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)

sample1.5s (35.9%)

Results

1.5s	8256×	body	256	valid
0.0ms	1×	body	256	infinite

Bogosity

preprocess132.0ms (3.1%)

Algorithm

2×	egg-herbie

Rules

1810×	`rational.json-simplify-35`
1346×	`rational.json-simplify-53`
998×	`rational.json-simplify-39`
864×	`rational.json-simplify-59`
602×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	12	17
2	18	17
3	38	17
4	191	17
5	1977	17
6	5951	17
7	7795	17
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify137.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1810×	`rational.json-simplify-35`
1346×	`rational.json-simplify-53`
998×	`rational.json-simplify-39`
864×	`rational.json-simplify-59`
602×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	12	17
2	18	17
3	38	17
4	191	17
5	1977	17
6	5951	17
7	7795	17

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

30.4b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.4b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	29.4b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 17 to 8 computations (52.9% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite70.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1972×	`rational.json-simplify-35`
1372×	`rational.json-1`
1372×	`rational.json-2`
1372×	`rational.json-4`
1372×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	54	30
2	125	30
3	286	30
4	1096	30
5	4437	30

Stop Event

1×	node limit

Counts

2 → 76

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (sqrt.f64 (.f64 x (+.f64 x x)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (sqrt.f64 (.f64 x (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (sqrt.f64 (.f64 x (+.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 x x) (.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 x (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (/.f64 (/.f64 1 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (+.f64 (/.f64 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)) (.f64 2 (/.f64 (/.f64 1 x) x))) (/.f64 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)) (.f64 2 (/.f64 (/.f64 1 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (.f64 x (.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)) (.f64 2 (/.f64 (/.f64 1 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (/.f64 (.f64 x x) (.f64 x (+.f64 x x))) (/.f64 (/.f64 1 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 1 (.f64 2 (/.f64 (/.f64 1 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (.f64 x 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fabs.f64 x) (/.f64 2 (.f64 (fabs.f64 x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4 (.f64 2 (/.f64 (/.f64 1 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))) (.f64 2 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 1 x) x)) (.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 1 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2)) (.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4)) (.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 (.f64 x x) 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Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 (*.f64 x (+.f64 x x)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (sqrt.f64 (*.f64 x (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (sqrt.f64 (*.f64 x (+.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4))) (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x x) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (/.f64 (/.f64 1 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (+.f64 (/.f64 (/.f64 (/.f64 (/.f64 1 x) x) (*.f64 x x)) (*.f64 2 (/.f64 (/.f64 1 x) x))) (/.f64 (/.f64 (/.f64 (/.f64 1 x) x) (*.f64 x x)) (*.f64 2 (/.f64 (/.f64 1 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (*.f64 x (*.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (/.f64 (/.f64 1 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simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1286×	`rational.json-simplify-39`
1148×	`rational.json-simplify-43`
952×	`rational.json-simplify-55`
862×	`rational.json-simplify-59`
678×	`rational.json-simplify-41`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	2004
1	575	1728
2	2117	1704
3	4597	1536

