Details

analyze5.0ms (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
0%	0%	75%	0%	0%	25%	0%	3
40%	25%	37.5%	0%	0%	37.5%	0%	4
66.7%	37.5%	18.7%	0%	0%	43.7%	0%	5
82.4%	43.7%	9.4%	0%	0%	46.9%	0%	6
90.9%	46.9%	4.7%	0%	0%	48.4%	0%	7
95.4%	48.4%	2.3%	0%	0%	49.2%	0%	8
97.7%	49.2%	1.2%	0%	0%	49.6%	0%	9
98.8%	49.6%	0.6%	0%	0%	49.8%	0%	10
99.4%	49.8%	0.3%	0%	0%	49.9%	0%	11
99.7%	49.9%	0.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.1s (28.4%)

Results

1.1s	8256×	body	256	valid
1.0ms	11×	body	256	invalid

Bogosity

preprocess111.0ms (2.9%)

Algorithm

2×	egg-herbie

Rules

2108×	`rational.json-simplify-35`
850×	`rational.json-simplify-51`
848×	`rational.json-simplify-2`
800×	`rational.json-simplify-1`
754×	`rational.json-simplify-48`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	19	33
2	29	33
3	59	33
4	140	33
5	410	33
6	690	33
7	1503	33
8	2846	33
9	4838	33
10	7351	33
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify104.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

2108×	`rational.json-simplify-35`
850×	`rational.json-simplify-51`
848×	`rational.json-simplify-2`
800×	`rational.json-simplify-1`
754×	`rational.json-simplify-48`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	19	33
2	29	33
3	59	33
4	140	33
5	410	33
6	690	33
7	1503	33
8	2846	33
9	4838	33
10	7351	33

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 23 to 19 computations (17.4% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize18.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
✓	0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
✓	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))

Compiler

Compiled 45 to 34 computations (24.4% saved)

series2.0ms (0.1%)

Counts

3 → 28

Calls

9 calls:

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

rewrite94.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1398×	`rational.json-1`
1398×	`rational.json-2`
1398×	`rational.json-4`
1398×	`rational.json-3`
1390×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	69
1	77	69
2	192	69
3	435	69
4	1038	69
5	3854	69

Stop Event

1×	node limit

Counts

3 → 113

Calls

Call 1

Inputs
(/.f64 (-.f64 1 x) (+.f64 1 x))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

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

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

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

simplify107.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1010×	`rational.json-simplify-35`
986×	`rational.json-simplify-44`
936×	`rational.json-simplify-41`
930×	`rational.json-simplify-61`
922×	`rational.json-simplify-51`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	277	4959
1	630	4729
2	1564	4495
3	5517	4275

