Details

analyze8.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample22.8s (32.6%)

Results

13.5s	4098×	body	1024	valid
5.9s	2105×	body	512	valid
2.0s	453×	body	2048	valid
1.2s	1600×	body	256	valid
1.0ms	6×	body	256	invalid

Bogosity

preprocess311.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

1200×	`rational_best-simplify-65`
1170×	`rational_best-simplify-49`
1084×	`rational_best-simplify-67`
950×	`rational_best-simplify-108`
862×	`rational_best-simplify-75`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	26	41
2	38	41
3	59	41
4	98	41
5	197	41
6	465	41
7	1291	41
8	3320	41
9	6793	41
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (/.f64 x 2))))))

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify418.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1200×	`rational_best-simplify-65`
1170×	`rational_best-simplify-49`
1084×	`rational_best-simplify-67`
950×	`rational_best-simplify-108`
862×	`rational_best-simplify-75`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	26	41
2	38	41
3	59	41
4	98	41
5	197	41
6	465	41
7	1291	41
8	3320	41
9	6793	41

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

Outputs
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (/.f64 x 2))))))

eval1.0ms (0%)

Compiler: Compiled 27 to 24 computations (11.1% saved)

prune2.0ms (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

58.2b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	58.2b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))

Compiler

Compiled 14 to 13 computations (7.1% saved)

localize140.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) 2))
✓	0.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))
✓	5.6b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))

Compiler

Compiled 51 to 42 computations (17.6% saved)

series6.0ms (0%)

Counts

3 → 28

Calls

9 calls:

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

rewrite321.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1230×	`rational_best-simplify-75`
1132×	`rational_best-simplify-56`
938×	`rational_best-4`
938×	`rational_best-2`
938×	`rational_best-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	79
1	102	79
2	212	79
3	575	79
4	2388	79

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

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

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

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

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

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

simplify411.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1446×	`rational_best-simplify-75`
1382×	`rational_best-simplify-76`
1322×	`rational_best-simplify-56`
928×	`rational_best-simplify-63`
770×	`rational_best-simplify-3`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	3784
1	451	3768
2	1073	3768
3	3508	3740

Stop Event

1×	node limit

Counts

120 → 124

Calls

Call 1

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

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

eval412.0ms (0.6%)

Compiler: Compiled 2113 to 1827 computations (13.5% saved)

prune201.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	122	3	125

Error

56.8b

Counts

125 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	57.3b	(/.f64 (-.f64 (.f64 (PI.f64) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4))) 2)
✓	58.2b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
▶	61.5b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))

Status

Error

Program

▶

57.3b

(/.f64 (-.f64 (*.f64 (PI.f64) 2) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4))) 2)

✓

58.2b

(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))

▶

61.5b

(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))

Compiler

Compiled 42 to 39 computations (7.1% saved)

localize112.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(asin.f64 (sqrt.f64 1/2))

Compiler

Compiled 26 to 24 computations (7.7% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite567.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

958×	`rational_best-simplify-48`
760×	`rational_best-simplify-1`
674×	`rational_best-simplify-47`
636×	`rational_best-simplify-51`
632×	`rational_best-simplify-52`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	33	9
2	67	9
3	139	9
4	376	9
5	1378	9
6	7457	9