Stop Event

1×	node limit

Counts

100 → 96

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 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 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x x))))
(+.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(.f64 2 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))
(.f64 2 (.f64 (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) 1))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)
(.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))
(.f64 (.f64 2 (sqrt.f64 (*.f64 x (+.f64 x x)))) 1/2)
(.f64 1/2 (.f64 2 (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(/.f64 (.f64 2 (sqrt.f64 (.f64 x (+.f64 x x)))) 2)
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4)) 8)
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) 16)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4)))) 32)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(+.f64 (.f64 x x) (.f64 x x))
(+.f64 (*.f64 x (+.f64 x x)) 0)
(+.f64 0 (*.f64 x (+.f64 x x)))
(-.f64 (.f64 x x) (.f64 x (neg.f64 x)))
(-.f64 (*.f64 x (+.f64 x x)) 0)
(-.f64 0 (neg.f64 (*.f64 x (+.f64 x x))))
(/.f64 2 (/.f64 (/.f64 1 x) x))
(/.f64 2 (+.f64 (/.f64 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)) (.f64 2 (/.f64 (/.f64 1 x) x))) (/.f64 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)) (.f64 2 (/.f64 (/.f64 1 x) x)))))
(/.f64 (*.f64 x (+.f64 x x)) 1)
(/.f64 1 (/.f64 2 (.f64 x (.f64 x 4))))
(/.f64 1 (/.f64 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)) (.f64 2 (/.f64 (/.f64 1 x) x))))
(/.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (*.f64 x (+.f64 x x))))
(/.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (/.f64 (.f64 x x) (*.f64 x (+.f64 x x))) (/.f64 (/.f64 1 x) x)))
(/.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 1 (.f64 2 (/.f64 (/.f64 1 x) x))))
(/.f64 (.f64 x (.f64 x 4)) 2)
(/.f64 (fabs.f64 x) (/.f64 2 (*.f64 (fabs.f64 x) 4)))
(/.f64 4 (*.f64 2 (/.f64 (/.f64 1 x) x)))
(/.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))) (.f64 x x))
(/.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))) (.f64 2 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (+.f64 x x)))))
(/.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))) (+.f64 (/.f64 (/.f64 (.f64 x x) (.f64 x (+.f64 x x))) (/.f64 (/.f64 1 x) x)) (/.f64 (/.f64 (.f64 x x) (*.f64 x (+.f64 x x))) (/.f64 (/.f64 1 x) x))))
(/.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))) (+.f64 (/.f64 1 (.f64 2 (/.f64 (/.f64 1 x) x))) (/.f64 1 (*.f64 2 (/.f64 (/.f64 1 x) x)))))
(/.f64 (.f64 (.f64 x x) 8) 4)
(/.f64 (*.f64 2 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
(/.f64 (.f64 2 (/.f64 (/.f64 1 x) x)) (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)))
(/.f64 8 (.f64 2 (.f64 2 (/.f64 (/.f64 1 x) x))))
(/.f64 (.f64 2 (.f64 (*.f64 x x) 8)) 8)
(/.f64 (.f64 2 (.f64 2 (/.f64 (/.f64 1 x) x))) (.f64 2 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x))))
(/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x 4))) (*.f64 x (+.f64 x x)))
(/.f64 (.f64 (fabs.f64 x) 4) (.f64 2 (/.f64 1 (fabs.f64 x))))
(/.f64 (neg.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x))))) (.f64 x (neg.f64 x)))
(/.f64 (neg.f64 (*.f64 x (+.f64 x x))) -1)
(/.f64 (.f64 (neg.f64 (.f64 x (+.f64 x x))) (neg.f64 (.f64 x (+.f64 x x)))) (.f64 x (+.f64 x x)))
(/.f64 -2 (neg.f64 (/.f64 (/.f64 1 x) x)))
(/.f64 (.f64 2 (.f64 (.f64 x x) (.f64 x (.f64 x 4)))) (.f64 x (*.f64 x 4)))
(/.f64 (.f64 2 (.f64 2 (.f64 (.f64 x x) 8))) 16)
(/.f64 (.f64 2 (neg.f64 (.f64 x (+.f64 x x)))) -2)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (/.f64 (/.f64 1 x) x)))) (.f64 2 (.f64 2 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)))))
(/.f64 (.f64 2 (neg.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))))) (.f64 2 (.f64 x (neg.f64 x))))
(/.f64 -4 (+.f64 (neg.f64 (/.f64 (/.f64 1 x) x)) (neg.f64 (/.f64 (/.f64 1 x) x))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (.f64 x (.f64 x 4)))) (neg.f64 (*.f64 x (+.f64 x x))))
(/.f64 (fabs.f64 (.f64 2 (.f64 (*.f64 x x) 8))) 8)
(/.f64 (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2)) (.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 2)))
(/.f64 (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4)) (.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 4)))
(/.f64 (+.f64 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2) (/.f64 (/.f64 1 x) x)) (.f64 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 2) (/.f64 (/.f64 1 x) x)))
(/.f64 (+.f64 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2)) (.f64 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 2)))
(/.f64 (+.f64 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4)) (.f64 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 4)))
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 1 x) x)) (.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 4) (/.f64 (/.f64 1 x) x)))
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2)) (.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 2)))
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4)) (.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 4)))