Stop Event

1×	node limit

Counts

141 → 208

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (.f64 -2 x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 -2 x) (*.f64 -2 (pow.f64 x 3)))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(-.f64 (.f64 2 (/.f64 1 x)) (+.f64 1 (.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 2 (/.f64 1 x)) (.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(-.f64 (.f64 2 (/.f64 1 x)) (+.f64 1 (.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 2 (/.f64 1 x)) (.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 x)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(sqrt.f64 -1)
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (-.f64 2 (.f64 -1 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))))
(sqrt.f64 -1)
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (.f64 1/2 (/.f64 (+.f64 2 (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)) (.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 -1 x)) (-.f64 1 (.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 -1 x)) (-.f64 1 (.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 -1 x)) (-.f64 1 (.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 -1 x)) (-.f64 1 (.f64 -1 x)))))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(+.f64 0 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(+.f64 -1 (-.f64 1 (/.f64 (-.f64 1 x) (-.f64 -1 x))))
(+.f64 (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))) (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))))
(-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(-.f64 0 (/.f64 (-.f64 1 x) (-.f64 -1 x)))
(-.f64 (*.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))) (/.f64 (/.f64 (-.f64 1 x) (-.f64 -1 x)) 2))
(-.f64 (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))) (/.f64 (-.f64 1 x) (.f64 2 (-.f64 -1 x))))
(*.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(*.f64 (-.f64 1 x) (/.f64 -1 (-.f64 -1 x)))
(.f64 (-.f64 1 x) (.f64 1/2 (*.f64 2 (/.f64 -1 (-.f64 -1 x)))))
(.f64 (-.f64 1 x) (.f64 1/2 (/.f64 2 (+.f64 1 x))))
(.f64 (+.f64 1 x) (/.f64 (/.f64 1 (-.f64 1 x)) (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(*.f64 -1 (/.f64 (-.f64 1 x) (-.f64 -1 x)))
(*.f64 (-.f64 (-.f64 2 x) x) (/.f64 -1/2 (-.f64 -1 x)))
(.f64 2 (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))))
(.f64 4 (/.f64 (-.f64 1 x) (.f64 (+.f64 1 x) 4)))
(*.f64 4 (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 4))
(.f64 (.f64 (-.f64 1 x) (/.f64 2 (+.f64 1 x))) 1/2)
(.f64 (.f64 (-.f64 1 x) 4) (/.f64 (/.f64 -1/2 (-.f64 -1 x)) 2))
(.f64 (.f64 (-.f64 1 x) 4) (*.f64 (/.f64 -1 (-.f64 -1 x)) 1/4))
(.f64 (.f64 (-.f64 1 x) 4) (*.f64 (/.f64 -1/2 (-.f64 -1 x)) 1/2))
(*.f64 (/.f64 -1 (-.f64 -1 x)) (-.f64 1 x))
(*.f64 (/.f64 -1 (-.f64 -1 x)) (/.f64 1 (/.f64 1 (-.f64 1 x))))
(*.f64 (+.f64 x -1) (/.f64 1 (-.f64 -1 x)))
(.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (/.f64 1 (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))))
(.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (/.f64 2 (.f64 2 (*.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x))))))
(.f64 (.f64 (+.f64 1 x) (/.f64 2 (-.f64 1 x))) (/.f64 1 (.f64 2 (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x))))))
(.f64 (.f64 (+.f64 1 x) (/.f64 2 (-.f64 1 x))) (/.f64 1/2 (*.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))))
(.f64 (.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 4) 1/4)
(.f64 (.f64 (-.f64 1 x) 8) (/.f64 1 (*.f64 (+.f64 1 x) 8)))
(*.f64 (+.f64 x (+.f64 x -2)) (/.f64 1/2 (-.f64 -1 x)))
(.f64 (+.f64 x (+.f64 x -2)) (/.f64 1 (.f64 2 (-.f64 -1 x))))
(*.f64 (/.f64 -1/2 (-.f64 -1 x)) (-.f64 (-.f64 2 x) x))
(.f64 1/2 (.f64 (-.f64 1 x) (/.f64 2 (+.f64 1 x))))
(.f64 (/.f64 1 (-.f64 1 x)) (/.f64 (+.f64 1 x) (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))))
(.f64 (.f64 2 (/.f64 -1 (-.f64 -1 x))) (*.f64 (-.f64 1 x) 1/2))
(*.f64 (/.f64 (-.f64 1 x) (-.f64 -1 x)) -1)
(.f64 (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))) 2)
(.f64 (/.f64 1/2 (-.f64 1 x)) (/.f64 (+.f64 x (+.f64 x 2)) (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))))
(.f64 (.f64 (+.f64 1 x) (/.f64 1/2 (-.f64 1 x))) (/.f64 2 (*.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))))
(.f64 (/.f64 2 (+.f64 1 x)) (.f64 (-.f64 1 x) 1/2))
(.f64 (/.f64 2 (-.f64 1 x)) (/.f64 (+.f64 1 x) (.f64 2 (*.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x))))))
(.f64 (/.f64 (/.f64 -1/2 (-.f64 -1 x)) 2) (.f64 (-.f64 1 x) 4))
(*.f64 (/.f64 1 (-.f64 -1 x)) (+.f64 x -1))
(.f64 (.f64 (-.f64 1 x) 1/2) (*.f64 2 (/.f64 -1 (-.f64 -1 x))))
(.f64 (.f64 (-.f64 1 x) 1/2) (/.f64 2 (+.f64 1 x)))
