Details

analyze3.0ms (0.1%)

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
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
87.5%	87.5%	12.5%	0%	0%	0%	0%	5
93.8%	93.7%	6.2%	0%	0%	0%	0%	6
96.9%	96.8%	3.1%	0%	0%	0%	0%	7
98.4%	98.4%	1.6%	0%	0%	0%	0%	8
99.2%	99.2%	0.8%	0%	0%	0%	0%	9
99.6%	99.6%	0.4%	0%	0%	0%	0%	10
99.8%	99.8%	0.2%	0%	0%	0%	0%	11
99.9%	99.9%	0.1%	0%	0%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample739.0ms (15.3%)

Results

729.0ms

8256×

body

256

valid

Bogosity

preprocess56.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

678×	`rational_best-simplify-113`
508×	`rational_best-simplify-126`
504×	`rational_best-simplify-124`
488×	`rational_best-simplify-96`
486×	`rational_best-simplify-117`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	13	17
2	19	17
3	28	17
4	52	17
5	217	17
6	1346	17
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(sqrt.f64 (.f64 (.f64 2 x) x))

Outputs
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 x (.f64 2 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify40.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

678×	`rational_best-simplify-113`
508×	`rational_best-simplify-126`
504×	`rational_best-simplify-124`
488×	`rational_best-simplify-96`
486×	`rational_best-simplify-117`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	13	17
2	19	17
3	28	17
4	52	17
5	217	17
6	1346	17

Stop Event

1×	node limit

Counts

1 → 3

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (.f64 2 x) x))

Outputs
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 x (.f64 2 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))

eval1.0ms (0%)

Compiler: Compiled 19 to 13 computations (31.6% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	2	2	4

Error

31.0b

Counts

4 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	29.9b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(sqrt.f64 (.f64 (.f64 2 x) x))
0.0ms	x	@	inf	(sqrt.f64 (.f64 (.f64 2 x) x))
0.0ms	x	@	-inf	(sqrt.f64 (.f64 (.f64 2 x) x))

rewrite62.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

678×	`rational_best-simplify-113`
508×	`rational_best-simplify-126`
504×	`rational_best-simplify-124`
488×	`rational_best-simplify-96`
486×	`rational_best-simplify-117`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	13	17
2	19	17
3	28	17
4	52	17
5	217	17
6	1346	17

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (.f64 2 x) x))

Outputs
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simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

968×	`rational_best-simplify-53`
796×	`rational_best-simplify-1`
750×	`rational_best-simplify-52`
624×	`rational_best-simplify-47`
610×	`rational_best-simplify-21`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	126	808
1	792	800
2	5447	800

Stop Event

1×	node limit

Counts

46 → 41

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 2))
(.f64 (fabs.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(.f64 (sqrt.f64 (fabs.f64 x)) (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))))
(.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (.f64 2 (fabs.f64 x))))
(.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (fabs.f64 (sqrt.f64 x)))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(.f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(/.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))
(/.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (/.f64 1 (fabs.f64 (sqrt.f64 x))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))))
(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))
(/.f64 (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (*.f64 2 x))))))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))))
(/.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))) (/.f64 1 (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (+.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (/.f64 1 (fabs.f64 (sqrt.f64 x)))))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x)))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))
(/.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))) (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))))
(/.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (+.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))))
(/.f64 (+.f64 (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))) (+.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))))
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))) (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x))))))) (+.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))))
(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
(/.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x)))) (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))) (.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))))))
(/.f64 (-.f64 (.f64 (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))) (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))) (-.f64 (.f64 (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))) (.f64 (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))) (-.f64 (.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))))
(/.f64 (-.f64 (.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))))) (-.f64 (.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x))))))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))) (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))))) (-.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))) (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))))))

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 -1 x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 -1 x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 -1 x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 -1 x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 2))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (fabs.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (fabs.f64 x)) (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (.f64 2 (fabs.f64 x))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (fabs.f64 (sqrt.f64 x)))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))
(/.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (/.f64 1 (fabs.f64 (sqrt.f64 x))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
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(/.f64 (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (*.f64 2 x))))))
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(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))) (/.f64 1 (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (+.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (/.f64 1 (fabs.f64 (sqrt.f64 x)))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x)))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))) (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (+.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (+.f64 (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))) (+.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))) (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x))))))) (+.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x)))) (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))) (.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (-.f64 (.f64 (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))) (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))) (-.f64 (.f64 (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))) (.f64 (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (+.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))) (-.f64 (.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))))) (-.f64 (.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))) (-.f64 (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))) (+.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 (.f64 2 x))))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x))))))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))) (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))))) (-.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))) (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))))))
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))

eval32.0ms (0.7%)

Compiler: Compiled 2321 to 1578 computations (32% saved)

prune13.0ms (0.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	33	8	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	9	42

Error

0.1b

Counts

42 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	39.5b	(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
	32.5b	(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
▶	0.6b	(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
	32.5b	(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
▶	0.4b	(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
▶	32.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	31.8b	(*.f64 (sqrt.f64 2) x)
✓	31.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 265 to 185 computations (30.2% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))

Compiler

Compiled 26 to 13 computations (50% saved)

series5.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
1.0ms	x	@	-inf	(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
0.0ms	x	@	0	(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))

rewrite123.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

676×	`rational_best-simplify-113`
508×	`rational_best-simplify-126`
504×	`rational_best-simplify-124`
496×	`rational_best-simplify-96`
494×	`rational_best-simplify-117`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	17	25
2	21	25
3	29	21
4	58	17
5	223	17
6	1369	17

Stop Event

1×	node limit

Counts

1 → 45

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (/.f64 1 (sqrt.f64 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))) (fabs.f64 (/.f64 -1 (sqrt.f64 (fabs.f64 x)))))))) (#(struct:change 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Outputs

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(fabs.f64 x)))))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 x x)))))))

simplify114.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

666×	`rational_best-simplify-124`
646×	`rational_best-simplify-65`
636×	`rational_best-simplify-61`
538×	`rational_best-simplify-113`
512×	`rational_best-simplify-117`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	217	4343
1	1611	4229

Stop Event

1×	node limit

Counts

57 → 56

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))
(/.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))
(/.f64 (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (/.f64 1 (sqrt.f64 (*.f64 x x)))))
(/.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))) (fabs.f64 (/.f64 -1 (sqrt.f64 (fabs.f64 x)))))
(/.f64 (+.f64 (.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))) (.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2))))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))))
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(sqrt.f64 (.f64 2 (.f64 x x)))

Outputs
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
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x)))))))))) (-.f64 (.f64 (.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))))))) (.f64 (.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))))))))
(/.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (.f64 (sqrt.f64 (.f64 x x)) 2)) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))
(/.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (.f64 2 (sqrt.f64 (.f64 x x)))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 2 x)))

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 9 to 7 computations (22.2% saved)

series0.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) x)
0.0ms	x	@	0	(*.f64 (sqrt.f64 2) x)
0.0ms	x	@	inf	(*.f64 (sqrt.f64 2) x)

rewrite14.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2×	`rational_best-simplify-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11

Stop Event

1×

saturated

Counts

1 → 0

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)

Outputs
()

simplify38.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
0.0ms	x	@	0	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
0.0ms	x	@	inf	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

rewrite112.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

676×	`rational_best-simplify-113`
504×	`rational_best-simplify-126`
500×	`rational_best-simplify-124`
484×	`rational_best-simplify-96`
482×	`rational_best-simplify-117`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	15	17
2	19	17
3	27	17
4	50	17
5	214	17
6	1340	17

Stop Event

1×	node limit

Counts

1 → 45

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Outputs

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(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))))))) (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))) (-.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))))) (*.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))) (-.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))))))) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))) (-.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))))) (-.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))) (*.f64 (sqrt.f64 (*.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 x x)))))))

simplify89.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

610×	`rational_best-simplify-124`
602×	`rational_best-simplify-113`
590×	`rational_best-simplify-61`
572×	`rational_best-simplify-65`
470×	`rational_best-simplify-96`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	214	2277
1	1508	2101

Stop Event

1×	node limit

Counts

57 → 56

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(/.f64 (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))
(/.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (/.f64 1 (fabs.f64 (sqrt.f64 x))))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x))))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (-.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x))))))
(/.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))
(/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))))
(/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))))
(/.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))))
(/.f64 (*.f64 (sqrt.f64 x) (-.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 2))) (-.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 x))))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (+.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (/.f64 1 (fabs.f64 (sqrt.f64 x)))))
(/.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (+.f64 (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))))
(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x))))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x))))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))))
(/.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (+.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))))
(/.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))) (+.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))))
(/.f64 (-.f64 (.f64 (sqrt.f64 2) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (fabs.f64 (sqrt.f64 x)))) (sqrt.f64 (.f64 (.f64 x x) 4))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (-.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
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(sqrt.f64 (.f64 2 x))))))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))))))))
(sqrt.f64 (.f64 2 (.f64 x x)))

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 (sqrt.f64 -1) (.f64 x (sqrt.f64 -2))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 (sqrt.f64 -1) (.f64 x (sqrt.f64 -2))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 (sqrt.f64 -1) (.f64 x (sqrt.f64 -2))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 (sqrt.f64 -1) (.f64 x (sqrt.f64 -2))))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(/.f64 (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))))
(/.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (/.f64 1 (fabs.f64 (sqrt.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x))))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (-.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x))))))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
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(-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))))) (.f64 (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))))) (-.f64 (.f64 (.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (-.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (-.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))))) (.f64 (.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (-.f64 (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))) (.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))))))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (-.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))))) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))))) (.f64 (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))))) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))))))) (-.f64 (.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (-.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))))) (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (-.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))))) (.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (-.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))))) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))) (.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))))))))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (fabs.f64 x)))
✓	0.3b	(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
✓	0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x)))

