Metrics for sqrt C (should all be same)

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

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)

sample709.0ms (18.4%)

Results

538.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 256.0ms

ival-mult: 139.0ms (54.3% of total)

ival-sqrt: 104.0ms (40.6% of total)

const: 10.0ms (3.9% of total)

backward-pass: 3.0ms (1.2% of total)

Bogosity

preprocess21.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

128×	`fma-define`
124×	`fmsub-define`
120×	`fnmsub-define`
120×	`fnmadd-define`
40×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	27	16
2	65	16
3	134	16
4	224	16
5	377	16
6	492	16
7	495	16
0	5	5
1	9	5
2	12	5
0	12	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

Symmetry

(abs x)

explain100.0ms (2.6%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
134	-	3	(2.3378134110701497e-161)	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
0	-	0	-	`(.f64 #s(literal 2 binary64) (.f64 x x))`
0	-	0	-	`x`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`#s(literal 2 binary64)`

Results

81.0ms

512×

valid

Compiler

Compiled 43 to 17 computations (60.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-mult: 43.0ms (77.4% of total)

ival-sqrt: 11.0ms (19.8% of total)

const: 1.0ms (1.8% 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
▶	51.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize29.0ms (0.7%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 x x))
✓	accuracy	51.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Results

22.0ms

256×

valid

Compiler

Compiled 18 to 6 computations (66.7% saved)

Precisions

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

ival-mult: 6.0ms (66.1% of total)

ival-sqrt: 2.0ms (22% 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)

rewrite230.0ms (6%)

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)))

simplify14.0ms (0.4%)

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 (0.6%)

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

prune32.0ms (0.8%)

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))
	99.3%	(.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))))
▶	70.1%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
▶	99.4%	(.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))))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
	51.5%	(sqrt.f64 (.f64 (pow.f64 x #s(literal 5/4 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/4 binary64)))))
▶	51.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 8 binary64))))
	51.2%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
✓	51.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 191 to 155 computations (18.8% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	123
1	37	123
2	44	123
3	46	123
0	46	123

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

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

localize178.0ms (4.6%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 x #s(literal 1/8 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	99.5%	(.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(.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))))
✓	accuracy	100.0%	(pow.f64 x #s(literal 1/4 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
✓	accuracy	99.5%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
✓	accuracy	69.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))))
✓	accuracy	100.0%	(pow.f64 x #s(literal 1/4 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 8 binary64)))
✓	accuracy	98.9%	(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 8 binary64))
✓	accuracy	51.5%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 8 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

140.0ms

256×

valid

Compiler

Compiled 130 to 27 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-pow: 31.0ms (56.8% of total)

ival-mult: 15.0ms (27.5% of total)

ival-sqrt: 8.0ms (14.7% of total)

const: 1.0ms (1.8% of total)

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

series185.0ms (4.8%)

Counts

16 → 180

Calls

Call 1

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

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

Calls

45 calls:

Time	Variable		Point	Expression
40.0ms	x	@	0	(* (pow x 3/8) (pow (* 2 x) 1/2))
30.0ms	x	@	0	(* (pow x 1/8) (* (pow x 3/8) (pow (* 2 x) 1/2)))
28.0ms	x	@	0	(pow x 1/4)
25.0ms	x	@	-inf	(pow x 1/4)
11.0ms	x	@	0	(sqrt (* 2 (pow x 3/2)))

rewrite170.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2426×	`-lowering-.f32`
2426×	`-lowering-.f64`
1582×	`pow-lowering-pow.f64`
1582×	`pow-lowering-pow.f32`
986×	`pow-to-exp`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	79
1	64	74
2	142	60
3	340	60
4	1226	60
5	5446	60
0	8167	60

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 498

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

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

simplify254.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

2610×	`-lowering-.f32`
2610×	`-lowering-.f64`
2378×	`fma-lowering-fma.f32`
2378×	`fma-lowering-fma.f64`
2090×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	952
1	166	904
2	478	888
3	1016	888
4	1288	884
5	1925	884
6	3362	884
7	6657	884
0	8453	884