Stop Event

1×	node limit

Counts

1 → 48

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (asin.f64 (sqrt.f64 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (asin.f64 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))) (.f64 1/2 (asin.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (neg.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 8) (.f64 1/2 (asin.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (asin.f64 (sqrt.f64 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (asin.f64 (sqrt.f64 1/2)) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) (.f64 1/2 (asin.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (asin.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) -3) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) (/.f64 (asin.f64 (sqrt.f64 1/2)) -8)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) -8))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8)) (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -8) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (asin.f64 (sqrt.f64 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (asin.f64 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (asin.f64 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (.f64 (asin.f64 (sqrt.f64 1/2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (neg.f64 (asin.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (asin.f64 (sqrt.f64 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (.f64 (asin.f64 (sqrt.f64 1/2)) 4)) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -2 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/8 (.f64 2 (.f64 (asin.f64 (sqrt.f64 1/2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) 1/16)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/16 (.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (asin.f64 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (asin.f64 (sqrt.f64 1/2)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) (.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4)) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (asin.f64 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (asin.f64 (sqrt.f64 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (asin.f64 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (asin.f64 (sqrt.f64 1/2))) (*.f64 1/2 (asin.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (neg.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 8) (*.f64 1/2 (asin.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (asin.f64 (sqrt.f64 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (asin.f64 (sqrt.f64 1/2)) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) (*.f64 1/2 (asin.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (asin.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 1/2 (asin.f64 (sqrt.f64 1/2))) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) -3) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) (/.f64 (asin.f64 (sqrt.f64 1/2)) -8)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) -8))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8)) (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -8) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (asin.f64 (sqrt.f64 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (asin.f64 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (asin.f64 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (asin.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (asin.f64 (sqrt.f64 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (asin.f64 (sqrt.f64 1/2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (asin.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 2 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) 1/16)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/16 (*.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (asin.f64 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 (asin.f64 (sqrt.f64 1/2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) (*.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4)) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (asin.f64 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))))))))

simplify457.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1018×	`rational_best-simplify-85`
1000×	`rational_best-simplify-108`
838×	`rational_best-simplify-1`
768×	`rational_best-simplify-97`
602×	`rational_best-simplify-49`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	432
1	195	432
2	778	432
3	3751	432
4	7184	432

Stop Event

1×	node limit

Counts

48 → 49

Calls

Call 1

Inputs
(+.f64 (asin.f64 (sqrt.f64 1/2)) 0)
(+.f64 0 (asin.f64 (sqrt.f64 1/2)))
(+.f64 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))) (.f64 1/2 (asin.f64 (sqrt.f64 1/2))))
(+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4))
(+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)))
(+.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4))
(+.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (neg.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -4)))
(+.f64 (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 8) (.f64 1/2 (asin.f64 (sqrt.f64 1/2)))))
(+.f64 (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4))
(-.f64 (asin.f64 (sqrt.f64 1/2)) 0)
(-.f64 (asin.f64 (sqrt.f64 1/2)) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) (*.f64 1/2 (asin.f64 (sqrt.f64 1/2)))))
(-.f64 0 (neg.f64 (asin.f64 (sqrt.f64 1/2))))
(-.f64 (*.f64 1/2 (asin.f64 (sqrt.f64 1/2))) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2))
(-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) -3) 4))
(-.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -4))
(-.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) (/.f64 (asin.f64 (sqrt.f64 1/2)) -8)))
(-.f64 (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) -4))
(-.f64 (-.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) -8))
(-.f64 (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8)) (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -8) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4)))
(.f64 1/2 (.f64 (asin.f64 (sqrt.f64 1/2)) 2))
(*.f64 (asin.f64 (sqrt.f64 1/2)) 1)
(*.f64 1 (asin.f64 (sqrt.f64 1/2)))
(.f64 2 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))))
(.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 2) 1/2)
(*.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))) -1)
(.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 1/4)
(.f64 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))) 2)
(.f64 4 (.f64 (asin.f64 (sqrt.f64 1/2)) 1/4))
(*.f64 -1 (neg.f64 (asin.f64 (sqrt.f64 1/2))))
(.f64 1/4 (.f64 (asin.f64 (sqrt.f64 1/2)) 4))
(.f64 (.f64 2 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) 1/8)
(*.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) -2)
(*.f64 -2 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2))
(.f64 1/8 (.f64 2 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)))
(.f64 (.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) 1/16)
(.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 1/4) 4)
(.f64 1/16 (.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4))
(/.f64 (asin.f64 (sqrt.f64 1/2)) 1)
(/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 2) 2)
(/.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))) -1)
(/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4)
(/.f64 (*.f64 1/2 (asin.f64 (sqrt.f64 1/2))) 1/2)
(/.f64 (.f64 2 (.f64 (asin.f64 (sqrt.f64 1/2)) 4)) 8)
(/.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) -1/2)
(/.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) 16)
(/.f64 (+.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) (.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4)) 32)
(pow.f64 (asin.f64 (sqrt.f64 1/2)) 1)
(neg.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))))

