0	(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))

Rules

32×	`-lowering-.f32`
32×	`-lowering-.f64`
16×	`*-commutative`
12×	`sqrt-lowering-sqrt.f64`
12×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	107
1	35	107
0	35	107

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
(sqrt (* 2 (pow (sqrt x) 4)))
(* 2 (pow (sqrt x) 4))
2
(pow (sqrt x) 4)
(sqrt x)
x
4
(* (pow x 1/8) (sqrt (* 2 (pow x 7/4))))
(pow x 1/8)
x
1/8
(sqrt (* 2 (pow x 7/4)))
(* 2 (pow x 7/4))
2
(pow x 7/4)
7/4
(* (pow (* 2 (sqrt x)) 1/2) (pow x 3/4))
(pow (* 2 (sqrt x)) 1/2)
(* 2 (sqrt x))
2
(sqrt x)
x
1/2
(pow x 3/4)
3/4

Outputs
(* (pow (* 2 x) 1/2) (sqrt x))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(pow (* 2 x) 1/2)
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(* 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
(sqrt (* 2 (pow (sqrt x) 4)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
(* 2 (pow (sqrt x) 4))
(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
2
#s(literal 2 binary64)
(pow (sqrt x) 4)
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(sqrt x)
(sqrt.f64 x)
x
4
#s(literal 4 binary64)
(* (pow x 1/8) (sqrt (* 2 (pow x 7/4))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64)))))
(pow x 1/8)
(pow.f64 x #s(literal 1/8 binary64))
x
1/8
#s(literal 1/8 binary64)
(sqrt (* 2 (pow x 7/4)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))))
(* 2 (pow x 7/4))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64)))
2
#s(literal 2 binary64)
(pow x 7/4)
(pow.f64 x #s(literal 7/4 binary64))
7/4
#s(literal 7/4 binary64)
(* (pow (* 2 (sqrt x)) 1/2) (pow x 3/4))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
(pow (* 2 (sqrt x)) 1/2)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
2
#s(literal 2 binary64)
(sqrt x)
(sqrt.f64 x)
x
1/2
#s(literal 1/2 binary64)
(pow x 3/4)
(pow.f64 x #s(literal 3/4 binary64))
3/4
#s(literal 3/4 binary64)

localize159.0ms (3.5%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(pow.f64 x #s(literal 3/4 binary64))
✓	accuracy	99.8%	(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
✓	accuracy	99.4%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
✓	accuracy	100.0%	(pow.f64 x #s(literal 1/8 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64)))
✓	accuracy	99.5%	(.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64)))))
✓	accuracy	67.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
✓	accuracy	99.1%	(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
✓	accuracy	58.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(*.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	99.4%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))

Results

124.0ms

256×

valid

Compiler

Compiled 113 to 26 computations (77% saved)

Precisions

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

ival-pow: 35.0ms (59.2% of total)

ival-mult: 15.0ms (25.4% of total)

ival-sqrt: 8.0ms (13.5% of total)

const: 1.0ms (1.7% of total)

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

series178.0ms (4%)

Counts

17 → 192

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 (sqrt (* 2 (pow (sqrt x) 4)))>
#<alt (* 2 (pow (sqrt x) 4))>
#<alt (pow (sqrt x) 4)>
#<alt (* (pow x 1/8) (sqrt (* 2 (pow x 7/4))))>
#<alt (pow x 1/8)>
#<alt (sqrt (* 2 (pow x 7/4)))>
#<alt (* 2 (pow x 7/4))>
#<alt (* (pow (* 2 (sqrt x)) 1/2) (pow x 3/4))>
#<alt (pow (* 2 (sqrt x)) 1/2)>
#<alt (* 2 (sqrt x))>
#<alt (pow x 3/4)>

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))>
#<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 (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* x (* (pow (sqrt -1) 2) (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) (pow (sqrt -1) 4)))>
#<alt (* 2 (* (pow x 2) (pow (sqrt -1) 4)))>
#<alt (* 2 (* (pow x 2) (pow (sqrt -1) 4)))>
#<alt (* 2 (* (pow x 2) (pow (sqrt -1) 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) (pow (sqrt -1) 4))>
#<alt (* (pow x 2) (pow (sqrt -1) 4))>
#<alt (* (pow x 2) (pow (sqrt -1) 4))>
#<alt (* (pow x 2) (pow (sqrt -1) 4))>
#<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 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))))))>
#<alt (* (pow (* 1 (pow x 7)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 7)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 7)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 7)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 7)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 7)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 7)) 1/8) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 7)) 1/8) (sqrt 2))>
#<alt (* (exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x)))))) (sqrt 2))>
#<alt (* (exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x)))))) (sqrt 2))>
#<alt (* (exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x)))))) (sqrt 2))>
#<alt (* (exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x)))))) (sqrt 2))>
#<alt (* 2 (pow (* 1 (pow x 7)) 1/4))>
#<alt (* 2 (pow (* 1 (pow x 7)) 1/4))>
#<alt (* 2 (pow (* 1 (pow x 7)) 1/4))>
#<alt (* 2 (pow (* 1 (pow x 7)) 1/4))>
#<alt (* 2 (pow (* 1 (pow x 7)) 1/4))>
#<alt (* 2 (pow (* 1 (pow x 7)) 1/4))>
#<alt (* 2 (pow (* 1 (pow x 7)) 1/4))>
#<alt (* 2 (pow (* 1 (pow x 7)) 1/4))>
#<alt (* 2 (exp (* 1/4 (+ (log -1) (* -7 (log (/ -1 x)))))))>
#<alt (* 2 (exp (* 1/4 (+ (log -1) (* -7 (log (/ -1 x)))))))>
#<alt (* 2 (exp (* 1/4 (+ (log -1) (* -7 (log (/ -1 x)))))))>
#<alt (* 2 (exp (* 1/4 (+ (log -1) (* -7 (log (/ -1 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)) (sqrt (sqrt -1)))))>
#<alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>

Calls

48 calls:

Time	Variable		Point	Expression
53.0ms	x	@	0	(* (pow x 1/8) (sqrt (* 2 (pow x 7/4))))
21.0ms	x	@	-inf	(* (pow x 1/8) (sqrt (* 2 (pow x 7/4))))
13.0ms	x	@	inf	(pow x 3/4)
11.0ms	x	@	-inf	(pow x 1/8)
10.0ms	x	@	0	(pow (* 2 (sqrt x)) 1/2)

rewrite490.0ms (10.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4300×	`-lowering-.f32`
4300×	`-lowering-.f64`
1958×	`log-prod`
1876×	`+-lowering-+.f64`
1876×	`+-lowering-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	80
1	66	75
2	144	63
3	307	63
4	915	63
5	5247	63
0	8135	63