Compiler

Compiled 34 to 18 computations (47.1% saved)

series4.0ms (0.1%)

Counts

3 → 24

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x)))
1.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x)))
0.0ms	x	@	inf	(/.f64 1 (sqrt.f64 (fabs.f64 x)))
0.0ms	x	@	-inf	(/.f64 1 (sqrt.f64 (fabs.f64 x)))
0.0ms	x	@	0	(/.f64 1 (sqrt.f64 (fabs.f64 x)))

rewrite89.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

580×	`rational_best-simplify-113`
430×	`rational_best-simplify-126`
428×	`rational_best-simplify-124`
420×	`rational_best-simplify-127`
400×	`rational_best-simplify-96`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	63
1	35	59
2	185	51
3	1161	47

Stop Event

1×	node limit

Counts

3 → 16

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x)))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 1 (sqrt.f64 (fabs.f64 x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (fabs.f64 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (*.f64 2 (fabs.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x x)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 x x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))))))))

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1190×	`rational_best-simplify-96`
862×	`rational_best-simplify-65`
832×	`rational_best-simplify-61`
656×	`rational_best-simplify-3`
408×	`rational_best-simplify-62`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	612
1	163	612
2	831	612
3	4109	612

Stop Event

1×	node limit

Counts

40 → 19

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(-.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) 0)
(-.f64 0 (neg.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x)))) -1)
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x)))))
(sqrt.f64 (*.f64 2 (fabs.f64 x)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (.f64 2 (fabs.f64 x))))
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 2))
(.f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(sqrt.f64 (.f64 2 (.f64 x x)))
(-.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) 0)
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))))
(*.f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))))
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))) -1)
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))))

Outputs
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(-.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) 0)
(sqrt.f64 (*.f64 2 (fabs.f64 x)))
(-.f64 0 (neg.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x)))))
(sqrt.f64 (*.f64 2 (fabs.f64 x)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x)))) -1)
(sqrt.f64 (*.f64 2 (fabs.f64 x)))
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x)))))
(sqrt.f64 (*.f64 2 (fabs.f64 x)))
(sqrt.f64 (*.f64 2 (fabs.f64 x)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (.f64 2 (fabs.f64 x))))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 2))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(-.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) 0)
(/.f64 1 (sqrt.f64 (fabs.f64 x)))
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))))
(/.f64 1 (sqrt.f64 (fabs.f64 x)))
(*.f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))))
(/.f64 1 (sqrt.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))) -1)
(/.f64 1 (sqrt.f64 (fabs.f64 x)))
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))))
(/.f64 1 (sqrt.f64 (fabs.f64 x)))

localize69.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))
✓	0.3b	(.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
✓	0.3b	(.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
✓	29.9b	(sqrt.f64 (*.f64 x x))

Compiler

Compiled 151 to 76 computations (49.7% saved)

series4.0ms (0.1%)

Counts

4 → 40

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
1.0ms	x	@	0	(.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
1.0ms	x	@	-inf	(.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))
0.0ms	x	@	inf	(sqrt.f64 (*.f64 x x))

rewrite123.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1154×	`rational_best-simplify-61`
970×	`rational_best-simplify-3`
610×	`rational_best-simplify-53`
554×	`rational_best-simplify-56`
520×	`rational_best-simplify-1`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	112
1	36	108
2	139	92
3	694	84
4	4680	84

Stop Event

1×	node limit

Counts

4 → 35

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 x x))
(.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (neg.f64 (sqrt.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (neg.f64 (fabs.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 (.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 (fabs.f64 x))) (neg.f64 (sqrt.f64 (fabs.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (fabs.f64 (sqrt.f64 (fabs.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fabs.f64 (sqrt.f64 x)) (/.f64 1 (fabs.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (neg.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (neg.f64 (sqrt.f64 (*.f64 x x))) 0))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1 (sqrt.f64 2)) (neg.f64 (.f64 (sqrt.f64 2) (/.f64 0 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 1 (sqrt.f64 2)) (.f64 (sqrt.f64 2) (/.f64 0 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (+.f64 (/.f64 0 (sqrt.f64 x)) -1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (.f64 (fabs.f64 (sqrt.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (fabs.f64 (.f64 (fabs.f64 (sqrt.f64 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (sqrt.f64 x) (.f64 (fabs.f64 (sqrt.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (sqrt.f64 (.f64 (.f64 x x) 2)) (fabs.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (.f64 (.f64 x x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (.f64 (fabs.f64 (sqrt.f64 x)) (sqrt.f64 2)) (fabs.f64 (.f64 (sqrt.f64 x) (sqrt.f64 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (sqrt.f64 2)))))))

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

578×	`rational_best-simplify-113`
476×	`rational_best-simplify-96`
470×	`rational_best-simplify-117`
460×	`rational_best-simplify-124`
442×	`rational_best-simplify-126`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1169
1	369	985
2	1590	951

Stop Event

1×	node limit

Counts

75 → 57

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))) 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))) 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))) 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))) 2))
(.f64 (sqrt.f64 2) (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))))
(.f64 (sqrt.f64 2) (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))))
(.f64 (sqrt.f64 2) (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))))
(.f64 (sqrt.f64 2) (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))))
(+.f64 0 (sqrt.f64 (*.f64 x x)))
(-.f64 0 (neg.f64 (sqrt.f64 (*.f64 x x))))
(.f64 1 (sqrt.f64 (.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 (.f64 x x)) 1)
(.f64 -1 (neg.f64 (sqrt.f64 (.f64 x x))))
(*.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (neg.f64 (fabs.f64 (sqrt.f64 x))))
(.f64 (neg.f64 (sqrt.f64 (.f64 x x))) -1)
(*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (sqrt.f64 (fabs.f64 x))) (neg.f64 (sqrt.f64 (fabs.f64 x))))
(*.f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (fabs.f64 (sqrt.f64 (fabs.f64 x))))
(/.f64 (fabs.f64 (sqrt.f64 x)) (/.f64 1 (fabs.f64 (sqrt.f64 x))))
(/.f64 (sqrt.f64 (*.f64 x x)) 1)
(/.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (neg.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 x x))) -1)
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 x x))))
(neg.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 x x))) 1))
(fabs.f64 (sqrt.f64 (*.f64 x x)))
(fabs.f64 (*.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 x))))
(fabs.f64 (-.f64 (neg.f64 (sqrt.f64 (*.f64 x x))) 0))
(+.f64 (.f64 1 (sqrt.f64 2)) (neg.f64 (.f64 (sqrt.f64 2) (/.f64 0 (sqrt.f64 x)))))
(-.f64 (.f64 1 (sqrt.f64 2)) (.f64 (sqrt.f64 2) (/.f64 0 (sqrt.f64 x))))
(neg.f64 (*.f64 (+.f64 (/.f64 0 (sqrt.f64 x)) -1) (sqrt.f64 2)))
(neg.f64 (*.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))))
(neg.f64 (.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (sqrt.f64 2))))
(neg.f64 (.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (.f64 (fabs.f64 (sqrt.f64 x)) 2)))
(neg.f64 (.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (fabs.f64 (.f64 (fabs.f64 (sqrt.f64 x)) 2))))
(fabs.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 x x) 2))))
(fabs.f64 (.f64 (sqrt.f64 x) (.f64 (fabs.f64 (sqrt.f64 x)) 2)))
(fabs.f64 (.f64 (sqrt.f64 (.f64 (*.f64 x x) 2)) (fabs.f64 (sqrt.f64 2))))
(fabs.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (.f64 (*.f64 x x) 2)))))
(fabs.f64 (.f64 (.f64 (fabs.f64 (sqrt.f64 x)) (sqrt.f64 2)) (fabs.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 2)))))
(neg.f64 (*.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (sqrt.f64 2)))