(/.f64 (+.f64 (.f64 2 (.f64 (.f64 x x) (.f64 x (.f64 x 4)))) (.f64 2 (.f64 (.f64 x x) (.f64 x (.f64 x 4))))) (.f64 (.f64 x x) 8))
(/.f64 (+.f64 (.f64 (neg.f64 (.f64 x (+.f64 x x))) (neg.f64 (.f64 x (+.f64 x x)))) (.f64 (neg.f64 (.f64 x (+.f64 x x))) (neg.f64 (.f64 x (+.f64 x x))))) (.f64 x (.f64 x 4)))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (.f64 x x) 8))) (.f64 2 (.f64 2 (.f64 (.f64 x x) 8)))) 32)
(/.f64 (+.f64 (neg.f64 (.f64 (.f64 x x) (.f64 x (.f64 x 4)))) (neg.f64 (.f64 (.f64 x x) (.f64 x (.f64 x 4))))) (.f64 2 (neg.f64 (.f64 x (+.f64 x x)))))
(/.f64 (+.f64 (fabs.f64 (.f64 2 (.f64 (.f64 x x) 8))) (fabs.f64 (.f64 2 (.f64 (.f64 x x) 8)))) 16)
(pow.f64 (*.f64 x (+.f64 x x)) 1)
(neg.f64 (neg.f64 (*.f64 x (+.f64 x x))))
(fabs.f64 (*.f64 x (+.f64 x x)))
(fabs.f64 (neg.f64 (*.f64 x (+.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 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 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 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 2 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 2 (.f64 (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) 1))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (.f64 2 (sqrt.f64 (*.f64 x (+.f64 x x)))) 1/2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 1/2 (.f64 2 (sqrt.f64 (*.f64 x (+.f64 x x)))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (.f64 2 (sqrt.f64 (.f64 x (+.f64 x x)))) 2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4) 4)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4)) 8)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) 16)
(sqrt.f64 (*.f64 x (+.f64 x x)))
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(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 x (+.f64 x x))
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(+.f64 (*.f64 x (+.f64 x x)) 0)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(+.f64 0 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(-.f64 (.f64 x x) (.f64 x (neg.f64 x)))
(*.f64 x (-.f64 x (neg.f64 x)))
(-.f64 (*.f64 x (+.f64 x x)) 0)
(*.f64 x (+.f64 x x))
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(-.f64 0 (neg.f64 (*.f64 x (+.f64 x x))))
(*.f64 x (+.f64 x x))
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(/.f64 2 (/.f64 (/.f64 1 x) x))
(/.f64 2 (/.f64 1 (*.f64 x x)))
(/.f64 x (/.f64 1/2 x))
(/.f64 (*.f64 x x) 1/2)
(/.f64 2 (+.f64 (/.f64 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)) (.f64 2 (/.f64 (/.f64 1 x) x))) (/.f64 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)) (.f64 2 (/.f64 (/.f64 1 x) x)))))
(*.f64 x (+.f64 x x))
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(/.f64 (*.f64 x (+.f64 x x)) 1)
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(/.f64 1 (/.f64 2 (.f64 x (.f64 x 4))))
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(/.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (/.f64 (.f64 x x) (*.f64 x (+.f64 x x))) (/.f64 (/.f64 1 x) x)))
(*.f64 x (+.f64 x x))
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(/.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 1 (.f64 2 (/.f64 (/.f64 1 x) x))))
(*.f64 x (+.f64 x x))
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(/.f64 (.f64 x (.f64 x 4)) 2)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (fabs.f64 x) (/.f64 2 (*.f64 (fabs.f64 x) 4)))
(*.f64 x (+.f64 x x))
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(/.f64 4 (*.f64 2 (/.f64 (/.f64 1 x) x)))
(/.f64 2 (/.f64 1 (*.f64 x x)))
(/.f64 x (/.f64 1/2 x))
(/.f64 (*.f64 x x) 1/2)
(/.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))) (.f64 x x))
(*.f64 x (+.f64 x x))
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(/.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))) (.f64 2 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (+.f64 x x)))))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))) (+.f64 (/.f64 (/.f64 (.f64 x x) (.f64 x (+.f64 x x))) (/.f64 (/.f64 1 x) x)) (/.f64 (/.f64 (.f64 x x) (*.f64 x (+.f64 x x))) (/.f64 (/.f64 1 x) x))))
(*.f64 x (+.f64 x x))
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(/.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))) (+.f64 (/.f64 1 (.f64 2 (/.f64 (/.f64 1 x) x))) (/.f64 1 (*.f64 2 (/.f64 (/.f64 1 x) x)))))
(*.f64 x (+.f64 x x))
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(/.f64 (.f64 (.f64 x x) 8) 4)
(*.f64 x (+.f64 x x))
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(/.f64 (*.f64 2 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))
(*.f64 x (+.f64 x x))
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(/.f64 (.f64 2 (/.f64 (/.f64 1 x) x)) (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)))
(*.f64 x (+.f64 x x))
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(/.f64 8 (.f64 2 (.f64 2 (/.f64 (/.f64 1 x) x))))
(/.f64 2 (/.f64 1 (*.f64 x x)))
(/.f64 x (/.f64 1/2 x))
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(/.f64 (.f64 2 (.f64 (*.f64 x x) 8)) 8)
(*.f64 x (+.f64 x x))