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 869

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)
(sqrt (* 2 (pow (sqrt x) 4)))
(* 2 (pow (sqrt x) 4))
(pow (sqrt x) 4)
(* (pow x 1/8) (sqrt (* 2 (pow x 7/4))))
(pow x 1/8)
(sqrt (* 2 (pow x 7/4)))
(* 2 (pow x 7/4))
(* (pow (* 2 (sqrt x)) 1/2) (pow x 3/4))
(pow (* 2 (sqrt x)) 1/2)
(* 2 (sqrt x))
(pow x 3/4)

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))))
(*.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 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 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)) (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 7/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 7/8 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 7/32 binary64)) (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 7/32 binary64)) (.f64 (pow.f64 x #s(literal 21/32 binary64)) (*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 1/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 1/32 binary64)) (.f64 (pow.f64 x #s(literal 7/32 binary64)) (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 5/4 binary64))) #s(literal 1/2 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 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 3/8 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))))
(.f64 (pow.f64 x #s(literal 21/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))))
(.f64 (pow.f64 x #s(literal 21/32 binary64)) (.f64 (pow.f64 x #s(literal 7/32 binary64)) (*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 9/16 binary64)) (.f64 (pow.f64 x #s(literal 3/16 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))))
(.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (pow.f64 x #s(literal 9/16 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))))
(.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (pow.f64 x #s(literal 1/16 binary64)) (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 7/16 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 9/8 binary64)))))
(.f64 (pow.f64 x #s(literal 7/16 binary64)) (.f64 (pow.f64 x #s(literal 1/16 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 7/16 binary64)) (.f64 (pow.f64 x #s(literal 7/16 binary64)) (*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 49/64 binary64)) (.f64 (pow.f64 x #s(literal 7/64 binary64)) (*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 15/8 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 7/16 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 1/16 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 3/16 binary64)) (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 1/64 binary64)) (.f64 (pow.f64 x #s(literal 7/64 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 7/64 binary64)) (.f64 (pow.f64 x #s(literal 1/64 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 7/64 binary64)) (.f64 (pow.f64 x #s(literal 49/64 binary64)) (*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 1/32 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 21/32 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 9/8 binary64)))) (pow.f64 x #s(literal 7/16 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 5/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 15/8 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 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 1/2 binary64)) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 7/16 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 (*.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 #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) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/64 binary64))) (pow.f64 x #s(literal 7/64 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 7/64 binary64))) (pow.f64 x #s(literal 1/64 binary64)))
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(.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 (*.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 #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) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/64 binary64))) (pow.f64 x #s(literal 7/64 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 7/64 binary64))) (pow.f64 x #s(literal 1/64 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/32 binary64))) (pow.f64 x #s(literal 1/32 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/32 binary64))) (pow.f64 x #s(literal 3/32 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/32 binary64))) (pow.f64 x #s(literal 21/32 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 21/32 binary64))) (pow.f64 x #s(literal 3/32 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 9/16 binary64))) (pow.f64 x #s(literal 3/16 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/16 binary64))) (pow.f64 x #s(literal 9/16 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 7/16 binary64))) (pow.f64 x #s(literal 7/16 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 7/64 binary64))) (pow.f64 x #s(literal 49/64 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 49/64 binary64))) (pow.f64 x #s(literal 7/64 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 21/32 binary64))) (pow.f64 x #s(literal 7/32 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 7/32 binary64))) (pow.f64 x #s(literal 21/32 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 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 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 7/32 binary64))) (pow.f64 x #s(literal 1/32 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 3/16 binary64)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (pow.f64 x #s(literal 7/32 binary64)) (.f64 (pow.f64 x #s(literal 1/32 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 1/32 binary64)) (.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (pow.f64 x #s(literal 1/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/32 binary64))) (pow.f64 x #s(literal 7/32 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/32 binary64))) (pow.f64 x #s(literal 1/32 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 3/16 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))
(.f64 (pow.f64 x #s(literal 7/16 binary64)) (.f64 (pow.f64 x #s(literal 1/16 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 7/16 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 7/16 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(exp.f64 (*.f64 #s(literal 3/4 binary64) (log.f64 x)))
(exp.f64 (.f64 #s(literal 4 binary64) (.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 3/8 binary64))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 x) #s(literal 3/2 binary64))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 3/8 binary64))))
(exp.f64 (.f64 #s(literal 2 binary64) (.f64 (log.f64 x) #s(literal 3/8 binary64))))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 3/16 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 3/2 binary64))) (/.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 3/8 binary64))) (.f64 #s(literal 2 binary64) (log.f64 x))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 3 binary64))) (.f64 (log.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 3/4 binary64) (log.f64 x)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fabs.f64 (pow.f64 x #s(literal 3/4 binary64)))
(fabs.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))))
(sqrt.f64 (pow.f64 x #s(literal 3/2 binary64)))
(pow.f64 x #s(literal 3/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 3/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/8 binary64))
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 3/4 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 4 binary64)) (*.f64 #s(literal 3/16 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 4 binary64)) (*.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 3/8 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 3/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 3/8 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 3/2 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 3/8 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 x) #s(literal 3/8 binary64)))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 3/16 binary64))
(pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 3/4 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 3/2 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 3/8 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (*.f64 (log.f64 x) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 x #s(literal 21/32 binary64)) (pow.f64 x #s(literal 3/32 binary64)))
(*.f64 (pow.f64 x #s(literal 21/32 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 x #s(literal 9/16 binary64)) (pow.f64 x #s(literal 3/16 binary64)))
(*.f64 (pow.f64 x #s(literal 3/16 binary64)) (pow.f64 x #s(literal 9/16 binary64)))
(*.f64 (pow.f64 x #s(literal 3/16 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 x #s(literal 3/32 binary64)) (pow.f64 x #s(literal 21/32 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/16 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal 7/16 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 7/16 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/16 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 3/8 binary64)) (pow.f64 (pow.f64 x #s(literal 15/8 binary64)) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 15/8 binary64)) #s(literal 3/8 binary64)) (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 3/8 binary64)) (pow.f64 (pow.f64 x #s(literal 5/4 binary64)) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3/8 binary64)) (pow.f64 x #s(literal 21/32 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 7/8 binary64)) #s(literal 3/8 binary64)) (pow.f64 (pow.f64 x #s(literal 9/8 binary64)) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 3/8 binary64)) (pow.f64 x #s(literal 3/16 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 9/8 binary64)) #s(literal 3/8 binary64)) (pow.f64 (pow.f64 x #s(literal 7/8 binary64)) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 5/4 binary64)) #s(literal 3/8 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 3/8 binary64)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/16 binary64))) (fabs.f64 (pow.f64 x #s(literal 9/16 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/32 binary64))) (fabs.f64 (pow.f64 x #s(literal 21/32 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 21/32 binary64))) (fabs.f64 (pow.f64 x #s(literal 3/32 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 9/16 binary64))) (fabs.f64 (pow.f64 x #s(literal 3/16 binary64))))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))

simplify196.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

2394×	`-lowering-.f32`
2394×	`-lowering-.f64`
1462×	`sum3-define`
1392×	`fma-lowering-fma.f32`
1392×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	1044
1	192	1008
2	541	976
3	1188	976
4	1770	964
5	3561	964
6	6231	964
0	8036	964