Outputs
(+.f64 (asin.f64 (sqrt.f64 1/2)) 0)
(asin.f64 (sqrt.f64 1/2))
(+.f64 0 (asin.f64 (sqrt.f64 1/2)))
(asin.f64 (sqrt.f64 1/2))
(+.f64 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))) (.f64 1/2 (asin.f64 (sqrt.f64 1/2))))
(asin.f64 (sqrt.f64 1/2))
(+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4))
(asin.f64 (sqrt.f64 1/2))
(+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)))
(asin.f64 (sqrt.f64 1/2))
(+.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4))
(asin.f64 (sqrt.f64 1/2))
(+.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (neg.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -4)))
(asin.f64 (sqrt.f64 1/2))
(+.f64 (/.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 8) (.f64 1/2 (asin.f64 (sqrt.f64 1/2)))))
(asin.f64 (sqrt.f64 1/2))
(+.f64 (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4))
(asin.f64 (sqrt.f64 1/2))
(-.f64 (asin.f64 (sqrt.f64 1/2)) 0)
(asin.f64 (sqrt.f64 1/2))
(-.f64 (asin.f64 (sqrt.f64 1/2)) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) (*.f64 1/2 (asin.f64 (sqrt.f64 1/2)))))
(asin.f64 (sqrt.f64 1/2))
(-.f64 0 (neg.f64 (asin.f64 (sqrt.f64 1/2))))
(asin.f64 (sqrt.f64 1/2))
(-.f64 (*.f64 1/2 (asin.f64 (sqrt.f64 1/2))) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2))
(asin.f64 (sqrt.f64 1/2))
(-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) -3) 4))
(asin.f64 (sqrt.f64 1/2))
(-.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -4))
(asin.f64 (sqrt.f64 1/2))
(-.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) (/.f64 (asin.f64 (sqrt.f64 1/2)) -8)))
(asin.f64 (sqrt.f64 1/2))
(-.f64 (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) -4))
(asin.f64 (sqrt.f64 1/2))
(-.f64 (-.f64 (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8) (/.f64 (asin.f64 (sqrt.f64 1/2)) -2)) (/.f64 (asin.f64 (sqrt.f64 1/2)) -8))
(asin.f64 (sqrt.f64 1/2))
(-.f64 (+.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) 4) (/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 3) 8)) (-.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -8) (/.f64 (asin.f64 (sqrt.f64 1/2)) 4)))
(asin.f64 (sqrt.f64 1/2))
(.f64 1/2 (.f64 (asin.f64 (sqrt.f64 1/2)) 2))
(asin.f64 (sqrt.f64 1/2))
(*.f64 (asin.f64 (sqrt.f64 1/2)) 1)
(asin.f64 (sqrt.f64 1/2))
(*.f64 1 (asin.f64 (sqrt.f64 1/2)))
(asin.f64 (sqrt.f64 1/2))
(.f64 2 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))))
(asin.f64 (sqrt.f64 1/2))
(.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 2) 1/2)
(asin.f64 (sqrt.f64 1/2))
(*.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))) -1)
(asin.f64 (sqrt.f64 1/2))
(.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 1/4)
(asin.f64 (sqrt.f64 1/2))
(.f64 (.f64 1/2 (asin.f64 (sqrt.f64 1/2))) 2)
(asin.f64 (sqrt.f64 1/2))
(.f64 4 (.f64 (asin.f64 (sqrt.f64 1/2)) 1/4))
(asin.f64 (sqrt.f64 1/2))
(*.f64 -1 (neg.f64 (asin.f64 (sqrt.f64 1/2))))
(asin.f64 (sqrt.f64 1/2))
(.f64 1/4 (.f64 (asin.f64 (sqrt.f64 1/2)) 4))
(asin.f64 (sqrt.f64 1/2))
(.f64 (.f64 2 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) 1/8)
(asin.f64 (sqrt.f64 1/2))
(*.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) -2)
(asin.f64 (sqrt.f64 1/2))
(*.f64 -2 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2))
(asin.f64 (sqrt.f64 1/2))
(.f64 1/8 (.f64 2 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)))
(asin.f64 (sqrt.f64 1/2))
(.f64 (.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) 1/16)
(asin.f64 (sqrt.f64 1/2))
(.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 1/4) 4)
(asin.f64 (sqrt.f64 1/2))
(.f64 1/16 (.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4))
(asin.f64 (sqrt.f64 1/2))
(/.f64 (asin.f64 (sqrt.f64 1/2)) 1)
(asin.f64 (sqrt.f64 1/2))
(/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 2) 2)
(asin.f64 (sqrt.f64 1/2))
(/.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))) -1)
(asin.f64 (sqrt.f64 1/2))
(/.f64 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4)
(asin.f64 (sqrt.f64 1/2))
(/.f64 (*.f64 1/2 (asin.f64 (sqrt.f64 1/2))) 1/2)
(asin.f64 (sqrt.f64 1/2))
(/.f64 (.f64 2 (.f64 (asin.f64 (sqrt.f64 1/2)) 4)) 8)
(asin.f64 (sqrt.f64 1/2))
(/.f64 (/.f64 (asin.f64 (sqrt.f64 1/2)) -2) -1/2)
(asin.f64 (sqrt.f64 1/2))
(/.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) 16)
(asin.f64 (sqrt.f64 1/2))
(/.f64 (+.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4) (.f64 (.f64 (asin.f64 (sqrt.f64 1/2)) 4) 4)) 32)
(asin.f64 (sqrt.f64 1/2))
(pow.f64 (asin.f64 (sqrt.f64 1/2)) 1)
(asin.f64 (sqrt.f64 1/2))
(neg.f64 (neg.f64 (asin.f64 (sqrt.f64 1/2))))
(asin.f64 (sqrt.f64 1/2))