Outputs
x
x
x
x
x
x
x
x
(*.f64 -1 x)
(*.f64 x -1)
(neg.f64 x)
(*.f64 -1 x)
(*.f64 x -1)
(neg.f64 x)
(*.f64 -1 x)
(*.f64 x -1)
(neg.f64 x)
(*.f64 -1 x)
(*.f64 x -1)
(neg.f64 x)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(sqrt.f64 2)
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))) 2))
(*.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))
(.f64 (sqrt.f64 2) (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))))
(.f64 (sqrt.f64 2) (.f64 1 (fabs.f64 (sqrt.f64 x))))
(.f64 1 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))))
(.f64 (sqrt.f64 2) (.f64 1 (fabs.f64 (sqrt.f64 x))))
(.f64 1 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))))
(.f64 (sqrt.f64 2) (.f64 1 (fabs.f64 (sqrt.f64 x))))
(.f64 1 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 2) (fabs.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (sqrt.f64 x))))
(.f64 (sqrt.f64 2) (.f64 1 (fabs.f64 (sqrt.f64 x))))
(.f64 1 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))
(+.f64 0 (sqrt.f64 (*.f64 x x)))
(sqrt.f64 (*.f64 x x))
(-.f64 0 (neg.f64 (sqrt.f64 (*.f64 x x))))
(sqrt.f64 (*.f64 x x))
(.f64 1 (sqrt.f64 (.f64 x x)))
(sqrt.f64 (*.f64 x x))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(sqrt.f64 (*.f64 x x))
(*.f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (sqrt.f64 x)))
(sqrt.f64 (*.f64 x x))
(.f64 (sqrt.f64 (.f64 x x)) 1)
(sqrt.f64 (*.f64 x x))
(.f64 -1 (neg.f64 (sqrt.f64 (.f64 x x))))
(sqrt.f64 (*.f64 x x))
(*.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (neg.f64 (fabs.f64 (sqrt.f64 x))))
(sqrt.f64 (*.f64 x x))
(.f64 (neg.f64 (sqrt.f64 (.f64 x x))) -1)
(sqrt.f64 (*.f64 x x))
(*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))
(sqrt.f64 (*.f64 x x))
(*.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x)))
(sqrt.f64 (*.f64 x x))
(*.f64 (neg.f64 (sqrt.f64 (fabs.f64 x))) (neg.f64 (sqrt.f64 (fabs.f64 x))))
(sqrt.f64 (*.f64 x x))
(*.f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (fabs.f64 (sqrt.f64 (fabs.f64 x))))
(sqrt.f64 (*.f64 x x))
(/.f64 (fabs.f64 (sqrt.f64 x)) (/.f64 1 (fabs.f64 (sqrt.f64 x))))
(sqrt.f64 (*.f64 x x))
(/.f64 (sqrt.f64 (*.f64 x x)) 1)
(sqrt.f64 (*.f64 x x))
(/.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (neg.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x)))))
(sqrt.f64 (*.f64 x x))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 x x))) -1)
(sqrt.f64 (*.f64 x x))
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 x x))))
(sqrt.f64 (*.f64 x x))
(neg.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 x x))) 1))
(sqrt.f64 (*.f64 x x))
(fabs.f64 (sqrt.f64 (*.f64 x x)))
(sqrt.f64 (*.f64 x x))
(fabs.f64 (*.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 x))))
(sqrt.f64 (*.f64 x x))
(fabs.f64 (-.f64 (neg.f64 (sqrt.f64 (*.f64 x x))) 0))
(sqrt.f64 (*.f64 x x))
(+.f64 (.f64 1 (sqrt.f64 2)) (neg.f64 (.f64 (sqrt.f64 2) (/.f64 0 (sqrt.f64 x)))))
(-.f64 (.f64 (sqrt.f64 2) 1) (.f64 (sqrt.f64 2) (/.f64 0 (sqrt.f64 x))))
(*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 x))))
(-.f64 (.f64 1 (sqrt.f64 2)) (.f64 (sqrt.f64 2) (/.f64 0 (sqrt.f64 x))))
(-.f64 (.f64 (sqrt.f64 2) 1) (.f64 (sqrt.f64 2) (/.f64 0 (sqrt.f64 x))))
(*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 x))))
(neg.f64 (*.f64 (+.f64 (/.f64 0 (sqrt.f64 x)) -1) (sqrt.f64 2)))
(-.f64 (.f64 (sqrt.f64 2) 1) (.f64 (sqrt.f64 2) (/.f64 0 (sqrt.f64 x))))
(*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 x))))
(neg.f64 (*.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))))
(*.f64 (/.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (neg.f64 (neg.f64 (fabs.f64 (sqrt.f64 x)))))
(*.f64 (fabs.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(neg.f64 (.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (sqrt.f64 2))))
(-.f64 (.f64 (sqrt.f64 2) 1) (.f64 (sqrt.f64 2) (/.f64 0 (sqrt.f64 x))))
(*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 x))))
(neg.f64 (.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (.f64 (fabs.f64 (sqrt.f64 x)) 2)))
(.f64 (.f64 2 (fabs.f64 (sqrt.f64 x))) (neg.f64 (neg.f64 (fabs.f64 (sqrt.f64 x)))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(neg.f64 (.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (fabs.f64 (.f64 (fabs.f64 (sqrt.f64 x)) 2))))
(.f64 (.f64 2 (fabs.f64 (sqrt.f64 x))) (neg.f64 (neg.f64 (fabs.f64 (sqrt.f64 x)))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 x x) 2))))
(.f64 (.f64 2 (fabs.f64 (sqrt.f64 x))) (neg.f64 (neg.f64 (fabs.f64 (sqrt.f64 x)))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 (sqrt.f64 x) (.f64 (fabs.f64 (sqrt.f64 x)) 2)))
(.f64 (.f64 2 (fabs.f64 (sqrt.f64 x))) (neg.f64 (neg.f64 (fabs.f64 (sqrt.f64 x)))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 (sqrt.f64 (.f64 (*.f64 x x) 2)) (fabs.f64 (sqrt.f64 2))))
(.f64 (.f64 2 (fabs.f64 (sqrt.f64 x))) (neg.f64 (neg.f64 (fabs.f64 (sqrt.f64 x)))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (.f64 (*.f64 x x) 2)))))
(.f64 (.f64 2 (fabs.f64 (sqrt.f64 x))) (neg.f64 (neg.f64 (fabs.f64 (sqrt.f64 x)))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 (.f64 (fabs.f64 (sqrt.f64 x)) (sqrt.f64 2)) (fabs.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 2)))))
(.f64 (fabs.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (fabs.f64 (sqrt.f64 (*.f64 x 2))))
(.f64 (fabs.f64 (sqrt.f64 (.f64 x 2))) (fabs.f64 (sqrt.f64 (*.f64 x 2))))
(fabs.f64 (.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (*.f64 x 2))))
(neg.f64 (*.f64 (neg.f64 (fabs.f64 (sqrt.f64 x))) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 1 (fabs.f64 (sqrt.f64 x))))
(.f64 1 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))

eval363.0ms (7.5%)

Compiler: Compiled 26721 to 16204 computations (39.4% saved)

prune36.0ms (0.7%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	207	6	213
Fresh	0	3	3
Picked	1	0	1
Done	1	4	5
Total	209	13	222

Error

0.0b

Counts

222 → 13

Alt Table

Click to see full alt table

Status	Error	Program
	39.5b	(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
▶	39.5b	(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (fabs.f64 (.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 x 2))))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
	31.2b	(/.f64 (-.f64 (.f64 (sqrt.f64 2) (.f64 (fabs.f64 (/.f64 -1 (sqrt.f64 (fabs.f64 x)))) (fabs.f64 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (*.f64 (fabs.f64 (/.f64 -1 (sqrt.f64 (fabs.f64 x)))) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))))
▶	32.5b	(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
	0.5b	(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
▶	0.4b	(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
	32.5b	(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
✓	0.4b	(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
✓	32.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	0.7b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x))))
▶	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.8b	(*.f64 (sqrt.f64 2) x)
✓	31.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 452 to 312 computations (31% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (sqrt.f64 (fabs.f64 x)))
✓	0.3b	(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))

Compiler

Compiled 34 to 18 computations (47.1% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))

0.0ms

inf

(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))

0.0ms

-inf

(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))

rewrite39.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

510×	`rational_best-simplify-113`
426×	`rational_best-simplify-126`
424×	`rational_best-simplify-124`
416×	`rational_best-simplify-127`
400×	`rational_best-simplify-96`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	34	29
2	179	21
3	1143	17

Stop Event

1×	node limit

Counts

1 → 6

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (*.f64 2 (fabs.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x x)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 x x)))))))

simplify63.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

750×	`rational_best-simplify-113`
576×	`rational_best-simplify-124`
562×	`rational_best-simplify-117`
562×	`rational_best-simplify-96`
546×	`rational_best-simplify-65`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	330
1	44	282
2	83	282
3	271	282
4	1561	282

Stop Event

1×	node limit

Counts

18 → 9

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (.f64 2 (fabs.f64 x))))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))
(.f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(sqrt.f64 (.f64 2 (.f64 x x)))

Outputs
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(sqrt.f64 (.f64 (.f64 2 (fabs.f64 x)) (fabs.f64 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 2 x)))
(.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (.f64 2 (fabs.f64 x))))
(sqrt.f64 (.f64 (.f64 2 (fabs.f64 x)) (fabs.f64 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 2 x)))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 2))
(sqrt.f64 (.f64 (.f64 2 (fabs.f64 x)) (fabs.f64 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 2 x)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))
(sqrt.f64 (.f64 (.f64 2 (fabs.f64 x)) (fabs.f64 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 2 x)))
(.f64 (fabs.f64 (sqrt.f64 (fabs.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(sqrt.f64 (.f64 (.f64 2 (fabs.f64 x)) (fabs.f64 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 2 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 (.f64 2 (fabs.f64 x)) (fabs.f64 x)))
(sqrt.f64 (.f64 x (.f64 2 x)))

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 12 to 8 computations (33.3% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) (neg.f64 x))

rewrite86.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1254×	`rational_best-simplify-3`
700×	`rational_best-simplify-1`
416×	`rational_best-simplify-96`
406×	`rational_best-simplify-124`
404×	`rational_best-simplify-117`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	18	15
2	60	15
3	286	15
4	1874	15
5	7380	15