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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

eval145.0ms (3.2%)

Compiler: Compiled 14481 to 2006 computations (86.1% saved)

prune84.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1163	4	1167
Fresh	4	0	4
Picked	4	1	5
Done	0	1	1
Total	1171	6	1177

Accuracy

100.0%

Counts

1177 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 7/16 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
▶	99.4%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
▶	99.4%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	99.1%	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))) x)
✓	58.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 52 to 41 computations (21.2% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(pow.f64 x #s(literal 1/16 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 7/16 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
✓	cost-diff	64	(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 7/16 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
✓	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))
✓	cost-diff	0	(log.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
✓	cost-diff	6528	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
✓	cost-diff	6528	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))) x)

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	103
1	36	99
2	46	97
3	50	97
0	50	97

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (exp (* 1/2 (log 2))) x)
(exp (* 1/2 (log 2)))
(* 1/2 (log 2))
1/2
(log 2)
2
x
(* (sqrt (* 2 x)) (sqrt x))
(sqrt (* 2 x))
(* 2 x)
2
x
(sqrt x)
(* (sqrt (* 2 (sqrt x))) (pow x 3/4))
(sqrt (* 2 (sqrt x)))
(* 2 (sqrt x))
2
(sqrt x)
x
(pow x 3/4)
3/4
(* (pow x 1/16) (* (pow x 7/16) (pow (* 2 x) 1/2)))
(pow x 1/16)
x
1/16
(* (pow x 7/16) (pow (* 2 x) 1/2))
(pow x 7/16)
7/16
(pow (* 2 x) 1/2)
(* 2 x)
2
1/2

Outputs
(* (exp (* 1/2 (log 2))) x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(exp (* 1/2 (log 2)))
(sqrt.f64 #s(literal 2 binary64))
(* 1/2 (log 2))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(log 2)
(log.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
x
(* (sqrt (* 2 x)) (sqrt x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) 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)
(* (sqrt (* 2 (sqrt x))) (pow x 3/4))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
(sqrt (* 2 (sqrt x)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
2
#s(literal 2 binary64)
(sqrt x)
(sqrt.f64 x)
x
(pow x 3/4)
(pow.f64 x #s(literal 3/4 binary64))
3/4
#s(literal 3/4 binary64)
(* (pow x 1/16) (* (pow x 7/16) (pow (* 2 x) 1/2)))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 7/16 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) x))))
(pow x 1/16)
(pow.f64 x #s(literal 1/16 binary64))
x
1/16
#s(literal 1/16 binary64)
(* (pow x 7/16) (pow (* 2 x) 1/2))
(.f64 (pow.f64 x #s(literal 7/16 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(pow x 7/16)
(pow.f64 x #s(literal 7/16 binary64))
7/16
#s(literal 7/16 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)

localize145.0ms (3.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(pow.f64 x #s(literal 1/16 binary64))
✓	accuracy	99.5%	(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 7/16 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
✓	accuracy	99.5%	(.f64 (pow.f64 x #s(literal 7/16 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(pow.f64 x #s(literal 3/4 binary64))
✓	accuracy	99.8%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
✓	accuracy	99.4%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 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	99.4%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))) x)
✓	accuracy	98.4%	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))

Results

112.0ms

256×

valid

Compiler

Compiled 108 to 24 computations (77.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-pow: 20.0ms (42.5% of total)

ival-mult: 14.0ms (29.7% of total)

ival-sqrt: 5.0ms (10.6% of total)

ival-log: 4.0ms (8.5% of total)

ival-exp: 3.0ms (6.4% of total)

const: 1.0ms (2.1% of total)

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

series33.0ms (0.7%)

Counts

16 → 156

Calls

Call 1

Inputs
#<alt (* (exp (* 1/2 (log 2))) x)>
#<alt (exp (* 1/2 (log 2)))>
#<alt (* 1/2 (log 2))>
#<alt (log 2)>
#<alt (* (sqrt (* 2 x)) (sqrt x))>
#<alt (sqrt (* 2 x))>
#<alt (* 2 x)>
#<alt (sqrt x)>
#<alt (* (sqrt (* 2 (sqrt x))) (pow x 3/4))>
#<alt (sqrt (* 2 (sqrt x)))>
#<alt (* 2 (sqrt x))>
#<alt (* (pow x 1/16) (* (pow x 7/16) (pow (* 2 x) 1/2)))>
#<alt (* (pow x 7/16) (pow (* 2 x) 1/2))>
#<alt (pow (* 2 x) 1/2)>
#<alt (pow x 1/16)>
#<alt (pow x 3/4)>

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 (* 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 (* -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 (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (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 (* -1 (* (pow -1 1/8) (* x (sqrt -2))))>
#<alt (* -1 (* (pow -1 1/8) (* x (sqrt -2))))>
#<alt (* -1 (* (pow -1 1/8) (* x (sqrt -2))))>
#<alt (* -1 (* (pow -1 1/8) (* x (sqrt -2))))>
#<alt (* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))>
#<alt (* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 x)))))) (sqrt -2))>
#<alt (* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 x)))))) (sqrt -2))>
#<alt (* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 x)))))) (sqrt -2))>
#<alt (* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 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 (* (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 (pow (* 1 x) 1/16)>
#<alt (pow (* 1 x) 1/16)>
#<alt (pow (* 1 x) 1/16)>
#<alt (pow (* 1 x) 1/16)>
#<alt (pow (* 1 x) 1/16)>
#<alt (pow (* 1 x) 1/16)>
#<alt (pow (* 1 x) 1/16)>
#<alt (pow (* 1 x) 1/16)>
#<alt (exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))>
#<alt (exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))>
#<alt (exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))>
#<alt (exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>

