Metrics for sqrt B (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
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

Precisions

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

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

const: 0.0ms (0% of total)

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

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

sample591.0ms (12.1%)

Results

421.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 220.0ms

ival-mult: 139.0ms (63.1% of total)

ival-sqrt: 68.0ms (30.9% of total)

const: 11.0ms (5% of total)

backward-pass: 3.0ms (1.4% of total)

Bogosity

preprocess24.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	27	19
2	64	19
3	154	19
4	230	19
5	387	19
6	502	19
7	505	19
0	5	6
1	9	6
2	10	6
0	10	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

Symmetry

(abs x)

explain50.0ms (1%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
133	-	4	(6.977749546540703e-159)	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
0	-	0	-	`(*.f64 #s(literal 2 binary64) x)`
0	-	0	-	`x`
0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
0	-	0	-	`#s(literal 2 binary64)`

Results

30.0ms

512×

valid

Compiler

Compiled 43 to 17 computations (60.5% saved)

Precisions

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

ival-mult: 10.0ms (65.7% of total)

ival-sqrt: 4.0ms (26.3% of total)

const: 1.0ms (6.6% 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
▶	52.1%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) 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 #s(literal 2 binary64) x)
✓	cost-diff	(.f64 (.f64 #s(literal 2 binary64) x) x)
✓	cost-diff	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
1	9	16
2	10	16
0	10	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

localize37.0ms (0.7%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 #s(literal 2 binary64) x) x)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	52.1%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) 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: 6.0ms

ival-mult: 4.0ms (62% of total)

ival-sqrt: 2.0ms (31% 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 (* 2 x)>

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

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	(* 2 x)

rewrite258.0ms (5.3%)

Algorithm

1×	batch-egg-rewrite

Rules

4528×	`-lowering-.f32`
4528×	`-lowering-.f64`
2564×	`/-lowering-/.f32`
2564×	`/-lowering-/.f64`
1504×	`frac-times`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	5	14
1	14	14
2	35	13
3	89	12
4	348	12
5	2148	12
0	9156	12

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 118

Calls

Call 1

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

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

simplify11.0ms (0.2%)

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	9	148
1	17	148
2	32	148
3	36	148
4	40	148
5	62	148
6	94	148
7	106	148
8	137	148
9	230	148
10	233	148
0	233	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))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

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

eval18.0ms (0.4%)

Compiler: Compiled 2078 to 361 computations (82.6% saved)

prune38.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	148	6	154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	148	7	155

Accuracy

100.0%

Counts

155 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	29.4%	(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 4 binary64)) #s(literal 1/4 binary64))
▶	99.4%	(.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 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
▶	99.3%	(.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 (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)))))
▶	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	52.1%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Compiler

Compiled 127 to 89 computations (29.9% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

78×	`-lowering-.f32`
78×	`-lowering-.f64`
26×	`*-commutative`
24×	`associate-r`
16×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	96
1	41	90
2	58	90
3	70	90
4	70	90
0	70	90

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

localize119.0ms (2.4%)

Localize:

Found 17 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	99.4%	(.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 (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	99.6%	(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.9%	(.f64 x (.f64 x (*.f64 x x)))
✓	accuracy	29.4%	(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 4 binary64)) #s(literal 1/4 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	accuracy	100.0%	(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.5%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))

Results

83.0ms

256×

valid

Compiler

Compiled 113 to 25 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-pow: 30.0ms (55.2% of total)

ival-mult: 19.0ms (35% of total)

ival-sqrt: 4.0ms (7.4% of total)

const: 1.0ms (1.8% of total)

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

series204.0ms (4.2%)

Counts

18 → 192

Calls

Call 1

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

48 calls:

Time	Variable		Point	Expression
71.0ms	x	@	0	(pow (* (* x (* x (* x x))) 4) 1/4)
30.0ms	x	@	-inf	(pow (* x 4) 1/4)
21.0ms	x	@	-inf	(pow x 3/4)
16.0ms	x	@	0	(* (pow (* x 4) 1/4) (pow x 3/4))
15.0ms	x	@	0	(* x (pow 2 1/4))

rewrite307.0ms (6.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2786×	`-lowering-.f32`
2786×	`-lowering-.f64`
2464×	`fma-lowering-fma.f32`
2464×	`fma-lowering-fma.f64`
1670×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	83
1	81	74
2	262	64
3	1100	64
4	4752	64
0	8195	64

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 596

Calls

Call 1

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

simplify594.0ms (12.2%)

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	60	872
1	140	868
2	329	848
3	589	824
4	1022	820
5	1735	820
6	3595	820
7	5407	820
8	7171	820
0	8091	820

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

eval116.0ms (2.4%)

Compiler: Compiled 10208 to 866 computations (91.5% saved)

prune38.0ms (0.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	798	3	801
Fresh	1	0	1
Picked	4	1	5
Done	0	1	1
Total	803	5	808

Accuracy

100.0%

Counts

808 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
▶	99.6%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))))
▶	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	52.1%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Rules