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (neg.f64 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 2) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (-.f64 -1 (*.f64 (sqrt.f64 2) x))) (+.f64 (*.f64 (sqrt.f64 2) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (+.f64 (*.f64 (sqrt.f64 2) x) 1)) (-.f64 -1 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) (*.f64 (sqrt.f64 2) (+.f64 x x))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (-.f64 -1 (*.f64 (sqrt.f64 2) x))) (*.f64 (*.f64 (sqrt.f64 2) x) (-.f64 -1 (*.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (*.f64 (sqrt.f64 2) x) 1) (+.f64 (*.f64 (sqrt.f64 2) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) (*.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (*.f64 (+.f64 (*.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (*.f64 (sqrt.f64 2) x)))) (*.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (-.f64 -1 (*.f64 (sqrt.f64 2) x))) (*.f64 (*.f64 (sqrt.f64 2) x) (-.f64 -1 (*.f64 (sqrt.f64 2) x))))) (*.f64 (+.f64 (*.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (*.f64 (sqrt.f64 2) x) 1) (*.f64 (*.f64 (sqrt.f64 2) x) (-.f64 -1 (*.f64 (sqrt.f64 2) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 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simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1268×	`rational_best-simplify-61`
1102×	`rational_best-simplify-3`
794×	`rational_best-simplify-62`
688×	`rational_best-simplify-53`
624×	`rational_best-simplify-56`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	672
1	589	664
2	3955	656

Stop Event

1×	node limit

Counts

38 → 33

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(+.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 0)
(+.f64 0 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(-.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 0)
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)
(/.f64 (*.f64 (sqrt.f64 2) x) -1)
(/.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2)
(/.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (+.f64 (.f64 (sqrt.f64 2) x) 1))
(/.f64 (.f64 (.f64 (sqrt.f64 2) x) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (-.f64 -1 (.f64 (sqrt.f64 2) x)))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) -4)
(/.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2)))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))
(/.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) -8)
(/.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (+.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))))
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))))) (+.f64 (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))))
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (+.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))))
(/.f64 (-.f64 (.f64 -4 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))))) (-.f64 16 (.f64 -4 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (*.f64 (sqrt.f64 2) (+.f64 x x))))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))) (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (-.f64 (.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))) (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)))))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))))) (-.f64 (.f64 (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)))))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))) (-.f64 (.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))))
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)
(neg.f64 (*.f64 (sqrt.f64 2) x))
(if (!=.f64 0 0) 1 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 2) (.f64 (sqrt.f64 2) (neg.f64 x))) (.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) (neg.f64 x)) 0) (/.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 2) (.f64 (sqrt.f64 2) (neg.f64 x))) (.f64 (sqrt.f64 2) (neg.f64 x)))

Outputs
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(+.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 0)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(+.f64 0 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(-.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 0)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (*.f64 (sqrt.f64 2) x) -1)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (+.f64 (.f64 (sqrt.f64 2) x) 1))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (.f64 (.f64 (sqrt.f64 2) x) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (-.f64 -1 (.f64 (sqrt.f64 2) x)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) -4)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) -8)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (+.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))))) (+.f64 (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (+.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 -4 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))))) (-.f64 16 (.f64 -4 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (*.f64 (sqrt.f64 2) (+.f64 x x))))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))) (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (-.f64 (.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))) (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))))) (-.f64 (.f64 (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))) (-.f64 (.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(if (!=.f64 0 0) 1 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 2) (.f64 (sqrt.f64 2) (neg.f64 x))) (.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (neg.f64 (.f64 2 (pow.f64 x 2))) (.f64 (sqrt.f64 2) x)) (.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x)) (.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) (neg.f64 x)) 0) (/.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 2) (.f64 (sqrt.f64 2) (neg.f64 x))) (.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) (neg.f64 x)) 0) (/.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 2) (*.f64 (sqrt.f64 2) (neg.f64 x))) 0)
(if (!=.f64 (.f64 (sqrt.f64 2) (neg.f64 x)) 0) (/.f64 (neg.f64 (.f64 2 (pow.f64 x 2))) (*.f64 (sqrt.f64 2) x)) 0)
(if (!=.f64 (.f64 (sqrt.f64 2) (neg.f64 x)) 0) (/.f64 (.f64 (pow.f64 x 2) -2) (*.f64 (sqrt.f64 2) x)) 0)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x))))
✓	0.5b	(*.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x)))

Compiler

Compiled 27 to 10 computations (63% saved)

series0.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x)))
0.0ms	x	@	0	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x))))
0.0ms	x	@	inf	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x))))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x)))
0.0ms	x	@	-inf	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x))))

rewrite214.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`rational_best-simplify-113`
446×	`rational_best-simplify-126`
444×	`rational_best-simplify-124`
438×	`rational_best-simplify-96`
436×	`rational_best-simplify-117`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	48
1	20	36
2	54	28
3	208	28
4	1223	28

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 x))) 0) (neg.f64 (sqrt.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fabs.f64 x)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))))))

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(*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))))) (-.f64 (*.f64 (*.f64 (-.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (*.f64 (*.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (*.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))))))) (*.f64 (*.f64 (-.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (*.f64 (*.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (*.f64 (-.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (*.f64 (*.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))))))) (-.f64 (*.f64 (*.f64 (*.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (-.f64 (*.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (*.f64 (-.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (*.f64 (*.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))))) (*.f64 (*.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (-.f64 (*.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (*.f64 (-.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (*.f64 (*.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))))))))) (*.f64 (*.f64 (*.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (-.f64 (*.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (*.f64 (-.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (*.f64 (*.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))))) (-.f64 (*.f64 (*.f64 (-.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (*.f64 (*.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (*.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))))))) (*.f64 (*.f64 (-.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (*.f64 (*.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (*.f64 (-.f64 (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (*.f64 (*.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (*.f64 (*.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (*.f64 x 2)))))))

simplify127.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

690×	`rational_best-simplify-124`
658×	`rational_best-simplify-61`
656×	`rational_best-simplify-65`
546×	`rational_best-simplify-113`
542×	`rational_best-simplify-117`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	224	3292
1	1682	3124

Stop Event

1×	node limit

Counts

76 → 64

Calls

Call 1

Inputs
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(-.f64 (.f64 (neg.f64 (sqrt.f64 (fabs.f64 x))) 0) (neg.f64 (sqrt.f64 (.f64 x x))))
(/.f64 (sqrt.f64 (fabs.f64 x)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (sqrt.f64 (*.f64 x x)) 1)
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 x x))))
(sqrt.f64 (*.f64 x x))
(fabs.f64 (sqrt.f64 (*.f64 x x)))
(fabs.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 2)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))
(/.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))
(/.f64 (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (/.f64 1 (sqrt.f64 (*.f64 x x)))))
(/.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))) (/.f64 1 (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(/.f64 (+.f64 (.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))) (.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2))))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))))
(/.f64 (.f64 (sqrt.f64 (.f64 (fabs.f64 x) 2)) (-.f64 (-.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (sqrt.f64 (.f64 (fabs.f64 x) 2))) (-.f64 (sqrt.f64 (.f64 (fabs.f64 x) 2)) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))) (.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (-.f64 (-.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (sqrt.f64 (.f64 (fabs.f64 x) 2))) (-.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 2)) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))))
(/.f64 (.f64 (.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))) (.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))) (-.f64 (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))) (*.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))))))
(/.f64 (.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 2))) (-.f64 (neg.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))
(/.f64 (.f64 (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (/.f64 1 (sqrt.f64 (.f64 x x)))))) (.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))))
(/.f64 (.f64 (.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))) (-.f64 (.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))) (-.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) (-.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 2)))) (+.f64 (/.f64 1 (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x)))))))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x)))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x))))) (+.f64 (/.f64 1 (fabs.f64 (sqrt.f64 (fabs.f64 x)))) (/.f64 1 (fabs.f64 (sqrt.f64 (fabs.f64 x))))))
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(sqrt.f64 (.f64 x (.f64 x 2)))

Outputs
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(fabs.f64 x)
(*.f64 (sqrt.f64 2) (fabs.f64 x))
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x)))))))))) (-.f64 (.f64 (.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))))))) (.f64 (.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))) (.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (+.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))) (-.f64 (sqrt.f64 (.f64 (.f64 x x) 4)) (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))))))))
(/.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (.f64 (sqrt.f64 (.f64 x x)) 2)) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (*.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x)))))))
(/.f64 (-.f64 (.f64 (sqrt.f64 2) (-.f64 1 (/.f64 0 (sqrt.f64 (fabs.f64 x))))) (.f64 2 (sqrt.f64 (.f64 x x)))) (+.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (*.f64 (sqrt.f64 2) (+.f64 (/.f64 0 (sqrt.f64 (fabs.f64 x))) -1))))
(sqrt.f64 (.f64 x (.f64 x 2)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))

localize79.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sqrt.f64 x))
✓	0.2b	(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
✓	0.3b	(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))

Compiler

Compiled 83 to 56 computations (32.5% saved)

series10.0ms (0.2%)

Counts

4 → 12

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
1.0ms	x	@	-inf	(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
1.0ms	x	@	inf	(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
1.0ms	x	@	0	(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
1.0ms	x	@	inf	(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))

rewrite69.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

924×	`rational_best-simplify-111`
778×	`rational_best-simplify-110`
772×	`rational_best-simplify-96`
748×	`rational_best-simplify-61`
744×	`rational_best-simplify-65`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	188
1	63	188
2	342	124
3	2235	118