(.f64 1/4 (.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 4))
(.f64 (/.f64 1 (+.f64 x -1)) (/.f64 (-.f64 -1 x) (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))))
(.f64 (.f64 (/.f64 -1 (-.f64 -1 x)) 1/4) (*.f64 (-.f64 1 x) 4))
(.f64 (.f64 (/.f64 -1/2 (-.f64 -1 x)) 1/2) (*.f64 (-.f64 1 x) 4))
(.f64 (.f64 1/2 (*.f64 2 (/.f64 -1 (-.f64 -1 x)))) (-.f64 1 x))
(.f64 (.f64 1/2 (/.f64 2 (+.f64 1 x))) (-.f64 1 x))
(.f64 (/.f64 1 (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))) (/.f64 (+.f64 1 x) (-.f64 1 x)))
(.f64 (/.f64 (+.f64 x (+.f64 x 2)) (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))) (/.f64 1/2 (-.f64 1 x)))
(.f64 (/.f64 2 (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))) (*.f64 (+.f64 1 x) (/.f64 1/2 (-.f64 1 x))))
(*.f64 (/.f64 1 (/.f64 1 (-.f64 1 x))) (/.f64 -1 (-.f64 -1 x)))
(.f64 (/.f64 (+.f64 1 x) (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))) (/.f64 1 (-.f64 1 x)))
(.f64 (/.f64 (-.f64 -1 x) (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))) (/.f64 1 (+.f64 x -1)))
(.f64 (/.f64 (/.f64 1 (-.f64 1 x)) (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))) (+.f64 1 x))
(.f64 (/.f64 1 (.f64 2 (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x))))) (.f64 (+.f64 1 x) (/.f64 2 (-.f64 1 x))))
(.f64 (/.f64 2 (.f64 2 (*.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x))))) (/.f64 (+.f64 1 x) (-.f64 1 x)))
(.f64 (/.f64 (-.f64 1 x) (.f64 (+.f64 1 x) 4)) 4)
(*.f64 (/.f64 1/2 (-.f64 -1 x)) (+.f64 x (+.f64 x -2)))
(.f64 (/.f64 1/2 (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))) (*.f64 (+.f64 1 x) (/.f64 2 (-.f64 1 x))))
(.f64 (/.f64 (+.f64 1 x) (.f64 2 (*.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x))))) (/.f64 2 (-.f64 1 x)))
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 4) 4)
(.f64 (/.f64 1 (.f64 (+.f64 1 x) 8)) (*.f64 (-.f64 1 x) 8))
(.f64 (/.f64 1 (.f64 2 (-.f64 -1 x))) (+.f64 x (+.f64 x -2)))
(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(neg.f64 (/.f64 (-.f64 1 x) (-.f64 -1 x)))
(neg.f64 (/.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (*.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))))
(+.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 0)
(+.f64 0 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(+.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1/2) (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1/2))
(-.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 0)
(*.f64 1 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(.f64 2 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1/2))
(.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2) 1/2)
(*.f64 4 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4))
(.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4) 1/4)
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2))
(.f64 1/4 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4))
(.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1/2) 2)
(*.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4) 4)
(/.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(/.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2) 2)
(/.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4)) 8)
(/.f64 (.f64 2 (.f64 2 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4))) 16)
(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(+.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 0)
(+.f64 0 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(+.f64 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1/2) (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1/2))
(-.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 0)
(*.f64 1 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1)
(.f64 2 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1/2))
(*.f64 4 (/.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4))
(.f64 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 2) 1/2)
(.f64 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4) 1/4)
(.f64 1/2 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 2))
(.f64 1/4 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4))
(.f64 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1/2) 2)
(*.f64 (/.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4) 4)
(/.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1)
(/.f64 (*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 2) 2)
(/.f64 (*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4) 4)
(/.f64 (.f64 2 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4)) 8)
(/.f64 (.f64 2 (.f64 2 (*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4))) 16)
(pow.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1)