Calls

39 calls:

Time	Variable		Point	Expression
11.0ms	x	@	inf	(* (pow x 7/16) (pow (* 2 x) 1/2))
8.0ms	x	@	0	(* (pow x 7/16) (pow (* 2 x) 1/2))
7.0ms	x	@	-inf	(* (pow x 7/16) (pow (* 2 x) 1/2))
1.0ms	x	@	-inf	(* (pow x 1/16) (* (pow x 7/16) (pow (* 2 x) 1/2)))
0.0ms	x	@	-inf	(sqrt (* 2 (sqrt x)))

rewrite217.0ms (4.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2354×	`-lowering-.f32`
2354×	`-lowering-.f64`
2250×	`pow-lowering-pow.f64`
2250×	`pow-lowering-pow.f32`
1422×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	75
1	58	60
2	117	58
3	318	58
4	987	58
5	4247	58
0	8216	58

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 455

Calls

Call 1

Inputs
(* (exp (* 1/2 (log 2))) x)
(exp (* 1/2 (log 2)))
(* 1/2 (log 2))
(log 2)
(* (sqrt (* 2 x)) (sqrt x))
(sqrt (* 2 x))
(* 2 x)
(sqrt x)
(* (sqrt (* 2 (sqrt x))) (pow x 3/4))
(sqrt (* 2 (sqrt x)))
(* 2 (sqrt x))
(* (pow x 1/16) (* (pow x 7/16) (pow (* 2 x) 1/2)))
(* (pow x 7/16) (pow (* 2 x) 1/2))
(pow (* 2 x) 1/2)
(pow x 1/16)
(pow x 3/4)

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(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) (sqrt.f64 x))) (.f64 (log.f64 x) #s(literal 3/2 binary64))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 (.f64 (log.f64 x) #s(literal 3/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 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 1/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 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 15/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 1/4 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)))
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(.f64 (pow.f64 x #s(literal 9/32 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/16 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/4 binary64)))) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 15/16 binary64)))) (pow.f64 x #s(literal 1/32 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 9/16 binary64)))) (pow.f64 x #s(literal 7/32 binary64)))
(exp.f64 (*.f64 #s(literal 1/16 binary64) (log.f64 x)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 x) #s(literal 1/8 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/32 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/64 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/32 binary64))) (.f64 #s(literal 2 binary64) (log.f64 x))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/8 binary64))) (/.f64 (log.f64 x) #s(literal 2 binary64))))
(fabs.f64 (pow.f64 x #s(literal 1/16 binary64)))
(fabs.f64 (neg.f64 (pow.f64 x #s(literal 1/16 binary64))))
(sqrt.f64 (pow.f64 x #s(literal 1/8 binary64)))
(pow.f64 x #s(literal 1/16 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 x #s(literal 1/16 binary64)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 1/8 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 1/8 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/32 binary64))
(pow.f64 (pow.f64 x #s(literal 1/32 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/16 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 1/16 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/64 binary64)) #s(literal 4 binary64))
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 1/64 binary64))
(pow.f64 (exp.f64 #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 1/8 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x))) #s(literal 1/128 binary64))
(pow.f64 (E.f64) (*.f64 #s(literal 1/16 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/32 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/32 binary64)) #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/32 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/32 binary64)) #s(literal 4 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) #s(literal 2 binary64)) (/.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) #s(literal 1 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/32 binary64)) (exp.f64 #s(literal 1/32 binary64))) (log.f64 x))
(*.f64 (pow.f64 x #s(literal 1/32 binary64)) (pow.f64 x #s(literal 1/32 binary64)))
(*.f64 (pow.f64 x #s(literal 1/256 binary64)) (pow.f64 x #s(literal 15/256 binary64)))
(*.f64 (pow.f64 x #s(literal 9/256 binary64)) (pow.f64 x #s(literal 7/256 binary64)))
(*.f64 (pow.f64 x #s(literal 3/64 binary64)) (pow.f64 x #s(literal 1/64 binary64)))
(*.f64 (pow.f64 x #s(literal 15/256 binary64)) (pow.f64 x #s(literal 1/256 binary64)))
(*.f64 (pow.f64 x #s(literal 1/64 binary64)) (pow.f64 x #s(literal 3/64 binary64)))
(*.f64 (pow.f64 x #s(literal 1/64 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/32 binary64))))
(*.f64 (pow.f64 x #s(literal 7/256 binary64)) (pow.f64 x #s(literal 9/256 binary64)))
(*.f64 (pow.f64 x #s(literal 7/128 binary64)) (pow.f64 x #s(literal 1/128 binary64)))
(*.f64 (pow.f64 x #s(literal 1/128 binary64)) (pow.f64 x #s(literal 7/128 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3/32 binary64))) (pow.f64 x #s(literal 1/64 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 7/128 binary64))) (sqrt.f64 (pow.f64 x #s(literal 9/128 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 9/128 binary64))) (sqrt.f64 (pow.f64 x #s(literal 7/128 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 1/128 binary64))) (sqrt.f64 (pow.f64 x #s(literal 15/128 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 15/128 binary64))) (sqrt.f64 (pow.f64 x #s(literal 1/128 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 7/256 binary64))) (fabs.f64 (pow.f64 x #s(literal 9/256 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 1/64 binary64))) (fabs.f64 (pow.f64 x #s(literal 3/64 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 1/256 binary64))) (fabs.f64 (pow.f64 x #s(literal 15/256 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 15/256 binary64))) (fabs.f64 (pow.f64 x #s(literal 1/256 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 9/256 binary64))) (fabs.f64 (pow.f64 x #s(literal 7/256 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/64 binary64))) (fabs.f64 (pow.f64 x #s(literal 1/64 binary64))))
(exp.f64 (*.f64 #s(literal 3/4 binary64) (log.f64 x)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 x) #s(literal 3/2 binary64))))
(exp.f64 (.f64 (.f64 #s(literal 3/8 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 3/16 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 3/8 binary64))) (.f64 #s(literal 2 binary64) (log.f64 x))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 3/2 binary64))) (/.f64 (log.f64 x) #s(literal 2 binary64))))
(fabs.f64 (pow.f64 x #s(literal 3/4 binary64)))
(fabs.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))))
(sqrt.f64 (pow.f64 x #s(literal 3/2 binary64)))
(pow.f64 x #s(literal 3/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 3/2 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 3/2 binary64)))
(pow.f64 (*.f64 x x) #s(literal 3/8 binary64))
(pow.f64 (exp.f64 #s(literal 3/4 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 3/4 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/16 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 3/16 binary64))
(pow.f64 (exp.f64 #s(literal 3/8 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 3/2 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x))) #s(literal 3/32 binary64))
(pow.f64 (E.f64) (*.f64 #s(literal 3/4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 3/8 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 3/8 binary64)) #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 3/8 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 3/8 binary64)) #s(literal 4 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 3/2 binary64)) #s(literal 2 binary64)) (/.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 3/2 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 3/2 binary64)) #s(literal 1 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 9/16 binary64)) (pow.f64 x #s(literal 3/16 binary64)))
(*.f64 (pow.f64 x #s(literal 9/16 binary64)) (fabs.f64 (pow.f64 x #s(literal 3/16 binary64))))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 x #s(literal 3/16 binary64)) (pow.f64 x #s(literal 9/16 binary64)))
(*.f64 (pow.f64 x #s(literal 3/64 binary64)) (pow.f64 x #s(literal 45/64 binary64)))
(*.f64 (pow.f64 x #s(literal 21/64 binary64)) (pow.f64 x #s(literal 27/64 binary64)))
(*.f64 (pow.f64 x #s(literal 45/64 binary64)) (pow.f64 x #s(literal 3/64 binary64)))
(*.f64 (pow.f64 x #s(literal 27/64 binary64)) (pow.f64 x #s(literal 21/64 binary64)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/16 binary64))) (pow.f64 x #s(literal 9/16 binary64)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/64 binary64))) (fabs.f64 (pow.f64 x #s(literal 45/64 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 45/64 binary64))) (fabs.f64 (pow.f64 x #s(literal 3/64 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 21/64 binary64))) (fabs.f64 (pow.f64 x #s(literal 27/64 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 27/64 binary64))) (fabs.f64 (pow.f64 x #s(literal 21/64 binary64))))