Stop Event

1×	node limit

Counts

4 → 50

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(/.f64 1 (sqrt.f64 x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (/.f64 1 (sqrt.f64 x)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 1 (sqrt.f64 x)) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))) (neg.f64 (/.f64 1 (sqrt.f64 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (/.f64 1 (sqrt.f64 x)) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0) (/.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))))) (.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) 0) (/.f64 (.f64 (sqrt.f64 (.f64 x 2)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))) (/.f64 1 (sqrt.f64 (.f64 x x))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) 0) (/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))) (/.f64 1 (sqrt.f64 (.f64 x x))))) (/.f64 1 (sqrt.f64 (.f64 x x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (sqrt.f64 (.f64 x 2)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) (neg.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (.f64 x 2)) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (neg.f64 (sqrt.f64 (.f64 x 2))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 (.f64 x 2)) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 x 2))) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (.f64 (sqrt.f64 (.f64 x 2)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0) (/.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))))) (.f64 (sqrt.f64 (.f64 x 2)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))))) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2)))) 0) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) 0) (/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2)))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (sqrt.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (/.f64 1 (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))))))))

simplify102.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1192×	`rational_best-simplify-61`
1154×	`rational_best-simplify-3`
554×	`rational_best-simplify-53`
512×	`rational_best-simplify-52`
502×	`rational_best-simplify-56`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	133	2812
1	757	2576
2	4936	2576

Stop Event

1×	node limit

Counts

62 → 70

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (*.f64 (/.f64 1 (sqrt.f64 x)) 0))
(+.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))))
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))
(+.f64 (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (.f64 x x))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0)
(-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))) 0))
(-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))))
(-.f64 0 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(-.f64 (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))) (neg.f64 (/.f64 1 (sqrt.f64 (.f64 x x)))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(-.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(-.f64 (.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))) -1)
(/.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) -2)
(neg.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(if (!=.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0) (/.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))))) (.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))
(if (!=.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) 0) (/.f64 (.f64 (sqrt.f64 (.f64 x 2)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))) (/.f64 1 (sqrt.f64 (.f64 x x))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(if (!=.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) 0) (/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))) (/.f64 1 (sqrt.f64 (.f64 x x))))) (/.f64 1 (sqrt.f64 (.f64 x x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))
(+.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))) 0)
(+.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (sqrt.f64 (*.f64 x 2)) 0))
(+.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0))
(+.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) (neg.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(+.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))))
(+.f64 (.f64 (sqrt.f64 (.f64 x 2)) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(+.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(-.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))) 0)
(-.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (neg.f64 (sqrt.f64 (*.f64 x 2))) 0))
(-.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2)))))
(-.f64 0 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(-.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))))
(-.f64 (.f64 (sqrt.f64 (.f64 x 2)) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(-.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(-.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 x 2))) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(/.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))) -1)
(/.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))) -2)
(neg.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(if (!=.f64 (.f64 (sqrt.f64 (.f64 x 2)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0) (/.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))))) (.f64 (sqrt.f64 (.f64 x 2)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))))) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))
(if (!=.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2)))) 0) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))
(if (!=.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) 0) (/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2)))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 0)
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 x))))
(*.f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 x))))
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))) -1)
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))))

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 (sqrt.f64 -2) (neg.f64 (.f64 x (sqrt.f64 -1))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 (sqrt.f64 -2) (neg.f64 (.f64 x (sqrt.f64 -1))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 (sqrt.f64 -2) (neg.f64 (.f64 x (sqrt.f64 -1))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 (sqrt.f64 -2) (neg.f64 (.f64 x (sqrt.f64 -1))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (*.f64 (/.f64 1 (sqrt.f64 x)) 0))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(+.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))))
(+.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 x)))))
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(+.f64 (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (.f64 x x))))
(+.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 x)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))) 0))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(-.f64 0 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(-.f64 (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))) (neg.f64 (/.f64 1 (sqrt.f64 (.f64 x x)))))
(+.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 x)))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(-.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(-.f64 (.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))) 0) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 1)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))) -1)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(/.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x)))) -2)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(neg.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(if (!=.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0) (/.f64 (-.f64 (/.f64 1 (sqrt.f64 (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))))) (.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) 0)
(.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))))
(if (!=.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) 0) (/.f64 (.f64 (sqrt.f64 (.f64 x 2)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))) (/.f64 1 (sqrt.f64 (.f64 x x))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(if (!=.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) 0) (/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (/.f64 1 (sqrt.f64 (.f64 x x))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(if (!=.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) 0) (/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))) (/.f64 1 (sqrt.f64 (.f64 x x))))) (/.f64 1 (sqrt.f64 (.f64 x x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))
(if (!=.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) 0) (/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (/.f64 1 (sqrt.f64 (.f64 x x))))) (/.f64 1 (sqrt.f64 (.f64 x x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))
(+.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))) 0)
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(+.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (sqrt.f64 (*.f64 x 2)) 0))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(+.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(+.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) (neg.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(+.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(+.f64 (.f64 (sqrt.f64 (.f64 x 2)) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(+.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(-.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))) 0)
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(-.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (.f64 (neg.f64 (sqrt.f64 (*.f64 x 2))) 0))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(-.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(-.f64 0 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(-.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (.f64 (sqrt.f64 x) (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 x))))
(-.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 2 x))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 x)))))
(-.f64 (.f64 (sqrt.f64 x) (neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 x))))) (sqrt.f64 (.f64 x (*.f64 x 4))))
(-.f64 (.f64 (sqrt.f64 (.f64 x 2)) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(-.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(-.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 x 2))) 0) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(/.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))) 1)
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(/.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))) -1)
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(/.f64 (.f64 (-.f64 (sqrt.f64 (.f64 x 2)) (/.f64 1 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))) -2)
(/.f64 (.f64 (-.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))) -2)
(/.f64 (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))) 2)
(neg.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (sqrt.f64 (*.f64 x 2)) (/.f64 1 (sqrt.f64 x)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(if (!=.f64 (.f64 (sqrt.f64 (.f64 x 2)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) 0) (/.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))))) (.f64 (sqrt.f64 (.f64 x 2)) (+.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))))) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(if (!=.f64 (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2)))) 0) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2))))) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2)))))
(+.f64 0 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x))))
(if (!=.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) 0) (/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 2))) (sqrt.f64 (.f64 2 (.f64 x (.f64 x 2)))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 x 2)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 2)))))
(if (!=.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) 0) (/.f64 (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 (.f64 x (.f64 2 x)))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(if (!=.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x))) 0) (/.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x))) (sqrt.f64 (.f64 x (.f64 x 4))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 2) (sqrt.f64 x)))) (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 0)
(/.f64 1 (sqrt.f64 x))
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 x))))
(/.f64 1 (sqrt.f64 x))
(*.f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 x))))
(/.f64 1 (sqrt.f64 x))
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))) -1)
(/.f64 1 (sqrt.f64 x))
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 x))))
(/.f64 1 (sqrt.f64 x))

localize63.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))
✓	0.3b	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (*.f64 x 2)))
	0.3b	(.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
	29.9b	(sqrt.f64 (*.f64 x x))

Compiler

Compiled 158 to 91 computations (42.4% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (*.f64 x 2)))
0.0ms	x	@	-inf	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (*.f64 x 2)))
0.0ms	x	@	0	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (*.f64 x 2)))

rewrite67.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1182×	`rational_best-simplify-3`
1050×	`rational_best-simplify-65`
1006×	`rational_best-simplify-61`
636×	`rational_best-simplify-62`
530×	`rational_best-simplify-52`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	15	23
2	25	23
3	51	17
4	96	17
5	194	17
6	370	17
7	831	17
8	3707	17

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (*.f64 x 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fabs.f64 (*.f64 x 4))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fabs.f64 (sqrt.f64 (fabs.f64 (*.f64 x 4)))) (/.f64 1 (fabs.f64 (sqrt.f64 (fabs.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fabs.f64 (sqrt.f64 (*.f64 x 4))) (fabs.f64 (/.f64 -1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 x 4)) (/.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 (*.f64 x 4)) (sqrt.f64 (*.f64 x 4))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 4))) (*.f64 (sqrt.f64 (*.f64 x 4)) (sqrt.f64 (*.f64 x 4)))) (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (sqrt.f64 (*.f64 x x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (*.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x (*.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (fabs.f64 (sqrt.f64 2)) (sqrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 (*.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (sqrt.f64 (*.f64 x 2)) (fabs.f64 (sqrt.f64 (*.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 2 (*.f64 (sqrt.f64 (fabs.f64 x)) (fabs.f64 (sqrt.f64 (fabs.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (sqrt.f64 (fabs.f64 (*.f64 x 2))) (fabs.f64 (sqrt.f64 (fabs.f64 (*.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (sqrt.f64 x) (/.f64 (fabs.f64 (sqrt.f64 (*.f64 x 2))) (/.f64 1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (sqrt.f64 x) (/.f64 (*.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (fabs.f64 (sqrt.f64 x)) (/.f64 (fabs.f64 (sqrt.f64 (*.f64 x 2))) (/.f64 1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (fabs.f64 (sqrt.f64 x)) (/.f64 (*.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (*.f64 (fabs.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x))))))))))

simplify48.0ms (1%)

Algorithm

1×	egg-herbie

Rules

582×	`rational_best-simplify-65`
582×	`rational_best-simplify-124`
582×	`rational_best-simplify-113`
568×	`rational_best-simplify-117`
562×	`rational_best-simplify-96`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	813
1	340	789
2	1777	519