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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

eval125.0ms (3.2%)

Compiler: Compiled 9465 to 1216 computations (87.2% saved)

prune69.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	808	2	810
Fresh	3	1	4
Picked	3	2	5
Done	0	1	1
Total	814	6	820

Accuracy

100.0%

Counts

820 → 6

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)))
✓	70.1%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 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)
✓	51.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 50 to 40 computations (20% saved)

simplify34.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 12 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	(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

24×	`-lowering-.f32`
24×	`-lowering-.f64`
12×	`*-commutative`
8×	`sqrt-lowering-sqrt.f64`
8×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	66
1	25	62
2	28	60
3	30	60
0	30	60

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

localize101.0ms (2.6%)

Localize:

Found 12 expressions of interest:

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

79.0ms

256×

valid

Compiler

Compiled 70 to 17 computations (75.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 10.0ms (29.7% of total)

ival-pow: 10.0ms (29.7% of total)

ival-log: 6.0ms (17.8% of total)

ival-sqrt: 4.0ms (11.9% of total)

ival-exp: 3.0ms (8.9% of total)

const: 1.0ms (3% of total)

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

series12.0ms (0.3%)

Counts

11 → 96

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

Calls

24 calls:

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

rewrite257.0ms (6.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2974×	`-lowering-.f32`
2974×	`-lowering-.f64`
1296×	`pow-lowering-pow.f64`
1296×	`pow-lowering-pow.f32`
1272×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	50
1	40	38
2	86	38
3	187	38
4	408	38
5	1828	38
6	7227	38
0	8065	38

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 277

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

simplify186.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

3126×	`fnmadd-define`
2160×	`fma-define`
1762×	`fma-lowering-fma.f32`
1762×	`fma-lowering-fma.f64`
1738×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	472
1	82	472
2	247	468
3	642	468
4	870	468
5	1361	468
6	2626	468
7	4336	468
8	5333	468
9	6864	468
10	7472	468
11	7873	468
0	8034	468

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

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)))

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 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (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 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 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))

eval47.0ms (1.2%)

Compiler: Compiled 5089 to 684 computations (86.6% saved)

prune31.0ms (0.8%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	436	1	437
Fresh	0	0	0
Picked	1	2	3
Done	0	3	3
Total	437	6	443

Accuracy

100.0%

Counts

443 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))
✓	70.1%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 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)
✓	51.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
✓	cost-diff	(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
✓	cost-diff	(pow.f64 x #s(literal 3/4 binary64))
✓	cost-diff	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))

Rules

8×	`-lowering-.f32`
8×	`-lowering-.f64`
4×	`*-commutative`
4×	`sqrt-lowering-sqrt.f64`
4×	`sqrt-lowering-sqrt.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	10	26
0	10	26

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize54.0ms (1.4%)

Localize:

Found 4 expressions of interest:

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

Results

43.0ms

256×

valid

Compiler

Compiled 28 to 9 computations (67.9% saved)

Precisions

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

ival-mult: 8.0ms (43% of total)

ival-pow: 6.0ms (32.3% of total)

ival-sqrt: 4.0ms (21.5% of total)

const: 1.0ms (5.4% of total)

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

series43.0ms (1.1%)

Counts

5 → 60

Calls

Call 1

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

Calls

15 calls:

Time	Variable		Point	Expression
24.0ms	x	@	-inf	(pow x 3/4)
10.0ms	x	@	0	(pow x 3/4)
7.0ms	x	@	inf	(pow x 3/4)
0.0ms	x	@	-inf	(sqrt (* 2 (sqrt x)))
0.0ms	x	@	inf	(sqrt (* 2 (sqrt x)))

rewrite196.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2232×	`-lowering-.f32`
2232×	`-lowering-.f64`
1758×	`+-lowering-+.f64`
1758×	`+-lowering-+.f32`
1644×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	19	23
2	38	20
3	74	18
4	133	18
5	265	18
6	560	18
7	2335	18
8	7295	18
0	8244	18