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(/.f64 (.f64 2 (.f64 2 (/.f64 (/.f64 1 x) x))) (.f64 2 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x))))
(*.f64 x (+.f64 x x))
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(/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x 4))) (*.f64 x (+.f64 x x)))
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(/.f64 (.f64 (fabs.f64 x) 4) (.f64 2 (/.f64 1 (fabs.f64 x))))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (neg.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x))))) (.f64 x (neg.f64 x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (neg.f64 (*.f64 x (+.f64 x x))) -1)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (.f64 (neg.f64 (.f64 x (+.f64 x x))) (neg.f64 (.f64 x (+.f64 x x)))) (.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 -2 (neg.f64 (/.f64 (/.f64 1 x) x)))
(/.f64 2 (/.f64 1 (*.f64 x x)))
(/.f64 x (/.f64 1/2 x))
(/.f64 (*.f64 x x) 1/2)
(/.f64 (.f64 2 (.f64 (.f64 x x) (.f64 x (.f64 x 4)))) (.f64 x (*.f64 x 4)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (.f64 2 (.f64 2 (.f64 (.f64 x x) 8))) 16)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (.f64 2 (neg.f64 (.f64 x (+.f64 x x)))) -2)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (/.f64 (/.f64 1 x) x)))) (.f64 2 (.f64 2 (/.f64 (/.f64 (/.f64 1 x) x) (.f64 x x)))))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (.f64 2 (neg.f64 (.f64 x (.f64 x (.f64 x (+.f64 x x)))))) (.f64 2 (.f64 x (neg.f64 x))))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 -4 (+.f64 (neg.f64 (/.f64 (/.f64 1 x) x)) (neg.f64 (/.f64 (/.f64 1 x) x))))
(/.f64 2 (/.f64 1 (*.f64 x x)))
(/.f64 x (/.f64 1/2 x))
(/.f64 (*.f64 x x) 1/2)
(/.f64 (neg.f64 (.f64 (.f64 x x) (.f64 x (.f64 x 4)))) (neg.f64 (*.f64 x (+.f64 x x))))
(*.f64 x (+.f64 x x))
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(/.f64 (fabs.f64 (.f64 2 (.f64 (*.f64 x x) 8))) 8)
(*.f64 x (+.f64 x x))
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(/.f64 (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2)) (.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 2)))
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(/.f64 (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4)) (.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 4)))
(+.f64 (/.f64 1 (/.f64 1 (.f64 x x))) (/.f64 1 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (.f64 x (/.f64 x x)))) 2)))
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(+.f64 (/.f64 1 (/.f64 1 (.f64 x x))) (/.f64 1 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (.f64 x (/.f64 x x)))) 2)))
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(+.f64 (.f64 x x) (/.f64 2 (/.f64 (.f64 2 (/.f64 1 x)) x)))
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 2)) (.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 2)))
(+.f64 (/.f64 1 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (.f64 x (/.f64 x x)))) 2)) (/.f64 1 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (.f64 x (/.f64 x x)))) 2)))
(+.f64 (/.f64 (.f64 x (.f64 x (/.f64 (.f64 x x) x))) x) (/.f64 (.f64 x (.f64 x (/.f64 (.f64 x x) x))) x))
(+.f64 (/.f64 2 (/.f64 (+.f64 (/.f64 1 x) (/.f64 1 x)) x)) (/.f64 2 (/.f64 (+.f64 (/.f64 1 x) (/.f64 1 x)) x)))
(.f64 2 (/.f64 2 (/.f64 (.f64 2 (/.f64 1 x)) x)))
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4)) (.f64 (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (.f64 x x) x))) 4) (/.f64 (/.f64 (.f64 x 4) (.f64 (.f64 x x) (/.f64 (*.f64 x x) x))) 4)))
(+.f64 (/.f64 1 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (.f64 x (/.f64 x x)))) 2)) (/.f64 1 (/.f64 (/.f64 (+.f64 x x) (.f64 (.f64 x x) (.f64 x (/.f64 x x)))) 2)))
(+.f64 (/.f64 (.f64 x (.f64 x (/.f64 (.f64 x x) x))) x) (/.f64 (.f64 x (.f64 x (/.f64 (.f64 x x) x))) x))
(+.f64 (/.f64 2 (/.f64 (+.f64 (/.f64 1 x) (/.f64 1 x)) x)) (/.f64 2 (/.f64 (+.f64 (/.f64 1 x) (/.f64 1 x)) x)))
(.f64 2 (/.f64 2 (/.f64 (.f64 2 (/.f64 1 x)) x)))
(/.f64 (+.f64 (.f64 2 (.f64 (.f64 x x) (.f64 x (.f64 x 4)))) (.f64 2 (.f64 (.f64 x x) (.f64 x (.f64 x 4))))) (.f64 (.f64 x x) 8))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (+.f64 (.f64 (neg.f64 (.f64 x (+.f64 x x))) (neg.f64 (.f64 x (+.f64 x x)))) (.f64 (neg.f64 (.f64 x (+.f64 x x))) (neg.f64 (.f64 x (+.f64 x x))))) (.f64 x (.f64 x 4)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (.f64 x x) 8))) (.f64 2 (.f64 2 (.f64 (.f64 x x) 8)))) 32)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (+.f64 (neg.f64 (.f64 (.f64 x x) (.f64 x (.f64 x 4)))) (neg.f64 (.f64 (.f64 x x) (.f64 x (.f64 x 4))))) (.f64 2 (neg.f64 (.f64 x (+.f64 x x)))))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(/.f64 (+.f64 (fabs.f64 (.f64 2 (.f64 (.f64 x x) 8))) (fabs.f64 (.f64 2 (.f64 (.f64 x x) 8)))) 16)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(pow.f64 (*.f64 x (+.f64 x x)) 1)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(neg.f64 (neg.f64 (*.f64 x (+.f64 x x))))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(fabs.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(fabs.f64 (neg.f64 (*.f64 x (+.f64 x x))))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))