simplify203.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

2626×	`-lowering-.f32`
2626×	`-lowering-.f64`
2172×	`sum3-define`
2044×	`fma-define`
1544×	`fnmadd-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	864
1	164	856
2	447	832
3	988	832
4	1292	824
5	1936	824
6	3715	824
7	7331	824
0	8269	824

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

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))
(* 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))
(* -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))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (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))
(* -1 (* (pow -1 1/8) (* x (sqrt -2))))
(* -1 (* (pow -1 1/8) (* x (sqrt -2))))
(* -1 (* (pow -1 1/8) (* x (sqrt -2))))
(* -1 (* (pow -1 1/8) (* x (sqrt -2))))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 x)))))) (sqrt -2))
(* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 x)))))) (sqrt -2))
(* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 x)))))) (sqrt -2))
(* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 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))
(* (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))))
(pow (* 1 x) 1/16)
(pow (* 1 x) 1/16)
(pow (* 1 x) 1/16)
(pow (* 1 x) 1/16)
(pow (* 1 x) 1/16)
(pow (* 1 x) 1/16)
(pow (* 1 x) 1/16)
(pow (* 1 x) 1/16)
(exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (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)))
(* 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)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) x))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) x))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) x))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 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 #s(literal -2 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 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)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64))))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64))))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 2 binary64) (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)))
(* -1 (* (pow -1 1/8) (* x (sqrt -2))))
(.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 9/8 binary64))))
(* -1 (* (pow -1 1/8) (* x (sqrt -2))))
(.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 9/8 binary64))))
(* -1 (* (pow -1 1/8) (* x (sqrt -2))))
(.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 9/8 binary64))))
(* -1 (* (pow -1 1/8) (* x (sqrt -2))))
(.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 9/8 binary64))))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 15 binary64)) #s(literal 1/16 binary64)))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 15 binary64)) #s(literal 1/16 binary64)))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 15 binary64)) #s(literal 1/16 binary64)))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 15 binary64)) #s(literal 1/16 binary64)))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 15 binary64)) #s(literal 1/16 binary64)))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 15 binary64)) #s(literal 1/16 binary64)))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 15 binary64)) #s(literal 1/16 binary64)))
(* (pow (* 1 (pow x 15)) 1/16) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 15 binary64)) #s(literal 1/16 binary64)))
(* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 x)))))) (sqrt -2))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/16 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -15/16 binary64))))
(* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 x)))))) (sqrt -2))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/16 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -15/16 binary64))))
(* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 x)))))) (sqrt -2))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/16 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -15/16 binary64))))
(* (exp (* 1/16 (+ (log -1) (* -15 (log (/ -1 x)))))) (sqrt -2))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/16 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -15/16 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 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(pow (* 1 x) 1/16)
(pow.f64 x #s(literal 1/16 binary64))
(pow (* 1 x) 1/16)
(pow.f64 x #s(literal 1/16 binary64))
(pow (* 1 x) 1/16)
(pow.f64 x #s(literal 1/16 binary64))
(pow (* 1 x) 1/16)
(pow.f64 x #s(literal 1/16 binary64))
(pow (* 1 x) 1/16)
(pow.f64 x #s(literal 1/16 binary64))
(pow (* 1 x) 1/16)
(pow.f64 x #s(literal 1/16 binary64))
(pow (* 1 x) 1/16)
(pow.f64 x #s(literal 1/16 binary64))
(pow (* 1 x) 1/16)
(pow.f64 x #s(literal 1/16 binary64))
(exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/16 binary64))
(exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/16 binary64))
(exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/16 binary64))
(exp (* 1/16 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/16 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3 binary64))) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3 binary64))) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3 binary64))) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3 binary64))) #s(literal 1/4 binary64))

eval88.0ms (2%)

Compiler: Compiled 8816 to 1149 computations (87% saved)

prune45.0ms (1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	718	1	719
Fresh	0	0	0
Picked	1	3	4
Done	0	2	2
Total	719	6	725

Accuracy

100.0%

Counts

725 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(.f64 (pow.f64 x #s(literal 9/32 binary64)) (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 7/32 binary64))))
✓	99.4%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
✓	99.4%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	99.1%	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))) x)
✓	58.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 51 to 40 computations (21.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
✓	cost-diff	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 7/32 binary64)))
✓	cost-diff	(pow.f64 x #s(literal 9/32 binary64))
✓	cost-diff	(.f64 (pow.f64 x #s(literal 9/32 binary64)) (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 7/32 binary64))))

Rules

28×	`-lowering-.f32`
28×	`-lowering-.f64`
12×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	15	37
2	22	37
3	24	37
0	24	37

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (pow x 9/32) (* (sqrt (* 2 x)) (pow x 7/32)))
(pow x 9/32)
x
9/32
(* (sqrt (* 2 x)) (pow x 7/32))
(sqrt (* 2 x))
(* 2 x)
2
(pow x 7/32)
7/32