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 121

Calls

Call 1

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

Outputs
(exp.f64 (+.f64 (log.f64 x) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))))
(*.f64 x (sqrt.f64 #s(literal 2 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 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/4 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 (.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 9/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64))))
(.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 1/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))))
(.f64 (pow.f64 x #s(literal 1/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 27/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))))
(.f64 (pow.f64 x #s(literal 27/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 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 7/16 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 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64))) (pow.f64 x #s(literal 3/16 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 13/16 binary64)))
(.f64 (pow.f64 x #s(literal 13/16 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 15/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 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 1/16 binary64))) (pow.f64 x #s(literal 15/16 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))) (pow.f64 x #s(literal 27/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 27/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))) (pow.f64 x #s(literal 1/64 binary64)))
(exp.f64 (*.f64 #s(literal 3/4 binary64) (log.f64 x)))
(pow.f64 x #s(literal 3/4 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 (E.f64) (*.f64 #s(literal 3/4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (E.f64) #s(literal 3/4 binary64)) (log.f64 x))
(pow.f64 (*.f64 (exp.f64 #s(literal 9/16 binary64)) (exp.f64 #s(literal 3/16 binary64))) (log.f64 x))
(pow.f64 (*.f64 (exp.f64 #s(literal 3/16 binary64)) (exp.f64 #s(literal 9/16 binary64))) (log.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 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 9/64 binary64)) (pow.f64 x #s(literal 39/64 binary64)))
(*.f64 (pow.f64 x #s(literal 27/64 binary64)) (pow.f64 x #s(literal 21/64 binary64)))
(*.f64 (pow.f64 x #s(literal 39/64 binary64)) (pow.f64 x #s(literal 9/64 binary64)))
(*.f64 (pow.f64 x #s(literal 45/64 binary64)) (pow.f64 x #s(literal 3/64 binary64)))
(*.f64 (pow.f64 x #s(literal 21/64 binary64)) (pow.f64 x #s(literal 27/64 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))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (log.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)))))
(*.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 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 1/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 1/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 1/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 1/16 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)))
(.f64 (.f64 (pow.f64 x #s(literal 1/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 1/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 1/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 3/64 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 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 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 3/8 binary64)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))))
(.f64 (pow.f64 x #s(literal 1/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 9/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 1/8 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 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 3/32 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 1/32 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))) (pow.f64 x #s(literal 3/32 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))) (pow.f64 x #s(literal 9/32 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 3/8 binary64)))
(exp.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)))
(sqrt.f64 x)
(/.f64 #s(literal 1 binary64) (pow.f64 (E.f64) (/.f64 (log.f64 x) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (log.f64 x) #s(literal -2 binary64))))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (E.f64) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (E.f64) #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/8 binary64)) (exp.f64 #s(literal 3/8 binary64))) (log.f64 x))
(pow.f64 (*.f64 (exp.f64 #s(literal 3/8 binary64)) (exp.f64 #s(literal 1/8 binary64))) (log.f64 x))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 x #s(literal 3/32 binary64)) (pow.f64 x #s(literal 13/32 binary64)))
(*.f64 (pow.f64 x #s(literal 1/32 binary64)) (pow.f64 x #s(literal 15/32 binary64)))
(*.f64 (pow.f64 x #s(literal 9/32 binary64)) (pow.f64 x #s(literal 7/32 binary64)))
(*.f64 (pow.f64 x #s(literal 3/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 61/64 binary64))))
(*.f64 (pow.f64 x #s(literal 1/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 63/64 binary64))))
(*.f64 (pow.f64 x #s(literal 13/32 binary64)) (pow.f64 x #s(literal 3/32 binary64)))
(*.f64 (pow.f64 x #s(literal 9/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 55/64 binary64))))
(*.f64 (pow.f64 x #s(literal 27/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 37/64 binary64))))
(*.f64 (pow.f64 x #s(literal 7/32 binary64)) (pow.f64 x #s(literal 9/32 binary64)))
(*.f64 (pow.f64 x #s(literal 15/32 binary64)) (pow.f64 x #s(literal 1/32 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 61/64 binary64))) (pow.f64 x #s(literal 3/128 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 63/64 binary64))) (pow.f64 x #s(literal 1/128 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 55/64 binary64))) (pow.f64 x #s(literal 9/128 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 37/64 binary64))) (pow.f64 x #s(literal 27/128 binary64)))