Stop Event

1×	node limit

Counts

31 → 29

Calls

Call 1

Inputs
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -2) 2) x))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -2) 2) x))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -2) 2) x))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -2) 2) x))
(/.f64 (sqrt.f64 (fabs.f64 (*.f64 x 4))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (fabs.f64 (sqrt.f64 (fabs.f64 (*.f64 x 4)))) (/.f64 1 (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(/.f64 (fabs.f64 (sqrt.f64 (*.f64 x 4))) (fabs.f64 (/.f64 -1 (sqrt.f64 x))))
(/.f64 (sqrt.f64 (*.f64 x 4)) (/.f64 1 (sqrt.f64 x)))
(/.f64 (+.f64 (sqrt.f64 (.f64 x 4)) (sqrt.f64 (.f64 x 4))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))
(/.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 4))) (.f64 (sqrt.f64 (.f64 x 4)) (sqrt.f64 (.f64 x 4)))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 4)))))
(neg.f64 (.f64 (sqrt.f64 (.f64 x x)) -2))
(sqrt.f64 (.f64 x (.f64 x 4)))
(fabs.f64 (sqrt.f64 (.f64 x (.f64 x 4))))
(fabs.f64 (.f64 (fabs.f64 (sqrt.f64 2)) (sqrt.f64 (.f64 2 (*.f64 x x)))))
(fabs.f64 (.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 (.f64 x 4)))))
(fabs.f64 (.f64 (sqrt.f64 (.f64 x 2)) (fabs.f64 (sqrt.f64 (*.f64 x 2)))))
(fabs.f64 (.f64 2 (.f64 (sqrt.f64 (fabs.f64 x)) (fabs.f64 (sqrt.f64 (fabs.f64 x))))))
(fabs.f64 (.f64 (sqrt.f64 (fabs.f64 (.f64 x 2))) (fabs.f64 (sqrt.f64 (fabs.f64 (*.f64 x 2))))))
(fabs.f64 (.f64 (sqrt.f64 x) (/.f64 (fabs.f64 (sqrt.f64 (.f64 x 2))) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (sqrt.f64 x) (/.f64 (.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (fabs.f64 (sqrt.f64 x)) (/.f64 (fabs.f64 (sqrt.f64 (.f64 x 2))) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (fabs.f64 (sqrt.f64 x)) (/.f64 (.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (.f64 (fabs.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x))))))

Outputs
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 2 x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 2 x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 2 x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 2 x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 2 x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 2 x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 2 x)
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 2 x)
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -2) 2) x))
(.f64 2 (.f64 -1 x))
(*.f64 x -2)
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -2) 2) x))
(.f64 2 (.f64 -1 x))
(*.f64 x -2)
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -2) 2) x))
(.f64 2 (.f64 -1 x))
(*.f64 x -2)
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -2) 2) x))
(.f64 2 (.f64 -1 x))
(*.f64 x -2)
(/.f64 (sqrt.f64 (fabs.f64 (*.f64 x 4))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(/.f64 (fabs.f64 (sqrt.f64 (fabs.f64 (*.f64 x 4)))) (/.f64 1 (fabs.f64 (sqrt.f64 (fabs.f64 x)))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(/.f64 (fabs.f64 (sqrt.f64 (*.f64 x 4))) (fabs.f64 (/.f64 -1 (sqrt.f64 x))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(/.f64 (sqrt.f64 (*.f64 x 4)) (/.f64 1 (sqrt.f64 x)))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(/.f64 (+.f64 (sqrt.f64 (.f64 x 4)) (sqrt.f64 (.f64 x 4))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 4))) (.f64 (sqrt.f64 (.f64 x 4)) (sqrt.f64 (.f64 x 4)))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 x 4)))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(neg.f64 (.f64 (sqrt.f64 (.f64 x x)) -2))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 x 4)))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (sqrt.f64 (.f64 x (.f64 x 4))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 (fabs.f64 (sqrt.f64 2)) (sqrt.f64 (.f64 2 (*.f64 x x)))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 (.f64 x 4)))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 (sqrt.f64 (.f64 x 2)) (fabs.f64 (sqrt.f64 (*.f64 x 2)))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 2 (.f64 (sqrt.f64 (fabs.f64 x)) (fabs.f64 (sqrt.f64 (fabs.f64 x))))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 (sqrt.f64 (fabs.f64 (.f64 x 2))) (fabs.f64 (sqrt.f64 (fabs.f64 (*.f64 x 2))))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))
(fabs.f64 (.f64 (sqrt.f64 x) (/.f64 (fabs.f64 (sqrt.f64 (.f64 x 2))) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (sqrt.f64 x) (/.f64 (fabs.f64 (sqrt.f64 (.f64 2 x))) (/.f64 1 (sqrt.f64 2)))))
(.f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (/.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (sqrt.f64 x) (/.f64 (.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (sqrt.f64 x) (/.f64 (fabs.f64 (sqrt.f64 (.f64 2 x))) (/.f64 1 (sqrt.f64 2)))))
(.f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (/.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (fabs.f64 (sqrt.f64 x)) (/.f64 (fabs.f64 (sqrt.f64 (.f64 x 2))) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (sqrt.f64 x) (/.f64 (fabs.f64 (sqrt.f64 (.f64 2 x))) (/.f64 1 (sqrt.f64 2)))))
(.f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (/.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (fabs.f64 (sqrt.f64 x)) (/.f64 (.f64 (sqrt.f64 x) (fabs.f64 (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (sqrt.f64 x) (/.f64 (fabs.f64 (sqrt.f64 (.f64 2 x))) (/.f64 1 (sqrt.f64 2)))))
(.f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (/.f64 (sqrt.f64 (.f64 2 x)) (/.f64 1 (sqrt.f64 2)))))
(fabs.f64 (.f64 (.f64 (fabs.f64 (sqrt.f64 2)) (sqrt.f64 (fabs.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 (fabs.f64 x))))))
(/.f64 (sqrt.f64 (*.f64 (fabs.f64 x) 4)) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 2 (sqrt.f64 (.f64 x x)))

eval293.0ms (6.1%)

Compiler: Compiled 20607 to 12906 computations (37.4% saved)

prune41.0ms (0.9%)

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	278	3	281
Fresh	3	1	4
Picked	1	0	1
Done	2	6	8
Total	284	10	294

Error

0.0b

Counts

294 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	48.0b	(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x)) (.f64 (sqrt.f64 2) (neg.f64 x)))
▶	39.5b	(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (fabs.f64 (.f64 x -2))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
✓	32.5b	(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
▶	0.3b	(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
▶	32.5b	(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
✓	0.4b	(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
✓	32.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.8b	(*.f64 (sqrt.f64 2) x)
✓	31.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 149 to 110 computations (26.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 1 (sqrt.f64 x))
✓	0.2b	(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))

Compiler

Compiled 26 to 17 computations (34.6% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
0.0ms	x	@	-inf	(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
0.0ms	x	@	inf	(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))

rewrite80.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

510×	`rational_best-simplify-113`
426×	`rational_best-simplify-126`
424×	`rational_best-simplify-124`
416×	`rational_best-simplify-127`
400×	`rational_best-simplify-96`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	32	21
2	177	17
3	1134	17

Stop Event

1×	node limit

Counts

1 → 6

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x x)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 x x)))))))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

838×	`rational_best-simplify-113`
592×	`rational_best-simplify-124`
574×	`rational_best-simplify-117`
572×	`rational_best-simplify-96`
558×	`rational_best-simplify-65`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	298
1	52	290
2	98	250
3	307	250
4	1655	250

Stop Event

1×	node limit

Counts

18 → 11

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))
(.f64 (fabs.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(sqrt.f64 (.f64 2 (.f64 x x)))

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 x (sqrt.f64 -2))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 2))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (fabs.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))

localize13.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (fabs.f64 x)))
✓	0.3b	(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))

Compiler

Compiled 35 to 21 computations (40% saved)

series0.0ms (0%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
0.0ms	x	@	-inf	(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
0.0ms	x	@	inf	(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
0.0ms	x	@	0	(sqrt.f64 (/.f64 1 (fabs.f64 x)))
0.0ms	x	@	-inf	(sqrt.f64 (/.f64 1 (fabs.f64 x)))

rewrite63.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

530×	`rational_best-simplify-113`
452×	`rational_best-simplify-126`
448×	`rational_best-simplify-124`
442×	`rational_best-simplify-127`
418×	`rational_best-simplify-65`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	37	50
2	196	50
3	1244	50

Stop Event

1×	node limit

Counts

2 → 6

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))

Outputs

()

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))))))))

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

668×	`rational_best-simplify-96`
636×	`rational_best-simplify-117`
506×	`rational_best-simplify-124`
452×	`rational_best-simplify-65`
442×	`rational_best-simplify-61`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	270
1	85	270
2	434	270
3	2244	270

Stop Event

1×	node limit

Counts

18 → 9

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(-.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x))) 0)
(-.f64 0 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))))
(*.f64 -1 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))))
(*.f64 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))) -1)
(/.f64 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))) -1)
(neg.f64 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))))

Outputs
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(*.f64 (sqrt.f64 2) (fabs.f64 x))
(-.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x))) 0)
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (fabs.f64 (/.f64 -1 x)))
(-.f64 0 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (fabs.f64 (/.f64 -1 x)))
(*.f64 -1 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (fabs.f64 (/.f64 -1 x)))
(*.f64 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))) -1)
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (fabs.f64 (/.f64 -1 x)))
(/.f64 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))) -1)
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (fabs.f64 (/.f64 -1 x)))
(neg.f64 (neg.f64 (sqrt.f64 (fabs.f64 (/.f64 -1 x)))))
(sqrt.f64 (/.f64 1 (fabs.f64 x)))
(sqrt.f64 (fabs.f64 (/.f64 -1 x)))

localize69.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (fabs.f64 (.f64 x -2))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
	0.3b	(*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))
	0.3b	(.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))
	29.9b	(sqrt.f64 (*.f64 x x))