eval55.0ms (1.3%)

Compiler: Compiled 1673 to 731 computations (56.3% saved)

prune11.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	4	97

Error

0.2b

Counts

97 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.8b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	32.0b	(*.f64 (sqrt.f64 2) x)
▶	30.5b	(sqrt.f64 (/.f64 x (/.f64 1/2 x)))
✓	30.4b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 25 to 19 computations (24% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 x (/.f64 1/2 x))
✓	29.4b	(sqrt.f64 (/.f64 x (/.f64 1/2 x)))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series0.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite72.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1824×	`rational.json-simplify-35`
1354×	`rational.json-simplify-2`
1236×	`rational.json-1`
1236×	`rational.json-2`
1236×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	55	30
2	145	30
3	429	30
4	1338	30
5	4222	30

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (/.f64 x (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 x (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 x (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 x (.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x 4) (.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (.f64 x 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 x) (.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 x) (/.f64 -1 (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 x (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (.f64 x (.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (.f64 x (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (.f64 1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x 8) (.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x -2) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (+.f64 x x)) (fabs.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (+.f64 x x)) (.f64 1/2 (fabs.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 x (/.f64 -1/2 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x 1/2) (.f64 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (.f64 x -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (/.f64 1/2 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 x) (fabs.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (.f64 x 1/2)) (fabs.f64 (.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (.f64 x 4)) (fabs.f64 (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (neg.f64 x)) (fabs.f64 (/.f64 -1 (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (/.f64 -1 (/.f64 1/2 x))) (fabs.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x 1/4) (.f64 x 8))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (.f64 x 1/2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2 (.f64 x x)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2 (fabs.f64 (+.f64 x x))) (fabs.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 x (.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 x (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 x (*.f64 x -2)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4))) (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (/.f64 x (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 x (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 x (*.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 4) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 x 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (*.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 -1 (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 x (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (*.f64 x (*.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 8) (*.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x -2) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (+.f64 x x)) (fabs.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (+.f64 x x)) (*.f64 1/2 (fabs.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (/.f64 -1/2 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/2) (*.f64 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 x -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (/.f64 1/2 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 x) (fabs.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (*.f64 x 1/2)) (fabs.f64 (*.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (*.f64 x 4)) (fabs.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (neg.f64 x)) (fabs.f64 (/.f64 -1 (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (/.f64 -1 (/.f64 1/2 x))) (fabs.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/4) (*.f64 x 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 x 1/2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (*.f64 x x)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (fabs.f64 (+.f64 x x))) (fabs.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 x (*.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 x (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 x (*.f64 x -2)))))))

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1282×	`rational.json-simplify-2`
1176×	`rational.json-simplify-53`
876×	`rational.json-simplify-59`
848×	`rational.json-simplify-55`
608×	`rational.json-simplify-39`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	1165
1	244	1165
2	671	1165
3	3197	1165

Stop Event

1×	node limit

Counts

85 → 67

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 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 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x x))))
(+.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(.f64 1/2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)
(.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))
(.f64 2 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) 1/2)
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4)) 8)
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) 16)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4)))) 32)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(+.f64 (*.f64 x (+.f64 x x)) 0)
(+.f64 0 (*.f64 x (+.f64 x x)))
(+.f64 -1 (-.f64 1 (/.f64 x (/.f64 -1/2 x))))
(+.f64 (.f64 x x) (.f64 x x))
(-.f64 (*.f64 x (+.f64 x x)) 0)
(-.f64 0 (/.f64 x (/.f64 -1/2 x)))
(*.f64 x (+.f64 x x))
(.f64 1/2 (.f64 x (*.f64 x 4)))
(.f64 (.f64 x (+.f64 x x)) 1)
(.f64 1 (.f64 x (+.f64 x x)))
(*.f64 (+.f64 x x) x)
(.f64 (.f64 x 4) (*.f64 x 1/2))
(.f64 (.f64 x (*.f64 x 4)) 1/2)
(.f64 2 (.f64 x x))
(.f64 (neg.f64 x) (.f64 x -2))
(*.f64 (neg.f64 x) (/.f64 -1 (/.f64 1/2 x)))
(*.f64 -1 (/.f64 x (/.f64 -1/2 x)))
(.f64 -1 (.f64 x (*.f64 x -2)))
(.f64 4 (.f64 x (*.f64 x 1/2)))
(.f64 4 (.f64 1/2 (*.f64 x x)))
(.f64 (.f64 x 8) (*.f64 x 1/4))
(.f64 (.f64 x x) 2)
(.f64 (.f64 x -2) (neg.f64 x))
(*.f64 (fabs.f64 (+.f64 x x)) (fabs.f64 x))
(.f64 (fabs.f64 (+.f64 x x)) (.f64 1/2 (fabs.f64 (+.f64 x x))))
(*.f64 (/.f64 x (/.f64 -1/2 x)) -1)
(.f64 (.f64 x 1/2) (*.f64 x 4))
(.f64 (.f64 x (*.f64 x -2)) -1)
(*.f64 (/.f64 -1 (/.f64 1/2 x)) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 (+.f64 x x)))
(.f64 (fabs.f64 (.f64 x 1/2)) (fabs.f64 (*.f64 x 4)))
(.f64 (fabs.f64 (.f64 x 4)) (fabs.f64 (*.f64 x 1/2)))
(*.f64 (fabs.f64 (neg.f64 x)) (fabs.f64 (/.f64 -1 (/.f64 1/2 x))))
(*.f64 (fabs.f64 (/.f64 -1 (/.f64 1/2 x))) (fabs.f64 (neg.f64 x)))
(.f64 (.f64 x 1/4) (*.f64 x 8))
(.f64 (.f64 x (*.f64 x 1/2)) 4)
(.f64 (.f64 1/2 (*.f64 x x)) 4)
(.f64 (.f64 1/2 (fabs.f64 (+.f64 x x))) (fabs.f64 (+.f64 x x)))
(pow.f64 (*.f64 x (+.f64 x x)) 1)
(neg.f64 (/.f64 x (/.f64 -1/2 x)))
(neg.f64 (.f64 x (.f64 x -2)))
(fabs.f64 (*.f64 x (+.f64 x x)))
(fabs.f64 (/.f64 x (/.f64 -1/2 x)))
(fabs.f64 (.f64 x (.f64 x -2)))