simplify126.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

2834×	`fma-define`
1646×	`fnmadd-define`
1070×	`sum3-define`
982×	`fma-lowering-fma.f32`
982×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	39	336
1	87	332
2	221	320
3	521	320
4	931	316
5	1327	316
6	2469	316
7	3419	316
8	4249	316
9	5087	316
10	5342	316
11	5347	316
12	5350	316
13	5350	316
14	5499	316
15	5503	316
0	5503	316

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

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

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 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (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 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (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 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (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 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 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))
(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)))
(* (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 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.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)

eval21.0ms (0.5%)

Compiler: Compiled 2244 to 431 computations (80.8% saved)

prune18.0ms (0.5%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	181	6	187

Accuracy

100.0%

Counts

187 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))
✓	70.1%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 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)
✓	51.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 162 to 92 computations (43.2% saved)

regimes41.0ms (1.1%)

Counts

13 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.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) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 8 binary64))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(sqrt.f64 (.f64 (pow.f64 x #s(literal 5/4 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/4 binary64)))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
(.f64 (pow.f64 (.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 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 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:

16.0ms	x
4.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
4.0ms	(*.f64 x x)
4.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Results

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes7.0ms (0.2%)

Accuracy

Total -31.0b remaining (-7344.9%)

Threshold costs -31b (-7344.9%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.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	(*.f64 x x)
2.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
2.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
99.3%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
99.3%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify10.0ms (0.3%)

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)))

soundness481.0ms (12.5%)

Rules

2622×	`-lowering-.f32`
2622×	`-lowering-.f64`
2426×	`-lowering-.f32`
2426×	`-lowering-.f64`
1850×	`fma-define`

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
0	26	79
1	64	74
2	142	60
3	340	60
4	1226	60
5	5446	60
0	8167	60

Stop Event

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

Compiler

Compiled 34 to 25 computations (26.5% saved)

preprocess27.0ms (0.7%)

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

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	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

analyze1.0ms (0%)

sample709.0ms (18.4%)

preprocess21.0ms (0.5%)

explain100.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize29.0ms (0.7%)

series3.0ms (0.1%)

rewrite230.0ms (6%)

simplify14.0ms (0.4%)

eval23.0ms (0.6%)

prune32.0ms (0.8%)

simplify6.0ms (0.2%)

localize178.0ms (4.6%)

series185.0ms (4.8%)

rewrite170.0ms (4.4%)

simplify254.0ms (6.6%)

eval125.0ms (3.2%)

prune69.0ms (1.8%)

simplify34.0ms (0.9%)

localize101.0ms (2.6%)

series12.0ms (0.3%)

rewrite257.0ms (6.7%)

simplify186.0ms (4.8%)

eval47.0ms (1.2%)

prune31.0ms (0.8%)

simplify4.0ms (0.1%)

localize54.0ms (1.4%)

series43.0ms (1.1%)

rewrite196.0ms (5.1%)

simplify126.0ms (3.3%)

eval21.0ms (0.5%)

prune18.0ms (0.5%)

regimes41.0ms (1.1%)

regimes7.0ms (0.2%)

simplify10.0ms (0.3%)

soundness481.0ms (12.5%)

preprocess27.0ms (0.7%)

end0.0ms (0%)

Profiling

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