Outputs
1
(+.f64 1 (*.f64 -2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (.f64 -2 x)))
(+.f64 1 (+.f64 (.f64 -2 x) (.f64 2 (pow.f64 x 2))))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 -2 x) (*.f64 -2 (pow.f64 x 3)))))
(+.f64 1 (+.f64 (+.f64 (.f64 -2 x) (.f64 -2 (pow.f64 x 3))) (*.f64 2 (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (+.f64 (pow.f64 x 3) x))))
(+.f64 1 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (+.f64 x (pow.f64 x 3)))))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (.f64 -2 (+.f64 x (pow.f64 x 3)))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(+.f64 (*.f64 2 (/.f64 1 x)) -1)
(+.f64 -1 (*.f64 2 (/.f64 1 x)))
(-.f64 (.f64 2 (/.f64 1 x)) (+.f64 1 (.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 -1 (-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 2 (/.f64 1 x))))
(-.f64 -1 (*.f64 2 (-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 x))))
(-.f64 (+.f64 (.f64 2 (/.f64 1 x)) (.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (-.f64 (.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
(-.f64 -1 (-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 2 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)))))
(-.f64 -1 (-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 2 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))))
(-.f64 -1 (*.f64 2 (-.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(+.f64 (*.f64 2 (/.f64 1 x)) -1)
(+.f64 -1 (*.f64 2 (/.f64 1 x)))
(-.f64 (.f64 2 (/.f64 1 x)) (+.f64 1 (.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 -1 (-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 2 (/.f64 1 x))))
(-.f64 -1 (*.f64 2 (-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 x))))
(-.f64 (+.f64 (.f64 2 (/.f64 1 x)) (.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (-.f64 (.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
(-.f64 -1 (-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 2 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)))))
(-.f64 -1 (-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 2 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))))
(-.f64 -1 (*.f64 2 (-.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (*.f64 x -1))
(+.f64 1 (neg.f64 x))
(-.f64 1 x)
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 x)))
(+.f64 1 (+.f64 (.f64 x -1) (.f64 (pow.f64 x 2) 1/2)))
(+.f64 (+.f64 1 (neg.f64 x)) (*.f64 (pow.f64 x 2) 1/2))
(+.f64 1 (+.f64 (neg.f64 x) (*.f64 (pow.f64 x 2) 1/2)))
(+.f64 (*.f64 (pow.f64 x 2) 1/2) (-.f64 1 x))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(+.f64 1 (+.f64 (+.f64 (.f64 x -1) (.f64 (pow.f64 x 2) 1/2)) (*.f64 (pow.f64 x 3) -1/2)))
(+.f64 (.f64 (pow.f64 x 2) 1/2) (+.f64 (+.f64 (neg.f64 x) (.f64 (pow.f64 x 3) -1/2)) 1))
(+.f64 1 (+.f64 (+.f64 (neg.f64 x) (.f64 (pow.f64 x 2) 1/2)) (.f64 (pow.f64 x 3) -1/2)))
(+.f64 (.f64 (pow.f64 x 2) 1/2) (+.f64 (.f64 (pow.f64 x 3) -1/2) (-.f64 1 x)))
(sqrt.f64 -1)
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1 x) (sqrt.f64 -1)))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (/.f64 1 (*.f64 x (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (-.f64 2 (.f64 -1 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))))
(+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 1/2 (/.f64 (-.f64 2 (.f64 -1 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) 1))) (.f64 (pow.f64 x 3) (sqrt.f64 -1)))))))
(+.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (+.f64 (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1))))) (.f64 1/2 (/.f64 (-.f64 2 (neg.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)))) (.f64 (pow.f64 x 3) (sqrt.f64 -1))))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 1/2 (/.f64 (-.f64 2 (neg.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)))) (*.f64 (pow.f64 x 3) (sqrt.f64 -1)))))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 1/2 (/.f64 (-.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) -2) (*.f64 (pow.f64 x 3) (sqrt.f64 -1)))))))
(sqrt.f64 -1)
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1 x) (sqrt.f64 -1)))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (/.f64 1 (*.f64 x (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (.f64 -1/2 (/.f64 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (sqrt.f64 -1)) (pow.f64 x 2)))))
(+.f64 (+.f64 (sqrt.f64 -1) (/.f64 1 (.f64 x (sqrt.f64 -1)))) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (.f64 1/2 (/.f64 (+.f64 2 (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)) (.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))))
(+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (+.f64 (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1))))) (.f64 1/2 (/.f64 5 (*.f64 (pow.f64 x 3) (sqrt.f64 -1))))))
(+.f64 (+.f64 (sqrt.f64 -1) (+.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1)))))) (.f64 1/2 (/.f64 5 (.f64 (pow.f64 x 3) (sqrt.f64 -1)))))
(+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (+.f64 (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (sqrt.f64 -1)) (pow.f64 x 2)))) (.f64 1/2 (/.f64 5 (.f64 (pow.f64 x 3) (sqrt.f64 -1))))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 5 (*.f64 (pow.f64 x 3) (sqrt.f64 -1)))))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 -1 x)) (-.f64 1 (.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 -1 x)) (-.f64 1 (.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 -1 x)) (-.f64 1 (.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 -1 x)) (-.f64 1 (.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(+.f64 0 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(+.f64 -1 (-.f64 1 (/.f64 (-.f64 1 x) (-.f64 -1 x))))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(+.f64 (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))) (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))))
(+.f64 (.f64 (-.f64 1 x) (/.f64 1/2 (+.f64 1 x))) (.f64 (-.f64 1 x) (/.f64 1/2 (+.f64 1 x))))
(*.f64 (/.f64 1/2 (+.f64 1 x)) (+.f64 (-.f64 1 x) (-.f64 1 x)))
(.f64 2 (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))))
(*.f64 2 (/.f64 (-.f64 1 x) (+.f64 x (+.f64 x 2))))
(-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(-.f64 0 (/.f64 (-.f64 1 x) (-.f64 -1 x)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(-.f64 (*.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))) (/.f64 (/.f64 (-.f64 1 x) (-.f64 -1 x)) 2))
(-.f64 (.f64 (-.f64 1 x) (/.f64 1/2 (+.f64 1 x))) (/.f64 (-.f64 1 x) (.f64 2 (-.f64 -1 x))))