localize227.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 x -2)))
✓	0.0b	(+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4))
✓	0.9b	(asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2))))
✓	5.7b	(-.f64 (.f64 (PI.f64) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4)))

Compiler

Compiled 83 to 68 computations (18.1% saved)

series75.0ms (0.1%)

Counts

4 → 40

Calls

12 calls:

Time	Variable		Point	Expression
70.0ms	x	@	0	(-.f64 (.f64 (PI.f64) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4)))
2.0ms	x	@	inf	(-.f64 (.f64 (PI.f64) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4)))
1.0ms	x	@	inf	(sqrt.f64 (+.f64 1/2 (/.f64 x -2)))
1.0ms	x	@	-inf	(-.f64 (.f64 (PI.f64) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4)))
0.0ms	x	@	0	(sqrt.f64 (+.f64 1/2 (/.f64 x -2)))

rewrite509.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1444×	`rational_best-1`
1438×	`rational_best-4`
1438×	`rational_best-2`
1438×	`rational_best-3`
1438×	`exponential-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	122
1	123	112
2	259	108
3	759	108
4	3727	108

Stop Event

1×	node limit

Counts

4 → 220

Calls

Call 1

Inputs
(-.f64 (.f64 (PI.f64) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4)))
(asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2))))
(+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4))
(sqrt.f64 (+.f64 1/2 (/.f64 x -2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (PI.f64) (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (.f64 (PI.f64) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (PI.f64) (+.f64 (PI.f64) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (PI.f64) (-.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) 2) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -8) (neg.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (+.f64 (PI.f64) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (-.f64 -1 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (PI.f64)) (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (-.f64 -1 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (+.f64 (PI.f64) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (neg.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64)) (.f64 (PI.f64) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) 3) (+.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) 3) (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (.f64 (PI.f64) 3)) (.f64 (PI.f64) -2))))) 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(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4) (PI.f64)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 2 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) (/.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1/2 (+.f64 1/2 (neg.f64 x)))) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1/2 (+.f64 1/2 (neg.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4) (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1)))))

simplify789.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1414×	`rational_best-simplify-48`
1328×	`rational_best-simplify-52`
1308×	`rational_best-simplify-57`
1234×	`rational_best-simplify-51`
1122×	`rational_best-simplify-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	453	10402
1	1054	10378
2	2731	8702