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) (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 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 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 1/2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 2 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 2) 1/2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4) 4)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 4)) 8)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) 16)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4))) (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 4)))) 32)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 (*.f64 x (+.f64 x x)) 0)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(+.f64 0 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(+.f64 -1 (-.f64 1 (/.f64 x (/.f64 -1/2 x))))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(-.f64 (*.f64 x (+.f64 x x)) 0)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(-.f64 0 (/.f64 x (/.f64 -1/2 x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 1/2 (.f64 x (*.f64 x 4)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 x (+.f64 x x)) 1)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 1 (.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 (+.f64 x x) x)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 x 4) (*.f64 x 1/2))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 x (*.f64 x 4)) 1/2)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(.f64 (neg.f64 x) (.f64 x -2))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 (neg.f64 x) (/.f64 -1 (/.f64 1/2 x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 -1 (/.f64 x (/.f64 -1/2 x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 -1 (.f64 x (*.f64 x -2)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 4 (.f64 x (*.f64 x 1/2)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 4 (.f64 1/2 (*.f64 x x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 x 8) (*.f64 x 1/4))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 x x) 2)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 x -2) (neg.f64 x))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 (fabs.f64 (+.f64 x x)) (fabs.f64 x))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (fabs.f64 (+.f64 x x)) (.f64 1/2 (fabs.f64 (+.f64 x x))))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 (/.f64 x (/.f64 -1/2 x)) -1)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 x 1/2) (*.f64 x 4))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 x (*.f64 x -2)) -1)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 (/.f64 -1 (/.f64 1/2 x)) (neg.f64 x))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 (fabs.f64 x) (fabs.f64 (+.f64 x x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (fabs.f64 (.f64 x 1/2)) (fabs.f64 (*.f64 x 4)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (fabs.f64 (.f64 x 4)) (fabs.f64 (*.f64 x 1/2)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 (fabs.f64 (neg.f64 x)) (fabs.f64 (/.f64 -1 (/.f64 1/2 x))))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 (fabs.f64 (/.f64 -1 (/.f64 1/2 x))) (fabs.f64 (neg.f64 x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 x 1/4) (*.f64 x 8))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 x (*.f64 x 1/2)) 4)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 1/2 (*.f64 x x)) 4)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(.f64 (.f64 1/2 (fabs.f64 (+.f64 x x))) (fabs.f64 (+.f64 x x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(pow.f64 (*.f64 x (+.f64 x x)) 1)
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(neg.f64 (/.f64 x (/.f64 -1/2 x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(neg.f64 (.f64 x (.f64 x -2)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(fabs.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(fabs.f64 (/.f64 x (/.f64 -1/2 x)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))
(fabs.f64 (.f64 x (.f64 x -2)))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 x x))

localize4.0ms (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	@	inf	(*.f64 (sqrt.f64 2) x)
0.0ms	x	@	0	(*.f64 (sqrt.f64 2) x)

rewrite212.0ms (5%)

Algorithm

1×	batch-egg-rewrite

Rules

1740×	`rational.json-simplify-35`
1606×	`rational.json-1`
1606×	`rational.json-2`
1508×	`rational.json-simplify-53`
1262×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	45	11
2	95	11
3	183	11
4	323	11
5	705	11
6	1680	11
7	2910	11
8	3832	11
9	4975	11
10	6124	11
11	7083	11
12	7083	11
13	7710	11

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) 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) (*.f64 x 1/2)) (*.f64 (sqrt.f64 2) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 2) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 2) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (*.f64 x 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (*.f64 x 8)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 16 (*.f64 (sqrt.f64 2) (*.f64 x 4)))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 16 (*.f64 (sqrt.f64 2) x)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (*.f64 8 (*.f64 x 4))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 16 (*.f64 (sqrt.f64 2) (*.f64 x 4))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 16 (*.f64 (sqrt.f64 2) (*.f64 x 4))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 16 (*.f64 (sqrt.f64 2) (*.f64 x 4)))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) x) 1)))))

simplify1.0s (23.9%)

Algorithm

1×	egg-herbie

Rules

3900×	`rational.json-simplify-35`
2832×	`rational.json-simplify-2`
1574×	`rational.json-simplify-53`
960×	`exponential.json-simplify-26`
930×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	165
1	136	165
2	291	165
3	819	165
4	2034	165
5	3334	165
6	4237	165
7	4530	165
8	4672	165
9	4779	165
10	4886	165
11	5468	165
12	5747	165
13	5965	165
14	6156	165
15	6258	165
16	6405	165
17	6484	165
18	6484	165
19	6591	165
20	6698	165
21	6805	165
22	6921	165
23	7028	165
24	7135	165
25	7466	165
26	7573	165
27	7680	165
28	7787	165
29	7894	165

