Metrics for sqrt D (should all be same)

analyze0.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 6 computations (25% saved)

Precisions

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

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

const: 0.0ms (0% of total)

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

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

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

sample741.0ms (18.7%)

Results

490.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 319.0ms

ival-mult: 129.0ms (40.5% of total)

ival-pow: 109.0ms (34.2% of total)

ival-sqrt: 67.0ms (21% of total)

const: 10.0ms (3.1% of total)

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

Bogosity

preprocess18.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	20	19
2	42	19
3	124	19
4	239	19
5	358	19
6	484	19
7	527	19
0	5	6
1	7	6
2	11	6
3	12	6
0	12	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

Symmetry

(abs x)

explain76.0ms (1.9%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
121	-	4	(2.7194061164858503e-157)	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`x`
0	-	0	-	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`

Results

38.0ms

512×

valid

Compiler

Compiled 43 to 17 computations (60.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-pow: 6.0ms (40% of total)

ival-mult: 4.0ms (26.7% of total)

ival-sqrt: 4.0ms (26.7% of total)

const: 1.0ms (6.7% 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
▶	57.4%	(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	16
1	8	16
2	11	16
0	11	16

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

localize23.0ms (0.6%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 x x))
✓	accuracy	57.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Results

14.0ms

256×

valid

Compiler

Compiled 18 to 6 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 4.0ms (60.6% of total)

ival-sqrt: 2.0ms (30.3% 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)

rewrite266.0ms (6.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3606×	`-lowering-.f32`
3606×	`-lowering-.f64`
1476×	`pow-lowering-pow.f64`
1476×	`pow-lowering-pow.f32`
1416×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	5	14
1	14	13
2	43	12
3	120	12
4	577	12
5	4098	12
0	8513	12

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 196

Calls

Call 1

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

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

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	64	148
6	96	148
7	108	148
8	139	148
9	232	148
10	235	148
0	235	148

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 #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)

eval31.0ms (0.8%)

Compiler: Compiled 2792 to 684 computations (75.5% saved)

prune42.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	228	4	232
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	228	5	233

Accuracy

100.0%

Counts

233 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
▶	99.2%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
▶	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	57.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 40 to 29 computations (27.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Rules

30×	`-lowering-.f32`
30×	`-lowering-.f64`
14×	`*-commutative`
8×	`pow-lowering-pow.f64`
8×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	65
1	26	65
2	29	65
3	32	65
4	32	65
0	32	65

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize98.0ms (2.5%)

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
✓	accuracy	100.0%	(pow.f64 x #s(literal 3/4 binary64))
✓	accuracy	100.0%	(*.f64 x #s(literal 4 binary64))
✓	accuracy	99.5%	(.f64 (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
✓	accuracy	100.0%	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
✓	accuracy	99.6%	(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
✓	accuracy	99.5%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Results

68.0ms

256×

valid

Compiler

Compiled 72 to 19 computations (73.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-pow: 20.0ms (49.9% of total)

ival-mult: 12.0ms (29.9% of total)

ival-sqrt: 7.0ms (17.5% of total)

const: 1.0ms (2.5% of total)

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

series165.0ms (4.2%)

Counts

13 → 132

Calls

Call 1

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

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

Calls

33 calls:

Time	Variable		Point	Expression
49.0ms	x	@	0	(* x (pow 2 1/4))
35.0ms	x	@	-inf	(pow (* x 4) 1/4)
19.0ms	x	@	0	(* (pow (* x 4) 1/4) (pow x 3/4))
14.0ms	x	@	0	(pow x 3/4)
14.0ms	x	@	-inf	(pow x 3/4)

rewrite517.0ms (13.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3432×	`-lowering-.f32`
3432×	`-lowering-.f64`
2632×	`+-lowering-+.f64`
2632×	`+-lowering-+.f32`
1952×	`prod-diff`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	55	46
2	159	46
3	611	46
4	4856	46
0	8251	46

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 682

Calls

Call 1

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

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

simplify218.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

2252×	`fnmadd-define`
1540×	`fma-lowering-fma.f32`
1540×	`fma-lowering-fma.f64`
1482×	`fma-define`
1432×	`fmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	640
1	136	636
2	324	616
3	584	592
4	1022	588
5	1736	588
6	3519	588
7	5332	588
8	7096	588
0	8016	588