Compiler

Compiled 128 to 67 computations (47.7% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

(/.f64 (-.f64 (*.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (fabs.f64 (*.f64 x -2))) (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))

1.0ms

inf

(/.f64 (-.f64 (*.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (fabs.f64 (*.f64 x -2))) (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))

1.0ms

(/.f64 (-.f64 (*.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (fabs.f64 (*.f64 x -2))) (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))

rewrite64.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1232×	`rational_best-simplify-61`
1230×	`rational_best-simplify-3`
780×	`rational_best-simplify-62`
550×	`rational_best-simplify-1`
538×	`rational_best-simplify-53`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	121
1	102	113
2	589	105
3	3847	97

Stop Event

1×	node limit

Counts

1 → 0

Calls

Call 1

Inputs

(/.f64 (-.f64 (*.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (fabs.f64 (*.f64 x -2))) (-.f64 (/.f64 1 (sqrt.f64 (*.f64 x x))) (*.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))

Outputs
()

simplify58.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

930×	`rational_best-simplify-61`
908×	`rational_best-simplify-65`
756×	`rational_best-simplify-96`
748×	`rational_best-simplify-62`
668×	`rational_best-simplify-111`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	1356
1	419	1320
2	2504	1222

Stop Event

1×	node limit

Counts

12 → 44

Calls

Call 1

Inputs
(.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) x)
(+.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (pow.f64 x 2))) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (*.f64 -2 x))) x))
(+.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (pow.f64 x 2))) (+.f64 (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) x) (.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (pow.f64 x 3)))))
(+.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (pow.f64 x 2))) (+.f64 (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) x) (+.f64 (.f64 (pow.f64 (sqrt.f64 2) 3) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (pow.f64 x 4))) (.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (*.f64 -2 x))) (pow.f64 x 3))))))
(.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2)))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2))) (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 2) x))) (/.f64 1 (*.f64 (sqrt.f64 2) x)))
(-.f64 (+.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2))) (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 2) x)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 2) x)) (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))) (+.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 4) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2))) (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 2) x))))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))) (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))))))
(.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2)))
(+.f64 (.f64 -1 (/.f64 (-.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (pow.f64 (sqrt.f64 2) 2)) (/.f64 1 (sqrt.f64 2))) x)) (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2))))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (pow.f64 (sqrt.f64 2) 2)) (/.f64 1 (sqrt.f64 2))) x)) (+.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))) (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2))))) (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (pow.f64 (sqrt.f64 2) 2)) (/.f64 1 (sqrt.f64 2))) (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 3)))) (+.f64 (.f64 -1 (/.f64 (-.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (pow.f64 (sqrt.f64 2) 2)) (/.f64 1 (sqrt.f64 2))) x)) (+.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))) (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2)))))) (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))))

Outputs
(.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) x)
(.f64 x (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))))
(.f64 x (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2)))
(.f64 x (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))))
(+.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (pow.f64 x 2))) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (*.f64 -2 x))) x))
(+.f64 (.f64 x (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x)))) (.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (*.f64 (sqrt.f64 2) (pow.f64 x 2))))
(+.f64 (.f64 x (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2))) (.f64 (pow.f64 x 2) (-.f64 2 (.f64 (sqrt.f64 2) (*.f64 2 (fabs.f64 x))))))
(.f64 (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))) (-.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 2)) (neg.f64 x)))
(+.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (pow.f64 x 2))) (+.f64 (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) x) (.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (pow.f64 x 3)))))
(+.f64 (.f64 x (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x)))) (+.f64 (.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (.f64 2 (pow.f64 x 3))) (.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (.f64 (sqrt.f64 2) (pow.f64 x 2)))))
(+.f64 (.f64 x (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2))) (+.f64 (.f64 (pow.f64 x 2) (-.f64 2 (.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))))) (.f64 (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2)) (.f64 2 (pow.f64 x 3)))))
(+.f64 (.f64 (pow.f64 x 2) (+.f64 2 (.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))))) (.f64 (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))) (-.f64 (.f64 2 (pow.f64 x 3)) (neg.f64 x))))
(+.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (pow.f64 x 2))) (+.f64 (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) x) (+.f64 (.f64 (pow.f64 (sqrt.f64 2) 3) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (pow.f64 x 4))) (.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (*.f64 -2 x))) (pow.f64 x 3))))))
(+.f64 (.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 x (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x)))) (+.f64 (.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (.f64 2 (pow.f64 x 3))) (.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (*.f64 (sqrt.f64 8) (pow.f64 x 4))))))
(+.f64 (.f64 (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2)) (.f64 2 (pow.f64 x 3))) (+.f64 (+.f64 (.f64 x (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2))) (.f64 (sqrt.f64 8) (.f64 (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2)) (pow.f64 x 4)))) (.f64 (pow.f64 x 2) (-.f64 2 (.f64 (sqrt.f64 2) (*.f64 2 (fabs.f64 x)))))))
(+.f64 (.f64 (pow.f64 x 2) (+.f64 2 (.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))))) (+.f64 (.f64 (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))) (-.f64 (.f64 2 (pow.f64 x 3)) (neg.f64 x))) (.f64 (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))) (*.f64 (sqrt.f64 8) (pow.f64 x 4)))))
(.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2)))
(.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (sqrt.f64 2)))
(neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (*.f64 (fabs.f64 x) -2)) (sqrt.f64 2)))
(neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (*.f64 -2 (fabs.f64 x))) (sqrt.f64 2)))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2))) (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 2) x))) (/.f64 1 (*.f64 (sqrt.f64 2) x)))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (sqrt.f64 2))) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 x 2))) (/.f64 1 (*.f64 (sqrt.f64 2) x)))
(-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2)) (sqrt.f64 2))) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 x 2))) (/.f64 1 (.f64 (sqrt.f64 2) x)))
(-.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 x 2)) (/.f64 (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))) (sqrt.f64 2))) (/.f64 1 (.f64 (sqrt.f64 2) x)))
(-.f64 (+.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2))) (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 2) x)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 2) x)) (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (sqrt.f64 2))) (+.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 x 2)) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8))))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 2) x)) (/.f64 1 (.f64 (pow.f64 x 2) 2))))
(-.f64 (+.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 x 2)) (+.f64 (neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2)) (sqrt.f64 2))) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8))))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 2) x)) (/.f64 1 (*.f64 (pow.f64 x 2) 2))))
(-.f64 (+.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 x 2)) (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8))) (/.f64 (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))) (sqrt.f64 2)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 2) x)) (/.f64 1 (*.f64 (pow.f64 x 2) 2))))
(-.f64 (+.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))) (+.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 4) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2))) (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 2) x))))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))) (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))))))
(-.f64 (+.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (sqrt.f64 2))) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 x 2))) (+.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8))) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 3) 4)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 (/.f64 1 (.f64 (pow.f64 x 2) 2)) (/.f64 1 (*.f64 (pow.f64 x 3) (sqrt.f64 8))))))
(-.f64 (+.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2)) (sqrt.f64 2))) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8)))) (+.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 x 2)) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 3) 4)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 (/.f64 1 (.f64 (pow.f64 x 2) 2)) (/.f64 1 (.f64 (pow.f64 x 3) (sqrt.f64 8))))))
(-.f64 (+.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8))) (/.f64 (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))) (sqrt.f64 2))) (+.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 x 2)) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 3) 4)))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 (/.f64 1 (.f64 (pow.f64 x 2) 2)) (/.f64 1 (.f64 (pow.f64 x 3) (sqrt.f64 8))))))
(.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2)))
(.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (sqrt.f64 2)))
(neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (*.f64 (fabs.f64 x) -2)) (sqrt.f64 2)))
(neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (*.f64 -2 (fabs.f64 x))) (sqrt.f64 2)))
(+.f64 (.f64 -1 (/.f64 (-.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (pow.f64 (sqrt.f64 2) 2)) (/.f64 1 (sqrt.f64 2))) x)) (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2))))
(+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (sqrt.f64 2))) (.f64 -1 (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) x)))
(+.f64 (neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2)) (sqrt.f64 2))) (neg.f64 (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) x)))
(-.f64 (neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))) (sqrt.f64 2))) (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) x))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (pow.f64 (sqrt.f64 2) 2)) (/.f64 1 (sqrt.f64 2))) x)) (+.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))) (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2))))) (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (sqrt.f64 2))) (+.f64 (.f64 -1 (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) x)) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8))))) (/.f64 1 (*.f64 (pow.f64 x 2) 2)))
(-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2)) (sqrt.f64 2))) (+.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8))) (neg.f64 (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) x)))) (/.f64 1 (*.f64 (pow.f64 x 2) 2)))
(-.f64 (-.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8))) (/.f64 (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))) (sqrt.f64 2))) (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) x)) (/.f64 1 (*.f64 (pow.f64 x 2) 2)))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (pow.f64 (sqrt.f64 2) 2)) (/.f64 1 (sqrt.f64 2))) (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 3)))) (+.f64 (.f64 -1 (/.f64 (-.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (pow.f64 (sqrt.f64 2) 2)) (/.f64 1 (sqrt.f64 2))) x)) (+.f64 (/.f64 (fabs.f64 (.f64 -2 x)) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))) (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (fabs.f64 (.f64 -2 x))) (sqrt.f64 2)))))) (/.f64 1 (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) x)) (+.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (sqrt.f64 2) (.f64 2 (fabs.f64 x))) (sqrt.f64 2))) (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8)))) (.f64 -1 (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) (.f64 2 (pow.f64 x 3)))))) (/.f64 1 (.f64 (pow.f64 x 2) 2)))
(-.f64 (+.f64 (+.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8))) (neg.f64 (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) x))) (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) (.f64 2 (pow.f64 x 3)))) (neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (.f64 (fabs.f64 x) -2)) (sqrt.f64 2))))) (/.f64 1 (*.f64 (pow.f64 x 2) 2)))
(-.f64 (-.f64 (-.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) (.f64 (pow.f64 x 2) (sqrt.f64 8))) (/.f64 (+.f64 (sqrt.f64 2) (.f64 -2 (fabs.f64 x))) (sqrt.f64 2))) (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) x)) (/.f64 (-.f64 (/.f64 (.f64 2 (fabs.f64 x)) 2) (/.f64 1 (sqrt.f64 2))) (.f64 2 (pow.f64 x 3)))) (/.f64 1 (*.f64 (pow.f64 x 2) 2)))