Stop Event

1×	node limit

Counts

15 → 16

Calls

Call 1

Inputs
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(+.f64 (.f64 (sqrt.f64 2) (.f64 x 1/2)) (.f64 (sqrt.f64 2) (.f64 x 1/2)))
(-.f64 (*.f64 (sqrt.f64 2) x) 0)
(/.f64 (*.f64 (sqrt.f64 2) x) 1)
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) x)) 2)
(/.f64 (.f64 (sqrt.f64 2) (.f64 x 4)) 4)
(/.f64 (.f64 (sqrt.f64 2) (.f64 x 8)) 8)
(/.f64 (.f64 2 (.f64 16 (.f64 (sqrt.f64 2) (.f64 x 4)))) 128)
(/.f64 (.f64 16 (.f64 (sqrt.f64 2) x)) 16)
(/.f64 (.f64 (sqrt.f64 2) (.f64 8 (*.f64 x 4))) 32)
(/.f64 (.f64 16 (.f64 (sqrt.f64 2) (*.f64 x 4))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 16 (.f64 (sqrt.f64 2) (*.f64 x 4))))) 256)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (.f64 (sqrt.f64 2) (.f64 x 4)))))) 512)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)

Outputs
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) x)
(+.f64 (.f64 (sqrt.f64 2) (.f64 x 1/2)) (.f64 (sqrt.f64 2) (.f64 x 1/2)))
(*.f64 (sqrt.f64 2) x)
(-.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(/.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 (sqrt.f64 2) x)
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) x)) 2)
(*.f64 (sqrt.f64 2) x)
(/.f64 (.f64 (sqrt.f64 2) (.f64 x 4)) 4)
(*.f64 (sqrt.f64 2) x)
(/.f64 (.f64 (sqrt.f64 2) (.f64 x 8)) 8)
(*.f64 (sqrt.f64 2) x)
(/.f64 (.f64 2 (.f64 16 (.f64 (sqrt.f64 2) (.f64 x 4)))) 128)
(*.f64 (sqrt.f64 2) x)
(/.f64 (.f64 16 (.f64 (sqrt.f64 2) x)) 16)
(*.f64 (sqrt.f64 2) x)
(/.f64 (.f64 (sqrt.f64 2) (.f64 8 (*.f64 x 4))) 32)
(*.f64 (sqrt.f64 2) x)
(/.f64 (.f64 16 (.f64 (sqrt.f64 2) (*.f64 x 4))) 64)
(*.f64 (sqrt.f64 2) x)
(/.f64 (.f64 2 (.f64 2 (.f64 16 (.f64 (sqrt.f64 2) (*.f64 x 4))))) 256)
(*.f64 (sqrt.f64 2) x)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (.f64 (sqrt.f64 2) (.f64 x 4)))))) 512)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 (sqrt.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))

rewrite123.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1910×	`rational.json-simplify-35`
1610×	`rational.json-1`
1610×	`rational.json-2`
1610×	`rational.json-4`
1610×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	55	15
2	125	15
3	260	15
4	512	15
5	1218	15
6	2586	15
7	4474	15
8	5728	15
9	7320	15

Stop Event

1×	node limit

Counts

1 → 25

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 -1 (-.f64 1 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (+.f64 (*.f64 (sqrt.f64 2) x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) (*.f64 x -1/2)) (*.f64 (sqrt.f64 2) (*.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (*.f64 (sqrt.f64 2) x)) -1)))) (#(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 -1 (+.f64 (*.f64 (sqrt.f64 2) x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 1 (*.f64 (sqrt.f64 2) x)) 1)))) (#(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) (*.f64 x -2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (*.f64 x -4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -8 (*.f64 (sqrt.f64 2) x)) 8)))) (#(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 2 (*.f64 -8 (*.f64 (sqrt.f64 2) x))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 2) (+.f64 x x))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 -8 (*.f64 (sqrt.f64 2) x)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 2) (+.f64 x x)))) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 -8 (*.f64 (sqrt.f64 2) x))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 -8 (*.f64 (sqrt.f64 2) x)))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 -8 (*.f64 (sqrt.f64 2) x)))))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 -8 (*.f64 (sqrt.f64 2) x))))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (sqrt.f64 2) x))))))

simplify264.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

2282×	`rational.json-simplify-2`
1868×	`rational.json-simplify-35`
1724×	`rational.json-simplify-1`
1168×	`rational.json-simplify-41`
1086×	`rational.json-simplify-53`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	577
1	174	577
2	373	577
3	909	577
4	2522	577
5	4652	577
6	5254	577
7	5617	577
8	5876	577
9	6143	577
10	6179	577
11	7445	577
12	7883	577