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

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

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

eval138.0ms (3.5%)

Compiler: Compiled 10885 to 1067 computations (90.2% saved)

prune75.0ms (1.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	829	1	830
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	830	5	835

Accuracy

100.0%

Counts

835 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))
✓	99.5%	(.f64 (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
✓	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	57.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 36 to 27 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`
2×	`/-lowering-/.f32`
2×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	4	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x (pow 1/4 1/4))
x
(pow 1/4 1/4)
1/4

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

localize24.0ms (0.6%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))
✓	accuracy	99.3%	(/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))

Results

15.0ms

256×

valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

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

ival-pow: 6.0ms (75.9% of total)

ival-div: 2.0ms (25.3% of total)

const: 0.0ms (0% of total)

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

series10.0ms (0.3%)

Counts

2 → 12

Calls

Call 1

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

Outputs
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>

Calls

3 calls:

Time	Variable		Point	Expression
10.0ms	x	@	0	(/ x (pow 1/4 1/4))
0.0ms	x	@	-inf	(/ x (pow 1/4 1/4))
0.0ms	x	@	inf	(/ x (pow 1/4 1/4))

rewrite121.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1440×	`-lowering-.f32`
1440×	`-lowering-.f64`
1036×	`/-lowering-/.f32`
1036×	`/-lowering-/.f64`
312×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	20	8
2	85	8
3	400	8
0	2759	8

Stop Event

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

Counts

2 → 185

Calls

Call 1

Inputs
(/ x (pow 1/4 1/4))
(pow 1/4 1/4)

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) #s(literal 0 binary64)) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x)))
(/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))
(/.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)))))
(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x)) #s(literal -1 binary64))
(/.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))
(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) x))
(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)) x))
(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) x)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))))
(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)) x))
(/.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)))
(/.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)))
(/.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64))) (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) x)) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) x))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64)) (.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (.f64 (*.f64 x x) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))) (.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -1 binary64)) (*.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))) (*.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)))) (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64))))
(/.f64 (*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)) x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)))) (.f64 (*.f64 x x) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)))) (*.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (*.f64 x x)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) x))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (*.f64 x x)))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x))
(/.f64 (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))) (*.f64 x x)))
(/.f64 (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))) x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) (*.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))) (*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64))) (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64))))
(/.f64 (*.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64))) #s(literal 1 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)))
(/.f64 (*.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64))) #s(literal -1 binary64)) (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64))))
(/.f64 (*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)) x) (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)))
(/.f64 (*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)) (-.f64 #s(literal 0 binary64) x)) (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64))))
(/.f64 (neg.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64))))
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(*.f64 (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64))) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))))
(*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (/.f64 (log.f64 #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (/.f64 (log.f64 #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/16 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/32 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/32 binary64)))
(*.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/16 binary64)))

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`
2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	60
1	6	60
0	6	60

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

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

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

eval25.0ms (0.6%)

Compiler: Compiled 2303 to 457 computations (80.2% saved)

prune22.0ms (0.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	0	0
Picked	0	1	1
Done	1	3	4
Total	197	5	202

Accuracy

100.0%

Counts

202 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) x))
✓	99.3%	(/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))
✓	99.5%	(.f64 (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	57.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))
✓	cost-diff	128	(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) x))

Rules

10×	`/-lowering-/.f32`
10×	`/-lowering-/.f64`
8×	`-lowering-.f32`
8×	`-lowering-.f64`
4×	`associate-/l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	12	14
2	15	14
3	22	14
4	22	14
0	22	14

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (pow 1/4 -1/4) (/ 1 x))
(pow 1/4 -1/4)
1/4
-1/4
(/ 1 x)
1
x

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

localize35.0ms (0.9%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	99.4%	(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) x))

Results

27.0ms

256×

valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-pow: 6.0ms (61.2% of total)

ival-div: 3.0ms (30.6% of total)

const: 1.0ms (10.2% of total)

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

series10.0ms (0.2%)