(-.f64 (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))) (/.f64 (-.f64 1 x) (.f64 2 (-.f64 -1 x))))
(-.f64 (/.f64 (-.f64 1 x) (+.f64 x (+.f64 x 2))) (/.f64 (-.f64 1 x) (*.f64 2 (-.f64 -1 x))))
(-.f64 (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))) (/.f64 (-.f64 1 x) (.f64 2 (-.f64 -1 x))))
(-.f64 (.f64 (-.f64 1 x) (/.f64 1/2 (+.f64 1 x))) (/.f64 (-.f64 1 x) (.f64 2 (-.f64 -1 x))))
(-.f64 (/.f64 (-.f64 1 x) (+.f64 x (+.f64 x 2))) (/.f64 (-.f64 1 x) (*.f64 2 (-.f64 -1 x))))
(*.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(*.f64 (-.f64 1 x) (/.f64 -1 (-.f64 -1 x)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(.f64 (-.f64 1 x) (.f64 1/2 (*.f64 2 (/.f64 -1 (-.f64 -1 x)))))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(.f64 (-.f64 1 x) (.f64 1/2 (/.f64 2 (+.f64 1 x))))
(.f64 1/2 (.f64 (-.f64 1 x) (/.f64 2 (+.f64 1 x))))
(.f64 1/2 (.f64 (-.f64 1 x) (/.f64 -2 (-.f64 -1 x))))
(.f64 (+.f64 1 x) (/.f64 (/.f64 1 (-.f64 1 x)) (.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))))
(.f64 (+.f64 1 x) (/.f64 (/.f64 1 (-.f64 1 x)) (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (*.f64 (-.f64 1 x) (-.f64 1 x))))))
(.f64 (+.f64 1 x) (/.f64 (.f64 (-.f64 1 x) (-.f64 1 x)) (/.f64 (+.f64 1 x) (/.f64 (/.f64 -1 (+.f64 x -1)) (+.f64 1 x)))))
(*.f64 (+.f64 1 x) (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (+.f64 1 x)))
(*.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)) (+.f64 1 x)))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(*.f64 -1 (/.f64 (-.f64 1 x) (-.f64 -1 x)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(*.f64 (-.f64 (-.f64 2 x) x) (/.f64 -1/2 (-.f64 -1 x)))
(*.f64 (/.f64 1/2 (+.f64 1 x)) (-.f64 (-.f64 2 x) x))
(*.f64 (/.f64 -1/2 (-.f64 -1 x)) (-.f64 (-.f64 2 x) x))
(.f64 2 (.f64 (-.f64 1 x) (/.f64 -1/2 (-.f64 -1 x))))
(+.f64 (.f64 (-.f64 1 x) (/.f64 1/2 (+.f64 1 x))) (.f64 (-.f64 1 x) (/.f64 1/2 (+.f64 1 x))))
(*.f64 (/.f64 1/2 (+.f64 1 x)) (+.f64 (-.f64 1 x) (-.f64 1 x)))
(*.f64 2 (/.f64 (-.f64 1 x) (+.f64 x (+.f64 x 2))))
(.f64 4 (/.f64 (-.f64 1 x) (.f64 (+.f64 1 x) 4)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(*.f64 4 (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 4))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(.f64 (.f64 (-.f64 1 x) (/.f64 2 (+.f64 1 x))) 1/2)
(.f64 1/2 (.f64 (-.f64 1 x) (/.f64 2 (+.f64 1 x))))
(.f64 1/2 (.f64 (-.f64 1 x) (/.f64 -2 (-.f64 -1 x))))
(.f64 (.f64 (-.f64 1 x) 4) (/.f64 (/.f64 -1/2 (-.f64 -1 x)) 2))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(.f64 (.f64 (-.f64 1 x) 4) (*.f64 (/.f64 -1 (-.f64 -1 x)) 1/4))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
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(neg.f64 (/.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (*.f64 (+.f64 1 x) (/.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) (-.f64 1 x)))))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(+.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 0)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(+.f64 0 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(+.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1/2) (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1/2))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(-.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 0)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(*.f64 1 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(.f64 2 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1/2))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2) 1/2)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(*.f64 4 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4) 1/4)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(.f64 1/4 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1/2) 2)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(*.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4) 4)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(/.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2) 2)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4) 4)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4)) 8)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(/.f64 (.f64 2 (.f64 2 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 4))) 16)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x)))
(+.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 0)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(+.f64 0 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(+.f64 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1/2) (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1/2))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(-.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 0)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(*.f64 1 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(.f64 2 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1/2))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(*.f64 4 (/.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(.f64 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 2) 1/2)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(.f64 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4) 1/4)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(.f64 1/2 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 2))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(.f64 1/4 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(.f64 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1/2) 2)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(*.f64 (/.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4) 4)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(/.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(/.f64 (*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 2) 2)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(/.f64 (*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4) 4)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(/.f64 (.f64 2 (.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4)) 8)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(/.f64 (.f64 2 (.f64 2 (*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 4))) 16)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))
(pow.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1)
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 x -1)) (-.f64 1 (.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 x -1) (-.f64 -1 x))))