Stop Event

1×	node limit

Counts

37 → 30

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 -1 (-.f64 1 (*.f64 (sqrt.f64 2) x)))
(+.f64 -2 (-.f64 1 (+.f64 (*.f64 (sqrt.f64 2) x) -1)))
(+.f64 (.f64 (sqrt.f64 2) (.f64 x -1/2)) (.f64 (sqrt.f64 2) (.f64 x -1/2)))
(+.f64 (-.f64 1 (*.f64 (sqrt.f64 2) x)) -1)
(-.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 0)
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(-.f64 -1 (+.f64 (*.f64 (sqrt.f64 2) x) -1))
(-.f64 (-.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)
(/.f64 (.f64 (sqrt.f64 2) (.f64 x -2)) 2)
(/.f64 (.f64 (sqrt.f64 2) (.f64 x -4)) 4)
(/.f64 (*.f64 (sqrt.f64 2) x) -1)
(/.f64 (.f64 -8 (.f64 (sqrt.f64 2) x)) 8)
(/.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2)
(/.f64 (.f64 2 (.f64 -8 (*.f64 (sqrt.f64 2) x))) 16)
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (+.f64 x x))) -4)
(/.f64 (.f64 2 (.f64 2 (.f64 -8 (.f64 (sqrt.f64 2) x)))) 32)
(/.f64 (.f64 2 (.f64 2 (*.f64 (sqrt.f64 2) (+.f64 x x)))) -8)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 -8 (*.f64 (sqrt.f64 2) x))))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 -8 (.f64 (sqrt.f64 2) x)))))) 128)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 -8 (.f64 (sqrt.f64 2) x)))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 -8 (.f64 (sqrt.f64 2) x))))))) 256)
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)
(neg.f64 (*.f64 (sqrt.f64 2) 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 -1 (-.f64 1 (*.f64 (sqrt.f64 2) x)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(+.f64 -2 (-.f64 1 (+.f64 (*.f64 (sqrt.f64 2) x) -1)))
(+.f64 -2 (-.f64 1 (+.f64 -1 (*.f64 (sqrt.f64 2) x))))
(+.f64 (.f64 (sqrt.f64 2) (.f64 x -1/2)) (.f64 (sqrt.f64 2) (.f64 x -1/2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(+.f64 (-.f64 1 (*.f64 (sqrt.f64 2) x)) -1)
(*.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 -1 (+.f64 (*.f64 (sqrt.f64 2) x) -1))
(-.f64 -1 (+.f64 -1 (*.f64 (sqrt.f64 2) x)))
(-.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) -1))
(-.f64 (-.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(*.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) (.f64 x -2)) 2)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (.f64 (sqrt.f64 2) (.f64 x -4)) 4)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (*.f64 (sqrt.f64 2) x) -1)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (.f64 -8 (.f64 (sqrt.f64 2) x)) 8)
(*.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 2 (.f64 -8 (*.f64 (sqrt.f64 2) x))) 16)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (+.f64 x x))) -4)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (.f64 2 (.f64 2 (.f64 -8 (.f64 (sqrt.f64 2) x)))) 32)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (.f64 2 (.f64 2 (*.f64 (sqrt.f64 2) (+.f64 x x)))) -8)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 -8 (*.f64 (sqrt.f64 2) x))))) 64)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 -8 (.f64 (sqrt.f64 2) x)))))) 128)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 -8 (.f64 (sqrt.f64 2) x)))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 -8 (.f64 (sqrt.f64 2) x))))))) 256)
(*.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))

eval63.0ms (1.5%)

Compiler: Compiled 1001 to 669 computations (33.2% saved)

prune13.0ms (0.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	113	4	117

Error

0.2b

Counts

117 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.8b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	32.0b	(*.f64 (sqrt.f64 2) x)
✓	30.5b	(sqrt.f64 (/.f64 x (/.f64 1/2 x)))
✓	30.4b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 25 to 19 computations (24% saved)

regimes31.0ms (0.7%)

Accuracy

Total -62.1b remaining (-14575.5%)

Threshold costs -62.1b (-14575.5%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

4 calls:

8.0ms	(.f64 2 (.f64 x x))
7.0ms	x
7.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
7.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 41 to 28 computations (31.7% saved)

bsearch14.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
13.0ms	-8.986000130584368e-304	2.4701352324181847e-307

Results

12.0ms

144×

body

256

valid

Compiler

Compiled 128 to 107 computations (16.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	46

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(if (<=.f64 x -2024022533073/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 2) x))

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

Outputs

(if (<=.f64 x -2024022533073/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 2) x))

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

Compiler

Compiled 19 to 15 computations (21.1% saved)

soundness197.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1286×	`rational.json-simplify-39`
1148×	`rational.json-simplify-43`
952×	`rational.json-simplify-55`
862×	`rational.json-simplify-59`
678×	`rational.json-simplify-41`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	2004
1	575	1728
2	2117	1704
3	4597	1536

Stop Event

1×	node limit

Compiler

Compiled 18 to 15 computations (16.7% saved)

end140.0ms (3.3%)

Compiler: Compiled 18 to 14 computations (22.2% saved)

Details

analyze3.0ms (0.1%)

sample1.5s (35.9%)

preprocess132.0ms (3.1%)

simplify137.0ms (3.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite70.0ms (1.7%)

simplify78.0ms (1.8%)

eval55.0ms (1.3%)

prune11.0ms (0.3%)

localize8.0ms (0.2%)

series0.0ms (0%)

rewrite72.0ms (1.7%)

simplify57.0ms (1.3%)

localize4.0ms (0.1%)

series0.0ms (0%)

rewrite212.0ms (5%)

simplify1.0s (23.9%)

localize6.0ms (0.1%)

series0.0ms (0%)

rewrite123.0ms (2.9%)

simplify264.0ms (6.2%)

eval63.0ms (1.5%)

prune13.0ms (0.3%)

regimes31.0ms (0.7%)

bsearch14.0ms (0.3%)

simplify2.0ms (0%)

soundness197.0ms (4.6%)

end140.0ms (3.3%)

Profiling