32×	`-lowering-.f32`
32×	`-lowering-.f64`
14×	`*-commutative`
6×	`pow-lowering-pow.f64`
6×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	53
1	22	53
2	29	53
3	31	53
0	31	53

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize76.0ms (1.6%)

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))
✓	accuracy	99.3%	(/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
✓	accuracy	100.0%	(pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64))
✓	accuracy	100.0%	(pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))
✓	accuracy	99.7%	(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
✓	accuracy	99.6%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))

Results

55.0ms

256×

valid

Compiler

Compiled 55 to 17 computations (69.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-pow: 14.0ms (37.9% of total)

ival-mult: 11.0ms (29.8% of total)

ival-sqrt: 9.0ms (24.4% of total)

ival-div: 2.0ms (5.4% of total)

const: 1.0ms (2.7% of total)

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

series36.0ms (0.7%)

Counts

10 → 84

Calls

Call 1

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

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 16 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) x)>
#<alt (* (pow 2 1/8) 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 (* (pow 4 1/4) x)>

Calls

21 calls:

Time	Variable		Point	Expression
20.0ms	x	@	0	(* (pow 2 3/8) (* x (pow 2 1/8)))
12.0ms	x	@	0	(/ x (pow 4 -1/4))
0.0ms	x	@	0	(* x (pow 2 1/8))
0.0ms	x	@	-inf	(/ x (pow 4 -1/4))
0.0ms	x	@	inf	(* (pow 2 3/8) (* x (pow 2 1/8)))

rewrite302.0ms (6.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4066×	`-lowering-.f32`
4066×	`-lowering-.f64`
1954×	`fma-lowering-fma.f32`
1954×	`fma-lowering-fma.f64`
1500×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	57	41
2	190	35
3	728	34
4	5716	34
0	8227	34

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 1043

Calls

Call 1

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

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) #s(literal 0 binary64)) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 1/4 binary64))) (log.f64 x)))
(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 #s(literal -1/4 binary64) (log.f64 #s(literal 1/4 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x)))
(/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) x))
(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64))))
(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) x))
(/.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)))))
(/.f64 (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))
(/.f64 (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64))) (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64))
(/.f64 (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))
(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 #s(literal 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 2 binary64) #s(literal -1/2 binary64))) (.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) x))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))))
(/.f64 (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) x)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) x)) (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))))
(/.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 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 2 binary64) #s(literal -1/2 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 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 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 2 binary64) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -1 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (*.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) (.f64 (*.f64 x x) (pow.f64 #s(literal 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 2 binary64) #s(literal 1/4 binary64)))) (*.f64 x (pow.f64 #s(literal 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 2 binary64) #s(literal -1/2 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 2 binary64) #s(literal -1/2 binary64))) x))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 x x)))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x))
(/.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (*.f64 x x)))
(/.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) (*.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) x))
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(fma.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (exp.f64 #s(literal -1/4 binary64)) (/.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1/4 binary64)) (/.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/32 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/32 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 0 binary64))
(neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64))) (*.f64 #s(literal -1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 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 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))
(pow.f64 #s(literal 16 binary64) #s(literal -1/8 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 4 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (exp.f64 #s(literal -1/4 binary64)) (log.f64 #s(literal 4 binary64)))
(pow.f64 #s(literal 256 binary64) #s(literal -1/16 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 16 binary64))) #s(literal -1/8 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (/.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (neg.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)))))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/32 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/32 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64))) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64))))
(*.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64))))
(*.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64))) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))
(*.f64 (pow.f64 (exp.f64 #s(literal -1/4 binary64)) (/.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1/4 binary64)) (/.f64 (log.f64 #s(literal 4 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))
(.f64 (.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal -3/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/32 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/32 binary64)))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal -1/16 binary64)))

simplify240.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

1748×	`fnmadd-define`
1624×	`fnmsub-define`
1496×	`fma-lowering-fma.f32`
1496×	`fma-lowering-fma.f64`
1494×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	380
1	55	380
2	129	380
3	255	380
4	484	380
5	918	380
6	2131	380
7	2849	380
8	3275	380
9	3491	380
10	3781	380
11	4604	380
12	5329	380
13	5355	380
14	5458	380
15	5518	380
16	5554	380
17	5610	380
18	5610	380
19	5614	380
20	5862	380
21	7527	380
22	7671	380
23	7811	380
0	8091	380

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 16 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) x)
(* (pow 2 1/8) 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)
(* (pow 4 1/4) x)

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 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)
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 16 1/8) x)
(*.f64 x (pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 2 1/8) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))

eval165.0ms (3.4%)

Compiler: Compiled 13834 to 1337 computations (90.3% saved)

prune67.0ms (1.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1125	2	1127
Fresh	0	0	0
Picked	2	1	3
Done	0	2	2
Total	1127	5	1132

Accuracy

100.0%

Counts

1132 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
✓	99.3%	(/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)))
▶	99.2%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	52.1%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Compiler