Stop Event

1×	node limit

Counts

260 → 264

Calls

Call 1

Inputs
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) (PI.f64)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/4 (/.f64 x (sqrt.f64 1/2))))
(+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/4 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))) (*.f64 -1/4 (/.f64 x (sqrt.f64 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4))
(+.f64 (PI.f64) (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (.f64 (PI.f64) -2)))
(+.f64 (PI.f64) (+.f64 (PI.f64) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64))))
(+.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4))))
(+.f64 (PI.f64) (-.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (.f64 (PI.f64) 2)))
(+.f64 (.f64 (PI.f64) 2) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4) (PI.f64)))
(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -8) (neg.f64 (PI.f64))))
(+.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) 0)
(+.f64 0 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)))
(+.f64 1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (+.f64 (PI.f64) -1)))
(+.f64 1 (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4)) (-.f64 -1 (PI.f64))))
(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64))
(+.f64 (neg.f64 (PI.f64)) (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4)))
(+.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (-.f64 -1 (PI.f64))))
(+.f64 -1 (-.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4)) (+.f64 (PI.f64) -1)))
(+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4)) (neg.f64 (PI.f64)))
(+.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64)) (*.f64 (PI.f64) 2))
(+.f64 (.f64 (PI.f64) 3) (+.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4) (PI.f64))))
(+.f64 (.f64 (PI.f64) 3) (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))) -1/2))
(+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (.f64 (PI.f64) 3)) (.f64 (PI.f64) -2))
(+.f64 (.f64 (PI.f64) -2) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (.f64 (PI.f64) 3)))
(+.f64 (-.f64 (/.f64 (PI.f64) 2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) (-.f64 (/.f64 (PI.f64) 2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))))
(+.f64 (/.f64 (PI.f64) 2) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (/.f64 (PI.f64) 2)))
(+.f64 (/.f64 (PI.f64) 2) (/.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -8)) 2))
(+.f64 (/.f64 (PI.f64) 2) (-.f64 (/.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)))
(+.f64 (+.f64 (PI.f64) -1) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) 1))
(+.f64 (+.f64 (PI.f64) -1) (-.f64 1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)))
(+.f64 (-.f64 -1 (PI.f64)) (-.f64 (.f64 (PI.f64) 2) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4) -1)))
(+.f64 (-.f64 -1 (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (+.f64 -1 (*.f64 (PI.f64) -2))))
(+.f64 (-.f64 -1 (PI.f64)) (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4)) 1))
(+.f64 (-.f64 -1 (PI.f64)) (-.f64 1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (*.f64 (PI.f64) -2))))
(+.f64 (+.f64 1 (.f64 (PI.f64) -2)) (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (+.f64 (PI.f64) -1)))
(+.f64 (+.f64 (PI.f64) 1) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) -1))
(+.f64 (+.f64 (PI.f64) 1) (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (+.f64 -1 (.f64 (PI.f64) -2))))
(+.f64 (+.f64 (PI.f64) 1) (neg.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) 1)))
(+.f64 (+.f64 (PI.f64) 1) (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)))
(+.f64 (-.f64 1 (PI.f64)) (+.f64 -1 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4))))
(+.f64 (-.f64 1 (PI.f64)) (-.f64 -1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (*.f64 (PI.f64) -2))))
(+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) -1) (+.f64 (PI.f64) 1))
(+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (/.f64 (PI.f64) 2)) (/.f64 (PI.f64) 2))
(+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (+.f64 (PI.f64) -1)) 1)
(+.f64 (+.f64 -1 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4))) (-.f64 1 (PI.f64)))
(+.f64 (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (.f64 (PI.f64) -2)) (PI.f64))
(+.f64 (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (+.f64 (PI.f64) -1)) (+.f64 1 (.f64 (PI.f64) -2)))
(+.f64 (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4)) (-.f64 -1 (PI.f64))) 1)
(+.f64 (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (+.f64 -1 (.f64 (PI.f64) -2))) (+.f64 (PI.f64) 1))
(+.f64 (+.f64 (PI.f64) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64))) (PI.f64))
(+.f64 (-.f64 (PI.f64) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4))) (PI.f64))