Counts

3 → 24

Calls

Call 1

Inputs
#<alt (/ (pow 1/4 -1/4) (/ 1 x))>
#<alt (pow 1/4 -1/4)>
#<alt (/ 1 x)>

Outputs
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (* (pow 4 1/4) x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	x	@	0	(/ (pow 1/4 -1/4) (/ 1 x))
0.0ms	x	@	inf	(/ (pow 1/4 -1/4) (/ 1 x))
0.0ms	x	@	-inf	(/ 1 x)
0.0ms	x	@	-inf	(/ (pow 1/4 -1/4) (/ 1 x))
0.0ms	x	@	0	(/ 1 x)

rewrite260.0ms (6.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1976×	`-lowering-.f32`
1976×	`-lowering-.f64`
1622×	`+-lowering-+.f64`
1622×	`+-lowering-+.f32`
1396×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	35	10
2	144	10
3	692	10
4	5030	10
0	8351	10

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 367

Calls

Call 1

Inputs
(/ (pow 1/4 -1/4) (/ 1 x))
(pow 1/4 -1/4)
(/ 1 x)

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) #s(literal 0 binary64)) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x))))
(exp.f64 (log.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))))
(exp.f64 (-.f64 (log.f64 x) (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 1/4 binary64)))))
(exp.f64 (-.f64 (*.f64 (log.f64 #s(literal 1/4 binary64)) #s(literal -1/8 binary64)) (log.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) x))))
(-.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(neg.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64)))))
(/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))
(/.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) x))
(/.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))
(/.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) x))
(/.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) #s(literal 1 binary64))
(/.f64 (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) #s(literal -1 binary64))
(/.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))))
(/.f64 (.f64 x (.f64 x x)) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (.f64 x x)))
(/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))))
(/.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (.f64 x x)))
(/.f64 (.f64 x x) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x))
(/.f64 (.f64 x x) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) x))
(/.f64 (.f64 x x) (.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(/.f64 (.f64 x x) (.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/4 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))))
(/.f64 (sqrt.f64 x) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))))
(/.f64 (sqrt.f64 x) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 x) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))))
(/.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))))) (*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) x))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) x)) (.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))))) (*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)))) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) x))
(/.f64 (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (.f64 x (.f64 x x))) (.f64 x x))
(/.f64 (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (.f64 x x)) x)
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (.f64 x (.f64 x x))) (.f64 x x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (.f64 x x)) x)
(/.f64 (.f64 (.f64 x (.f64 x x)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (.f64 x x))
(/.f64 (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)))) (.f64 x x))
(/.f64 (.f64 (.f64 x x) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) x)
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)))) x)
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/4 binary64))) #s(literal 1 binary64)) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/4 binary64))) x) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
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(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/4 binary64))) #s(literal -1 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/4 binary64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/4 binary64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/4 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) #s(literal 3 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/2 binary64)))
(pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(pow.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)) #s(literal 4 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal -1/4 binary64)) (log.f64 #s(literal 1/4 binary64)))
(pow.f64 #s(literal 1/256 binary64) #s(literal -1/16 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 1/16 binary64))) #s(literal -1/8 binary64))
(*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)))
(*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64)))
(*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)) (neg.f64 (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64)))))
(.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)) (.f64 (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))))
(.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/32 binary64)) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/32 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64))) (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64))))
(*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)))
(*.f64 (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64))) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64))))
(*.f64 (pow.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64)))
(*.f64 (pow.f64 (exp.f64 #s(literal -1/4 binary64)) (/.f64 (log.f64 #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1/4 binary64)) (/.f64 (log.f64 #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)))
(.f64 (.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/16 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -3/16 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/32 binary64))) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/32 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x))
(exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64)) (.f64 (log.f64 x) #s(literal -1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))) #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (*.f64 x x) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))) #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (sqrt.f64 x) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (pow.f64 x #s(literal -1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (pow.f64 x #s(literal -1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal -1/2 binary64)) #s(literal 0 binary64))
(neg.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) x)
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 x))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (.f64 (pow.f64 x #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))))
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal -1/2 binary64)))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`
2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	84
1	11	84
0	11	84

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

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

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

eval46.0ms (1.2%)