Outputs
(* (pow x 9/32) (* (sqrt (* 2 x)) (pow x 7/32)))
(.f64 (pow.f64 x #s(literal 7/32 binary64)) (.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
(pow x 9/32)
(pow.f64 x #s(literal 9/32 binary64))
x
9/32
#s(literal 9/32 binary64)
(* (sqrt (* 2 x)) (pow x 7/32))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 7/32 binary64)))
(sqrt (* 2 x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(pow x 7/32)
(pow.f64 x #s(literal 7/32 binary64))
7/32
#s(literal 7/32 binary64)

localize59.0ms (1.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(pow.f64 x #s(literal 9/32 binary64))
✓	accuracy	99.4%	(.f64 (pow.f64 x #s(literal 9/32 binary64)) (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 7/32 binary64))))
✓	accuracy	99.4%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 7/32 binary64)))

Results

45.0ms

256×

valid

Compiler

Compiled 39 to 11 computations (71.8% saved)

Precisions

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

ival-pow: 11.0ms (58.6% of total)

ival-mult: 5.0ms (26.6% of total)

ival-sqrt: 2.0ms (10.7% of total)

const: 1.0ms (5.3% of total)

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

series71.0ms (1.6%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (* (pow x 9/32) (* (sqrt (* 2 x)) (pow x 7/32)))>
#<alt (pow x 9/32)>
#<alt (* (sqrt (* 2 x)) (pow x 7/32))>
#<alt (sqrt (* 2 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 (* (pow -1 1/16) (* x (sqrt -2))))>
#<alt (* -1 (* (pow -1 1/16) (* x (sqrt -2))))>
#<alt (* -1 (* (pow -1 1/16) (* x (sqrt -2))))>
#<alt (* -1 (* (pow -1 1/16) (* x (sqrt -2))))>
#<alt (pow (* 1 (pow x 9)) 1/32)>
#<alt (pow (* 1 (pow x 9)) 1/32)>
#<alt (pow (* 1 (pow x 9)) 1/32)>
#<alt (pow (* 1 (pow x 9)) 1/32)>
#<alt (pow (* 1 (pow x 9)) 1/32)>
#<alt (pow (* 1 (pow x 9)) 1/32)>
#<alt (pow (* 1 (pow x 9)) 1/32)>
#<alt (pow (* 1 (pow x 9)) 1/32)>
#<alt (exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))>
#<alt (exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))>
#<alt (exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))>
#<alt (exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))>
#<alt (* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))>
#<alt (* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))>
#<alt (* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 x)))))) (sqrt -2))>
#<alt (* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 x)))))) (sqrt -2))>
#<alt (* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 x)))))) (sqrt -2))>
#<alt (* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 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 (* (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))))>

Calls

12 calls:

Time	Variable		Point	Expression
15.0ms	x	@	0	(* (pow x 9/32) (* (sqrt (* 2 x)) (pow x 7/32)))
12.0ms	x	@	-inf	(pow x 9/32)
12.0ms	x	@	0	(pow x 9/32)
9.0ms	x	@	inf	(* (sqrt (* 2 x)) (pow x 7/32))
8.0ms	x	@	0	(* (sqrt (* 2 x)) (pow x 7/32))

rewrite288.0ms (6.4%)

Algorithm

1×	batch-egg-rewrite

Rules

5436×	`-lowering-.f32`
5436×	`-lowering-.f64`
2188×	`pow-lowering-pow.f64`
2188×	`pow-lowering-pow.f32`
1688×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	25	27
2	50	20
3	113	17
4	294	17
5	968	17
6	5676	17
0	8153	17

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 257

Calls

Call 1

Inputs
(* (pow x 9/32) (* (sqrt (* 2 x)) (pow x 7/32)))
(pow x 9/32)
(* (sqrt (* 2 x)) (pow x 7/32))
(sqrt (* 2 x))