eval76.0ms (2%)

Compiler: Compiled 4155 to 3552 computations (14.5% saved)

prune28.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	206	2	208
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	206	3	209

Error

Counts

209 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.3b	(*.f64 2 (atan.f64 (-.f64 1 x)))
▶	0.2b	(.f64 2 (atan.f64 (+.f64 (.f64 (pow.f64 x 2) 1/2) (-.f64 1 x))))
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

Compiler

Compiled 32 to 27 computations (15.6% saved)

localize19.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 (*.f64 (pow.f64 x 2) 1/2) (-.f64 1 x)))
✓	0.0b	(+.f64 (*.f64 (pow.f64 x 2) 1/2) (-.f64 1 x))

Compiler

Compiled 47 to 37 computations (21.3% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite251.0ms (6.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2194×	`rational.json-simplify-2`
1784×	`rational.json-simplify-35`
1350×	`rational.json-simplify-1`
1134×	`exponential.json-3`
1134×	`rational.json-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	54
1	84	54
2	162	54
3	302	54
4	543	54
5	1210	54
6	2832	54
7	3968	54
8	4821	54
9	5790	54
10	6372	54
11	6454	54
12	7480	54
13	7576	54

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

Inputs
(+.f64 (*.f64 (pow.f64 x 2) 1/2) (-.f64 1 x))
(atan.f64 (+.f64 (*.f64 (pow.f64 x 2) 1/2) (-.f64 1 x)))

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

Outputs

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

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

simplify673.0ms (17.5%)

Algorithm

1×	egg-herbie

Rules

2938×	`rational.json-simplify-2`
2658×	`rational.json-simplify-51`
2126×	`rational.json-simplify-35`
1132×	`rational.json-simplify-1`
1094×	`rational.json-simplify-48`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	2212
1	251	2168
2	602	2164
3	1835	2084
4	3058	2084
5	3684	2084
6	3791	2084
7	3908	2084
8	4020	2084
9	4106	2084
10	4186	2084
11	4293	2084
12	4390	2084
13	4502	2084
14	4619	2084
15	4744	2084
16	4874	2084
17	5010	2084
18	5091	2084
19	5172	2084
20	6434	2084
21	7365	2084
22	7443	2084
23	7559	2084
24	7687	2084
25	7867	2084
26	7993	2084

Stop Event

1×	node limit

Counts

76 → 75

Calls

Call 1

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

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

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (-.f64 1 x))