Compiled 33 to 27 computations (18.2% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	128	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x))

Rules

44×	`-lowering-.f32`
44×	`-lowering-.f64`
32×	`/-lowering-/.f32`
32×	`/-lowering-/.f64`
10×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	18	29
2	25	28
3	36	28
4	53	28
5	57	28
6	66	28
7	69	28
8	70	28
0	70	28

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize44.0ms (0.9%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.4%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x))
✓	accuracy	99.2%	(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x)

Results

32.0ms

256×

valid

Compiler

Compiled 35 to 11 computations (68.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-div: 9.0ms (51.1% of total)

ival-pow: 6.0ms (34% of total)

ival-sqrt: 2.0ms (11.3% of total)

const: 1.0ms (5.7% of total)

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

series3.0ms (0.1%)

Counts

6 → 48

Calls

Call 1

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

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

12 calls:

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

rewrite216.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2862×	`-lowering-.f32`
2862×	`-lowering-.f64`
2106×	`/-lowering-/.f32`
2106×	`/-lowering-/.f64`
1412×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	53	20
2	234	18
3	1127	18
4	7476	18
0	8173	18

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 645

Calls

Call 1

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

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

simplify19.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

6×	`/-lowering-/.f32`
6×	`/-lowering-/.f64`
4×	`sqrt-lowering-sqrt.f64`
4×	`-lowering-.f32`
4×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	168
1	14	168
0	14	168

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

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

eval82.0ms (1.7%)

Compiler: Compiled 9350 to 1358 computations (85.5% saved)

prune78.0ms (1.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	691	2	693
Fresh	0	0	0
Picked	1	1	2
Done	1	2	3
Total	693	5	698

Accuracy

100.0%

Counts

698 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
	99.3%	(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	99.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	52.1%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Compiler

Compiled 136 to 75 computations (44.9% saved)

regimes35.0ms (0.7%)

Counts

14 → 1

Calls

Call 1

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

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

Calls

3 calls:

25.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)
4.0ms	x
4.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.2%)

Counts

11 → 1

Calls

Call 1

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

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.2%)

Accuracy

Total -30.6b remaining (-7525.2%)

Threshold costs -30.6b (-7525.2%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
2.0ms	x
2.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify7.0ms (0.1%)

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	17	26
1	25	26

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.0s (21%)

Rules

4528×	`-lowering-.f32`
4528×	`-lowering-.f64`
4066×	`-lowering-.f32`
4066×	`-lowering-.f64`
2786×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	57	41
2	190	35
3	728	34
4	5716	34
0	8227	34
0	5	14
1	14	14
2	35	13
3	89	12
4	348	12
5	2148	12
0	9156	12
0	24	83
1	81	74
2	262	64
3	1100	64
4	4752	64
0	8195	64

Stop Event

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

Compiler

Compiled 83 to 61 computations (26.5% saved)

preprocess32.0ms (0.7%)

Compiler: Compiled 108 to 76 computations (29.6% saved)

Iter	Nodes	Cost
0	9	148
1	17	148
2	32	148
3	36	148
4	40	148
5	62	148
6	94	148
7	106	148
8	137	148
9	230	148
10	233	148
0	233	148

Iter	Nodes	Cost
0	9	148
1	17	148
2	32	148
3	36	148
4	40	148
5	62	148
6	94	148
7	106	148
8	137	148
9	230	148
10	233	148
0	233	148

analyze0.0ms (0%)

sample591.0ms (12.1%)

preprocess24.0ms (0.5%)

explain50.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize37.0ms (0.7%)

series3.0ms (0.1%)

rewrite258.0ms (5.3%)

simplify11.0ms (0.2%)

eval18.0ms (0.4%)

prune38.0ms (0.8%)

simplify8.0ms (0.2%)

localize119.0ms (2.4%)

series204.0ms (4.2%)

rewrite307.0ms (6.3%)

simplify594.0ms (12.2%)

eval116.0ms (2.4%)

prune38.0ms (0.8%)

simplify5.0ms (0.1%)

localize76.0ms (1.6%)

series36.0ms (0.7%)

rewrite302.0ms (6.2%)

simplify240.0ms (4.9%)

eval165.0ms (3.4%)

prune67.0ms (1.4%)

simplify6.0ms (0.1%)

localize44.0ms (0.9%)

series3.0ms (0.1%)

rewrite216.0ms (4.4%)

simplify19.0ms (0.4%)

eval82.0ms (1.7%)

prune78.0ms (1.6%)

regimes35.0ms (0.7%)

regimes11.0ms (0.2%)

regimes9.0ms (0.2%)

regimes8.0ms (0.2%)

simplify7.0ms (0.1%)

soundness1.0s (21%)

preprocess32.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	9	148
1	17	148
2	32	148
3	36	148
4	40	148
5	62	148
6	94	148
7	106	148
8	137	148
9	230	148
10	233	148
0	233	148