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 x (*.f64 x #s(literal 2 binary64))))))
(sqrt.f64 (.f64 x (.f64 x #s(literal 2 binary64))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 x (.f64 x #s(literal 2 binary64)))))
(pow.f64 (.f64 x (.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 9/32 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64))))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 7/32 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64))) (pow.f64 x #s(literal 9/32 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64))) (pow.f64 x #s(literal 7/32 binary64)))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 25/32 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 23/32 binary64)))
(.f64 (pow.f64 x #s(literal 23/32 binary64)) (.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 25/32 binary64)) (.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 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 (pow.f64 x #s(literal 9/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 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 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64))) (pow.f64 x #s(literal 9/16 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1/2 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 x #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 161/1024 binary64)) (.f64 (pow.f64 x #s(literal 63/1024 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64)))))
(.f64 (pow.f64 x #s(literal 161/1024 binary64)) (.f64 (pow.f64 x #s(literal 575/1024 binary64)) (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 49/1024 binary64)) (.f64 (pow.f64 x #s(literal 175/1024 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64)))))
(.f64 (pow.f64 x #s(literal 7/64 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 57/32 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 7/64 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 57/32 binary64)))))
(.f64 (pow.f64 x #s(literal 7/64 binary64)) (.f64 (pow.f64 x #s(literal 7/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64)))))
(.f64 (pow.f64 x #s(literal 7/64 binary64)) (.f64 (pow.f64 x #s(literal 25/64 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 207/1024 binary64)) (.f64 (pow.f64 x #s(literal 81/1024 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64)))))
(.f64 (pow.f64 x #s(literal 207/1024 binary64)) (.f64 (pow.f64 x #s(literal 529/1024 binary64)) (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 529/1024 binary64)) (.f64 (pow.f64 x #s(literal 207/1024 binary64)) (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 23/64 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 41/32 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 23/64 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 41/32 binary64)))))
(.f64 (pow.f64 x #s(literal 23/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 23/64 binary64)) (.f64 (pow.f64 x #s(literal 23/64 binary64)) (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 81/1024 binary64)) (.f64 (pow.f64 x #s(literal 207/1024 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64)))))
(.f64 (pow.f64 x #s(literal 63/1024 binary64)) (.f64 (pow.f64 x #s(literal 225/1024 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64)))))
(.f64 (pow.f64 x #s(literal 63/1024 binary64)) (.f64 (pow.f64 x #s(literal 161/1024 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 55/32 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 55/32 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 23/64 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 225/1024 binary64)) (.f64 (pow.f64 x #s(literal 63/1024 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64)))))
(.f64 (pow.f64 x #s(literal 225/1024 binary64)) (.f64 (pow.f64 x #s(literal 575/1024 binary64)) (*.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 575/1024 binary64)) (.f64 (pow.f64 x #s(literal 161/1024 binary64)) (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 575/1024 binary64)) (.f64 (pow.f64 x #s(literal 225/1024 binary64)) (*.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 175/1024 binary64)) (.f64 (pow.f64 x #s(literal 49/1024 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64)))))
(.f64 (pow.f64 x #s(literal 175/1024 binary64)) (.f64 (pow.f64 x #s(literal 625/1024 binary64)) (*.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 625/1024 binary64)) (.f64 (pow.f64 x #s(literal 175/1024 binary64)) (*.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 25/64 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 39/32 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 25/64 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 39/32 binary64)))))
(.f64 (pow.f64 x #s(literal 25/64 binary64)) (.f64 (pow.f64 x #s(literal 7/64 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(.f64 (pow.f64 x #s(literal 25/64 binary64)) (.f64 (pow.f64 x #s(literal 25/64 binary64)) (*.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 41/32 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 23/64 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 39/32 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 25/64 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 55/32 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 57/32 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 7/64 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 41/32 binary64)))) (pow.f64 x #s(literal 23/64 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 39/32 binary64)))) (pow.f64 x #s(literal 25/64 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 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 55/32 binary64)))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 57/32 binary64)))) (pow.f64 x #s(literal 7/64 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 9/64 binary64))) (pow.f64 x #s(literal 23/64 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 23/64 binary64))) (pow.f64 x #s(literal 23/64 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 7/64 binary64))) (pow.f64 x #s(literal 25/64 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 25/64 binary64))) (pow.f64 x #s(literal 25/64 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 23/64 binary64))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 25/64 binary64))) (pow.f64 x #s(literal 7/64 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64))) (pow.f64 x #s(literal 81/1024 binary64))) (pow.f64 x #s(literal 207/1024 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64))) (pow.f64 x #s(literal 207/1024 binary64))) (pow.f64 x #s(literal 81/1024 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64))) (pow.f64 x #s(literal 63/1024 binary64))) (pow.f64 x #s(literal 225/1024 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64))) (pow.f64 x #s(literal 225/1024 binary64))) (pow.f64 x #s(literal 63/1024 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 23/32 binary64))) (pow.f64 x #s(literal 9/64 binary64))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64))) (pow.f64 x #s(literal 63/1024 binary64))) (pow.f64 x #s(literal 161/1024 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64))) (pow.f64 x #s(literal 161/1024 binary64))) (pow.f64 x #s(literal 63/1024 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64))) (pow.f64 x #s(literal 49/1024 binary64))) (pow.f64 x #s(literal 175/1024 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64))) (pow.f64 x #s(literal 175/1024 binary64))) (pow.f64 x #s(literal 49/1024 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64))) (pow.f64 x #s(literal 7/64 binary64))) (pow.f64 x #s(literal 7/64 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 225/1024 binary64))) (pow.f64 x #s(literal 575/1024 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 575/1024 binary64))) (pow.f64 x #s(literal 225/1024 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 175/1024 binary64))) (pow.f64 x #s(literal 625/1024 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 7/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 625/1024 binary64))) (pow.f64 x #s(literal 175/1024 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 207/1024 binary64))) (pow.f64 x #s(literal 529/1024 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 529/1024 binary64))) (pow.f64 x #s(literal 207/1024 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 161/1024 binary64))) (pow.f64 x #s(literal 575/1024 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 575/1024 binary64))) (pow.f64 x #s(literal 161/1024 binary64)))
(exp.f64 (*.f64 #s(literal 9/32 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 9/64 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 9/64 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 9/128 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 9/64 binary64))) (.f64 #s(literal 2 binary64) (log.f64 x))))
(pow.f64 x #s(literal 9/32 binary64))
(pow.f64 (pow.f64 x #s(literal 9/32 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 9/16 binary64))
(pow.f64 (exp.f64 #s(literal 9/32 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 9/16 binary64)))
(pow.f64 (*.f64 x x) #s(literal 9/64 binary64))
(pow.f64 (pow.f64 x #s(literal 9/16 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 9/64 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 9/32 binary64) (log.f64 x)))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 9/128 binary64))
(pow.f64 (exp.f64 #s(literal 9/16 binary64)) (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 9/64 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 9/64 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 9/8 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 9/32 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 9/16 binary64)) (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 9/64 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 9/16 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 9/64 binary64)) #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 9/64 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 9/64 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 9/64 binary64)) (*.f64 (log.f64 x) #s(literal 1/2 binary64))) #s(literal 4 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 9/64 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 9/64 binary64)) #s(literal 4 binary64)) (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 207/1024 binary64)) (pow.f64 x #s(literal 81/1024 binary64)))
(*.f64 (pow.f64 x #s(literal 81/1024 binary64)) (pow.f64 x #s(literal 207/1024 binary64)))
(*.f64 (pow.f64 x #s(literal 63/1024 binary64)) (pow.f64 x #s(literal 225/1024 binary64)))
(*.f64 (pow.f64 x #s(literal 9/64 binary64)) (pow.f64 x #s(literal 9/64 binary64)))
(*.f64 (pow.f64 x #s(literal 225/1024 binary64)) (pow.f64 x #s(literal 63/1024 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 7/16 binary64)) #s(literal 9/32 binary64)) (pow.f64 (pow.f64 x #s(literal 9/16 binary64)) #s(literal 9/32 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 9/16 binary64)) #s(literal 9/32 binary64)) (pow.f64 (pow.f64 x #s(literal 7/16 binary64)) #s(literal 9/32 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 9/32 binary64)) #s(literal 9/16 binary64)) (pow.f64 (pow.f64 x #s(literal 7/32 binary64)) #s(literal 9/16 binary64)))
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(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64))))
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(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 63/1024 binary64))) (pow.f64 x #s(literal 161/1024 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 49/1024 binary64))) (pow.f64 x #s(literal 175/1024 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 9/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 175/1024 binary64))) (pow.f64 x #s(literal 49/1024 binary64)))

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1128×	`fma-define`
948×	`sum3-define`
368×	`fnmadd-define`
352×	`fma-lowering-fma.f32`
352×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	43	356
1	88	348
2	199	328
3	353	328
4	392	320
5	511	320
6	729	320
7	816	320
8	975	320
9	1984	320
10	2069	320
11	2076	320
12	2082	320
0	2082	320