Compiler

Compiled 17 to 13 computations (23.5% saved)

series0.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite249.0ms (6.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2300×	`rational.json-simplify-35`
1980×	`rational.json-simplify-2`
1484×	`rational.json-simplify-1`
1092×	`exponential.json-3`
1092×	`rational.json-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	53	11
2	121	11
3	225	11
4	401	11
5	841	11
6	2046	11
7	3438	11
8	4147	11
9	5116	11
10	5780	11
11	5904	11
12	6034	11
13	6770	11
14	7413	11

Stop Event

1×	node limit

Counts

1 → 27

Calls

Call 1

Inputs
(atan.f64 (-.f64 1 x))

Outputs

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

simplify904.0ms (23.6%)

Algorithm

1×	egg-herbie

Rules

6302×	`rational.json-simplify-51`
3690×	`rational.json-simplify-35`
1352×	`rational.json-simplify-49`
1250×	`rational.json-simplify-2`
984×	`rational.json-simplify-1`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	527
1	130	465
2	426	465
3	1187	341
4	1946	341
5	2775	341
6	3199	341
7	3286	341
8	3345	341
9	3383	341
10	3420	341
11	3457	341
12	3494	341
13	3531	341
14	3568	341
15	3605	341
16	3642	341
17	3679	341
18	3716	341
19	4623	341
20	4906	341
21	5003	341
22	5096	341
23	5187	341
24	5187	341
25	5421	341
26	5421	341
27	5512	341
28	5603	341
29	5694	341
30	5785	341
31	5876	341
32	5967	341
33	6058	341
34	6149	341
35	6240	341
36	6331	341

Stop Event

1×	node limit

Counts

31 → 30

Calls

Call 1

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

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

eval33.0ms (0.9%)

Compiler: Compiled 1488 to 1306 computations (12.2% saved)

prune13.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	104	4	108

Error

Counts

108 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.3b	(*.f64 2 (atan.f64 (-.f64 1 x)))
✓	0.2b	(.f64 2 (atan.f64 (+.f64 (.f64 (pow.f64 x 2) 1/2) (-.f64 1 x))))
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
▶	1.0b	(*.f64 2 (atan.f64 1))

Compiler

Compiled 37 to 32 computations (13.5% saved)

localize4.0ms (0.1%)

Compiler: Compiled 9 to 9 computations (0% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

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

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.3b	(*.f64 2 (atan.f64 (-.f64 1 x)))
✓	0.2b	(.f64 2 (atan.f64 (+.f64 (.f64 (pow.f64 x 2) 1/2) (-.f64 1 x))))
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
✓	1.0b	(*.f64 2 (atan.f64 1))

Compiler

Compiled 37 to 32 computations (13.5% saved)

regimes13.0ms (0.3%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

4.0ms	x
2.0ms	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
2.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
2.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
2.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))`
0.0b	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))`
0.0b	1	`(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))`
0.0b	1	`(/.f64 (-.f64 1 x) (+.f64 1 x))`

Compiler

Compiled 75 to 61 computations (18.7% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.7b remaining (-209.6%)

Threshold costs -0.7b (-209.6%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 2 (atan.f64 1))
(*.f64 2 (atan.f64 (-.f64 1 x)))

Outputs
(*.f64 2 (atan.f64 (-.f64 1 x)))

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.3b	1	`x`

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	61

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 24 to 21 computations (12.5% saved)

soundness0.0ms (0%)

end23.0ms (0.6%)

Compiler: Compiled 22 to 19 computations (13.6% saved)

Details

analyze5.0ms (0.1%)

sample1.1s (28.4%)

preprocess111.0ms (2.9%)

simplify104.0ms (2.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize18.0ms (0.5%)

series2.0ms (0.1%)

rewrite94.0ms (2.4%)

simplify107.0ms (2.8%)

eval76.0ms (2%)

prune28.0ms (0.7%)

localize19.0ms (0.5%)

series1.0ms (0%)

rewrite251.0ms (6.5%)

simplify673.0ms (17.5%)

localize7.0ms (0.2%)

series0.0ms (0%)

rewrite249.0ms (6.5%)

simplify904.0ms (23.6%)

eval33.0ms (0.9%)

prune13.0ms (0.3%)

localize4.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes13.0ms (0.3%)

regimes4.0ms (0.1%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

end23.0ms (0.6%)

Profiling