(+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) 1) (+.f64 (PI.f64) -1))
(+.f64 (-.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (.f64 (PI.f64) 2)) (PI.f64))
(+.f64 (+.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64))) (*.f64 (PI.f64) 3))
(+.f64 (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -1/2) (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))))
(+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3))
(+.f64 (neg.f64 (/.f64 (PI.f64) 2)) (-.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4)) (/.f64 (PI.f64) 2)))
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(-.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (.f64 (PI.f64) -2)) (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))))
(-.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (-.f64 1 (PI.f64))) (-.f64 -1 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))))
(-.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (+.f64 1 (.f64 (PI.f64) -2))) (-.f64 (+.f64 (PI.f64) -1) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))))
(-.f64 (+.f64 (.f64 (PI.f64) 4) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) (-.f64 (.f64 (PI.f64) 3) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))))
(-.f64 (-.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64))) -1)
(-.f64 (+.f64 (-.f64 (PI.f64) (-.f64 -1 (PI.f64))) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (+.f64 (PI.f64) -1))) 2)
(-.f64 (+.f64 (-.f64 (PI.f64) (-.f64 -1 (PI.f64))) (-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (*.f64 (PI.f64) -2)) (-.f64 -1 (PI.f64)))) 2)
(-.f64 (+.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (+.f64 (PI.f64) -1)) (-.f64 (PI.f64) (-.f64 -1 (PI.f64)))) 2)
(-.f64 (+.f64 (-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (*.f64 (PI.f64) -2)) (-.f64 -1 (PI.f64))) (-.f64 (PI.f64) (-.f64 -1 (PI.f64)))) 2)
(-.f64 (+.f64 (-.f64 -1 (.f64 (PI.f64) -2)) (-.f64 -1 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4)))) -2)
(-.f64 (+.f64 (-.f64 -1 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4))) (-.f64 -1 (*.f64 (PI.f64) -2))) -2)
(.f64 2 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1/2))
(.f64 1/2 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 8)))
(.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)) 1)
(.f64 1 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)))
(.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4) (PI.f64)) -1)
(.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 8)) 1/2)
(.f64 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 4) 1/4)
(.f64 1/4 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 4))
(/.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1)
(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64)) -1)
(/.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 8)) 2)
(/.f64 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)) 4) 4)
(/.f64 (+.f64 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 4) (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 4)) 8)
(/.f64 (+.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 16)) 4)
(/.f64 (-.f64 (.f64 (PI.f64) 4) (.f64 2 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)))) 2)
(/.f64 (-.f64 (.f64 (PI.f64) 8) (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) 4)) 4)
(pow.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1)
(neg.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64)))
(+.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 0)
(+.f64 0 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2))
(-.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 0)
(-.f64 (.f64 2 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) (/.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 2))
(.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1/2))
(.f64 1/2 (.f64 2 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 1)
(.f64 1 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))
(.f64 (.f64 2 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 1/2)
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 4) 1/4)
(.f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 4))
(*.f64 (sqrt.f64 (+.f64 1/2 (+.f64 1/2 (neg.f64 x)))) (sqrt.f64 1/2))
(*.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1/2 (+.f64 1/2 (neg.f64 x)))))
(/.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1)
(/.f64 (.f64 2 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 2)
(/.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4) 4)
(/.f64 (+.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4) (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4)) 8)
(pow.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1)