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 x 2) -2)
✓	0.4b	(*.f64 (sqrt.f64 2) x)
	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	30.1b	(/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x))

Compiler

Compiled 64 to 49 computations (23.4% saved)

series2.0ms (0%)

Counts

3 → 24

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x))
0.0ms	x	@	0	(*.f64 (pow.f64 x 2) -2)
0.0ms	x	@	-inf	(/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x))
0.0ms	x	@	inf	(/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x))
0.0ms	x	@	inf	(*.f64 (pow.f64 x 2) -2)

rewrite80.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1372×	`rational_best-simplify-61`
1130×	`rational_best-simplify-52`
806×	`rational_best-simplify-53`
748×	`rational_best-simplify-56`
564×	`rational_best-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	53
1	22	53
2	103	53
3	640	53
4	4407	53

Stop Event

1×	node limit

Counts

3 → 16

Calls

Call 1

Inputs
(/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) x)
(*.f64 (pow.f64 x 2) -2)

Outputs

()

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 (sqrt.f64 2) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 2) -2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 x 2) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (pow.f64 x 2) -2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 2 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 x 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 2) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 2 (pow.f64 x 2)))))))

simplify94.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

910×	`rational_best-simplify-3`
838×	`rational_best-simplify-61`
832×	`rational_best-simplify-65`
470×	`rational_best-simplify-53`
458×	`rational_best-simplify-52`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	600
1	161	552
2	905	552
3	4896	552

Stop Event

1×	node limit

Counts

40 → 20

Calls

Call 1

Inputs
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(-.f64 (*.f64 x (sqrt.f64 2)) 0)
(-.f64 0 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(/.f64 (*.f64 x (sqrt.f64 2)) 1)
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) -1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(+.f64 (*.f64 (pow.f64 x 2) -2) 0)
(+.f64 0 (*.f64 (pow.f64 x 2) -2))
(-.f64 (*.f64 (pow.f64 x 2) -2) 0)
(-.f64 0 (*.f64 2 (pow.f64 x 2)))
(/.f64 (*.f64 (pow.f64 x 2) -2) 1)
(/.f64 (*.f64 2 (pow.f64 x 2)) -1)
(pow.f64 (*.f64 (pow.f64 x 2) -2) 1)
(neg.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(-.f64 (*.f64 x (sqrt.f64 2)) 0)
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(-.f64 0 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(/.f64 (*.f64 x (sqrt.f64 2)) 1)
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) -1)
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(+.f64 (*.f64 (pow.f64 x 2) -2) 0)
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(+.f64 0 (*.f64 (pow.f64 x 2) -2))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(-.f64 (*.f64 (pow.f64 x 2) -2) 0)
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(-.f64 0 (*.f64 2 (pow.f64 x 2)))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(/.f64 (*.f64 (pow.f64 x 2) -2) 1)
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(/.f64 (*.f64 2 (pow.f64 x 2)) -1)
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(pow.f64 (*.f64 (pow.f64 x 2) -2) 1)
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(neg.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))

eval149.0ms (3.1%)

Compiler: Compiled 6719 to 4835 computations (28% saved)

prune28.0ms (0.6%)

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	0	0	0
Picked	1	0	1
Done	1	8	9
Total	189	10	199

Error

0.0b

Counts

199 → 10

Alt Table

Click to see full alt table

Status	Error	Program
	31.2b	(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (.f64 -2 (/.f64 x (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (neg.f64 x)))
✓	32.5b	(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
✓	0.3b	(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
✓	32.5b	(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
✓	0.4b	(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
✓	32.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.8b	(*.f64 (sqrt.f64 2) x)
✓	31.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	31.1b	(neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (*.f64 (fabs.f64 x) -2)) (sqrt.f64 2)))

Compiler

Compiled 119 to 93 computations (21.8% saved)

regimes33.0ms (0.7%)

Counts

20 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (.f64 (.f64 2 x) x))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (.f64 -2 (/.f64 x (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (neg.f64 x)))
(neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (*.f64 (fabs.f64 x) -2)) (sqrt.f64 2)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x)) (.f64 (sqrt.f64 2) (neg.f64 x)))
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (fabs.f64 x))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (.f64 2 x)))) (.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (*.f64 2 x)))))
(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (fabs.f64 (.f64 x -2))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (.f64 2 (pow.f64 (fabs.f64 (sqrt.f64 x)) 2))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (fabs.f64 (.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 x 2))))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))
(/.f64 (-.f64 (.f64 (sqrt.f64 2) (.f64 (fabs.f64 (/.f64 -1 (sqrt.f64 (fabs.f64 x)))) (fabs.f64 (sqrt.f64 (fabs.f64 x))))) (sqrt.f64 (.f64 (.f64 x x) 4))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (sqrt.f64 2) (*.f64 (fabs.f64 (/.f64 -1 (sqrt.f64 (fabs.f64 x)))) (fabs.f64 (sqrt.f64 (fabs.f64 x)))))))
(/.f64 (-.f64 (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x)))) (.f64 (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))) (-.f64 (/.f64 1 (sqrt.f64 (.f64 x x))) (.f64 (/.f64 1 (fabs.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 2) (fabs.f64 (sqrt.f64 x))))))

Outputs
(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))

Calls

3 calls:

11.0ms	x
7.0ms	(.f64 (.f64 2 x) x)
6.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))

Results

Error	Segments	Branch
0.3b	1	`x`
0.3b	1	`(sqrt.f64 (.f64 (.f64 2 x) x))`
0.3b	1	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 401 to 245 computations (38.9% saved)

regimes23.0ms (0.5%)

Counts

9 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (.f64 (.f64 2 x) x))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (.f64 -2 (/.f64 x (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (neg.f64 x)))
(neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (*.f64 (fabs.f64 x) -2)) (sqrt.f64 2)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x)) (.f64 (sqrt.f64 2) (neg.f64 x)))
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))

Outputs
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))

Calls

3 calls:

8.0ms	x
8.0ms	(.f64 (.f64 2 x) x)
4.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))

Results

Error	Segments	Branch
0.4b	1	`x`
0.4b	1	`(sqrt.f64 (.f64 (.f64 2 x) x))`
0.4b	1	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 107 to 79 computations (26.2% saved)

regimes37.0ms (0.8%)

Counts

8 → 2

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (.f64 (.f64 2 x) x))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(/.f64 (sqrt.f64 (*.f64 2 x)) (/.f64 1 (sqrt.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (.f64 -2 (/.f64 x (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (neg.f64 x)))
(neg.f64 (/.f64 (+.f64 (sqrt.f64 2) (*.f64 (fabs.f64 x) -2)) (sqrt.f64 2)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x)) (.f64 (sqrt.f64 2) (neg.f64 x)))

Outputs
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Calls

3 calls:

12.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
12.0ms	x
11.0ms	(.f64 (.f64 2 x) x)

Results

Error	Segments	Branch
0.4b	2	`x`
7.4b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
7.4b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 98 to 74 computations (24.5% saved)

bsearch16.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
16.0ms	-1.3475538675960855e-297	2.570630597080787e-302

Results

14.0ms

160×

body

256

valid

Compiler

Compiled 171 to 138 computations (19.3% saved)

regimes29.0ms (0.6%)

Accuracy

Total -62.2b remaining (-13840.5%)

Threshold costs -62.2b (-13840.5%)

Counts

3 → 2

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (.f64 (.f64 2 x) x))

Outputs
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 (sqrt.f64 2) x)

Calls

3 calls:

12.0ms	(.f64 (.f64 2 x) x)
8.0ms	x
8.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))

Results

Error	Segments	Branch
0.4b	2	`x`
14.3b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
14.3b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 31 to 22 computations (29% saved)

bsearch15.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
14.0ms	-1.3475538675960855e-297	2.570630597080787e-302

Results

13.0ms

160×

body

256

valid

Compiler

Compiled 141 to 118 computations (16.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	155

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) x)

Outputs
(/.f64 (sqrt.f64 (*.f64 2 (fabs.f64 x))) (sqrt.f64 (/.f64 1 (fabs.f64 x))))
(.f64 (sqrt.f64 (.f64 2 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 58 to 44 computations (24.1% saved)

soundness0.0ms (0%)

end39.0ms (0.8%)

Compiler: Compiled 54 to 38 computations (29.6% saved)