Compiler: Compiled 5000 to 807 computations (83.9% saved)

prune44.0ms (1.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	390	1	391
Fresh	0	0	0
Picked	0	1	1
Done	1	3	4
Total	391	5	396

Accuracy

100.0%

Counts

396 → 5

Alt Table

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Status	Accuracy	Program
✓	99.4%	(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) x))
	99.1%	(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) x))
✓	99.3%	(/.f64 x (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	57.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 99 to 60 computations (39.4% saved)

regimes24.0ms (0.6%)

Counts

9 → 1

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))

Calls

4 calls:

14.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
3.0ms	x
3.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
3.0ms	(pow.f64 x #s(literal 2 binary64))

Results

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

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes13.0ms (0.3%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes12.0ms (0.3%)

Counts

6 → 1

Calls

Call 1

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

Outputs
(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) x))

Calls

4 calls:

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

Results

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

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes2.0ms (0.1%)

Accuracy

Total -27.3b remaining (-6068.6%)

Threshold costs -27.3b (-6068.6%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	27
1	28	27

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness794.0ms (20.1%)

Rules

3606×	`-lowering-.f32`
3606×	`-lowering-.f64`
2252×	`fnmadd-define`
1540×	`fma-lowering-fma.f32`
1540×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	20	8
2	85	8
3	400	8
0	2759	8
0	5	6
1	7	6
2	11	6
3	12	6
0	12	6
0	5	14
1	14	13
2	43	12
3	120	12
4	577	12
5	4098	12
0	8513	12
0	57	640
1	136	636
2	324	616
3	584	592
4	1022	588
5	1736	588
6	3519	588
7	5332	588
8	7096	588
0	8016	588

Stop Event

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

Compiler

Compiled 85 to 63 computations (25.9% saved)

preprocess56.0ms (1.4%)

Compiler: Compiled 130 to 98 computations (24.6% saved)

Iter	Nodes	Cost
0	10	20
1	20	19
2	42	19
3	124	19
4	239	19
5	358	19
6	484	19
7	527	19
0	5	6
1	7	6
2	11	6
3	12	6
0	12	6

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	64	148
6	96	148
7	108	148
8	139	148
9	232	148
10	235	148
0	235	148

Iter	Nodes	Cost
0	10	20
1	20	19
2	42	19
3	124	19
4	239	19
5	358	19
6	484	19
7	527	19
0	5	6
1	7	6
2	11	6
3	12	6
0	12	6

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	64	148
6	96	148
7	108	148
8	139	148
9	232	148
10	235	148
0	235	148

analyze0.0ms (0%)

sample741.0ms (18.7%)

preprocess18.0ms (0.5%)

explain76.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize23.0ms (0.6%)

series3.0ms (0.1%)

rewrite266.0ms (6.7%)

simplify13.0ms (0.3%)

eval31.0ms (0.8%)

prune42.0ms (1.1%)

simplify5.0ms (0.1%)

localize98.0ms (2.5%)

series165.0ms (4.2%)

rewrite517.0ms (13.1%)

simplify218.0ms (5.5%)

eval138.0ms (3.5%)

prune75.0ms (1.9%)

simplify3.0ms (0.1%)

localize24.0ms (0.6%)

series10.0ms (0.3%)

rewrite121.0ms (3.1%)

simplify5.0ms (0.1%)

eval25.0ms (0.6%)

prune22.0ms (0.6%)

simplify4.0ms (0.1%)

localize35.0ms (0.9%)

series10.0ms (0.2%)

rewrite260.0ms (6.6%)

simplify6.0ms (0.2%)

eval46.0ms (1.2%)

prune44.0ms (1.1%)

regimes24.0ms (0.6%)

regimes13.0ms (0.3%)

regimes12.0ms (0.3%)

regimes2.0ms (0.1%)

simplify7.0ms (0.2%)

soundness794.0ms (20.1%)

preprocess56.0ms (1.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	20
1	20	19
2	42	19
3	124	19
4	239	19
5	358	19
6	484	19
7	527	19
0	5	6
1	7	6
2	11	6
3	12	6
0	12	6

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	64	148
6	96	148
7	108	148
8	139	148
9	232	148
10	235	148
0	235	148