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

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 (* (pow -1 1/16) (* x (sqrt -2))))
(* -1 (* (pow -1 1/16) (* x (sqrt -2))))
(* -1 (* (pow -1 1/16) (* x (sqrt -2))))
(* -1 (* (pow -1 1/16) (* x (sqrt -2))))
(pow (* 1 (pow x 9)) 1/32)
(pow (* 1 (pow x 9)) 1/32)
(pow (* 1 (pow x 9)) 1/32)
(pow (* 1 (pow x 9)) 1/32)
(pow (* 1 (pow x 9)) 1/32)
(pow (* 1 (pow x 9)) 1/32)
(pow (* 1 (pow x 9)) 1/32)
(pow (* 1 (pow x 9)) 1/32)
(exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))
(exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))
(exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))
(exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 x)))))) (sqrt -2))
(* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 x)))))) (sqrt -2))
(* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 x)))))) (sqrt -2))
(* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 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))
(* (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))))

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 (* (pow -1 1/16) (* x (sqrt -2))))
(.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 17/16 binary64))))
(* -1 (* (pow -1 1/16) (* x (sqrt -2))))
(.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 17/16 binary64))))
(* -1 (* (pow -1 1/16) (* x (sqrt -2))))
(.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 17/16 binary64))))
(* -1 (* (pow -1 1/16) (* x (sqrt -2))))
(.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 17/16 binary64))))
(pow (* 1 (pow x 9)) 1/32)
(pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/32 binary64))
(pow (* 1 (pow x 9)) 1/32)
(pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/32 binary64))
(pow (* 1 (pow x 9)) 1/32)
(pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/32 binary64))
(pow (* 1 (pow x 9)) 1/32)
(pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/32 binary64))
(pow (* 1 (pow x 9)) 1/32)
(pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/32 binary64))
(pow (* 1 (pow x 9)) 1/32)
(pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/32 binary64))
(pow (* 1 (pow x 9)) 1/32)
(pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/32 binary64))
(pow (* 1 (pow x 9)) 1/32)
(pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/32 binary64))
(exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/32 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -9/32 binary64)))
(exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/32 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -9/32 binary64)))
(exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/32 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -9/32 binary64)))
(exp (* 1/32 (+ (log -1) (* -9 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/32 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -9/32 binary64)))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 23 binary64)) #s(literal 1/32 binary64)))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 23 binary64)) #s(literal 1/32 binary64)))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 23 binary64)) #s(literal 1/32 binary64)))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 23 binary64)) #s(literal 1/32 binary64)))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 23 binary64)) #s(literal 1/32 binary64)))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 23 binary64)) #s(literal 1/32 binary64)))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 23 binary64)) #s(literal 1/32 binary64)))
(* (pow (* 1 (pow x 23)) 1/32) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 23 binary64)) #s(literal 1/32 binary64)))
(* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 x)))))) (sqrt -2))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -23/32 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/32 binary64))))
(* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 x)))))) (sqrt -2))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -23/32 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/32 binary64))))
(* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 x)))))) (sqrt -2))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -23/32 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/32 binary64))))
(* (exp (* 1/32 (+ (log -1) (* -23 (log (/ -1 x)))))) (sqrt -2))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -23/32 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/32 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 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))

eval33.0ms (0.7%)

Compiler: Compiled 4600 to 791 computations (82.8% saved)

prune55.0ms (1.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	304	1	305
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	305	6	311

Accuracy

100.0%

Counts

311 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(.f64 (pow.f64 x #s(literal 7/32 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 binary64))))
✓	99.4%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
✓	99.4%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	99.1%	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))) x)
✓	58.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 202 to 112 computations (44.6% saved)

regimes23.0ms (0.5%)

Counts

17 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))) x)
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (.f64 x (.f64 x x))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
(sqrt.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64)))))
(.f64 (pow.f64 x #s(literal 7/32 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 25/32 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 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 9/32 binary64)) (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 7/32 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (pow.f64 x #s(literal 7/16 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 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:

6.0ms	x
6.0ms	(pow.f64 x #s(literal 2 binary64))
5.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
5.0ms	(*.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)

regimes8.0ms (0.2%)

Accuracy

Total -26.5b remaining (-6164%)

Threshold costs -26.5b (-6164%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	x
2.0ms	(pow.f64 x #s(literal 2 binary64))
2.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (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
99.3%	1	`x`
99.3%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
99.3%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
99.3%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11

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)

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)))

soundness540.0ms (12%)

Rules

4300×	`-lowering-.f32`
4300×	`-lowering-.f64`
2622×	`-lowering-.f32`
2622×	`-lowering-.f64`
1958×	`log-prod`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	80
1	66	75
2	144	63
3	307	63
4	915	63
5	5247	63
0	8135	63
0	5	11
1	15	11
2	39	10
3	79	10
4	242	10
5	796	10
6	3966	10
0	8155	10
0	5	6
1	7	5
2	12	5
3	13	5
0	13	5

Stop Event

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

Compiler

Compiled 48 to 35 computations (27.1% saved)

preprocess25.0ms (0.6%)

Compiler: Compiled 70 to 50 computations (28.6% saved)

Iter	Nodes	Cost
0	10	20
1	20	16
2	41	16
3	113	16
4	205	16
5	330	16
6	465	16
7	508	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	41	16
3	113	16
4	205	16
5	330	16
6	465	16
7	508	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%)

sample886.0ms (19.7%)

preprocess18.0ms (0.4%)

explain75.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize27.0ms (0.6%)

series3.0ms (0.1%)

rewrite240.0ms (5.3%)

simplify24.0ms (0.5%)

eval23.0ms (0.5%)

prune28.0ms (0.6%)

simplify7.0ms (0.2%)

localize159.0ms (3.5%)

series178.0ms (4%)

rewrite490.0ms (10.9%)

simplify196.0ms (4.4%)

eval145.0ms (3.2%)

prune84.0ms (1.9%)

simplify6.0ms (0.1%)

localize145.0ms (3.2%)

series33.0ms (0.7%)

rewrite217.0ms (4.8%)

simplify203.0ms (4.5%)

eval88.0ms (2%)

prune45.0ms (1%)

simplify7.0ms (0.1%)

localize59.0ms (1.3%)

series71.0ms (1.6%)

rewrite288.0ms (6.4%)

simplify51.0ms (1.1%)

eval33.0ms (0.7%)

prune55.0ms (1.2%)

regimes23.0ms (0.5%)

regimes8.0ms (0.2%)

simplify7.0ms (0.2%)

soundness540.0ms (12%)

preprocess25.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	20
1	20	16
2	41	16
3	113	16
4	205	16
5	330	16
6	465	16
7	508	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