Outputs
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2)))))))
(+.f64 (PI.f64) (neg.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2)))))))
(+.f64 (PI.f64) (neg.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2)))))))
(+.f64 (PI.f64) (neg.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2)))))))
(+.f64 (PI.f64) (neg.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) (PI.f64)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/4 (/.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (*.f64 x (/.f64 -1/4 (sqrt.f64 1/2))))
(+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/4 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (.f64 x (/.f64 -1/4 (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (pow.f64 x 2) (sqrt.f64 1/8)))))
(+.f64 (.f64 x (/.f64 -1/4 (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (.f64 (pow.f64 x 2) (/.f64 -1/32 (sqrt.f64 1/8)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 x (/.f64 -1/4 (sqrt.f64 1/2))) (.f64 (pow.f64 x 2) (/.f64 -1/32 (sqrt.f64 1/8)))))
(+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))) (*.f64 -1/4 (/.f64 x (sqrt.f64 1/2))))))
(+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 2) (sqrt.f64 1/8))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 x (/.f64 -1/4 (sqrt.f64 1/2))) (*.f64 (pow.f64 x 3) (/.f64 -1/128 (sqrt.f64 1/32))))))
(+.f64 (.f64 (pow.f64 x 2) (/.f64 -1/32 (sqrt.f64 1/8))) (+.f64 (.f64 x (/.f64 -1/4 (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) (/.f64 -1/128 (sqrt.f64 1/32))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 (pow.f64 x 2) (/.f64 -1/32 (sqrt.f64 1/8))) (+.f64 (.f64 x (/.f64 -1/4 (sqrt.f64 1/2))) (*.f64 (pow.f64 x 3) (/.f64 -1/128 (sqrt.f64 1/32))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(+.f64 (PI.f64) (+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (.f64 (PI.f64) -2)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(+.f64 (PI.f64) (+.f64 (PI.f64) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64))))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(+.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4))))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))
(+.f64 (PI.f64) (-.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (.f64 (PI.f64) 2)))
(-.f64 (.f64 2 (PI.f64)) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
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(-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (/.f64 (PI.f64) 2)) (neg.f64 (/.f64 (PI.f64) 2)))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (.f64 (PI.f64) 3))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (PI.f64) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4))) (neg.f64 (PI.f64)))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (PI.f64))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (-.f64 -1 (PI.f64))) 1)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)) (+.f64 (PI.f64) -1)) 1)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (.f64 (PI.f64) 4) (.f64 2 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)))) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)))
(-.f64 (.f64 (PI.f64) 4) (+.f64 (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (.f64 2 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4)))))
(-.f64 (-.f64 (.f64 (PI.f64) 4) (+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4))))
(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (-.f64 (.f64 (PI.f64) 4) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -8) (.f64 (PI.f64) 3))))
(-.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (PI.f64)) (-.f64 (.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (/.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) (neg.f64 (/.f64 (PI.f64) 2)))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (neg.f64 (PI.f64))) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -1/2))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (+.f64 (PI.f64) 1)) (-.f64 (+.f64 -1 (.f64 (PI.f64) -2)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) -1) (-.f64 (-.f64 -1 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (.f64 (PI.f64) -2)) (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (-.f64 1 (PI.f64))) (-.f64 -1 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (+.f64 1 (.f64 (PI.f64) -2))) (-.f64 (+.f64 (PI.f64) -1) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 (PI.f64) 4) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) (-.f64 (.f64 (PI.f64) 3) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (-.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64))) -1)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (-.f64 (PI.f64) (-.f64 -1 (PI.f64))) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (+.f64 (PI.f64) -1))) 2)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (-.f64 (PI.f64) (-.f64 -1 (PI.f64))) (-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (*.f64 (PI.f64) -2)) (-.f64 -1 (PI.f64)))) 2)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (+.f64 (PI.f64) -1)) (-.f64 (PI.f64) (-.f64 -1 (PI.f64)))) 2)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (*.f64 (PI.f64) -2)) (-.f64 -1 (PI.f64))) (-.f64 (PI.f64) (-.f64 -1 (PI.f64)))) 2)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (-.f64 -1 (.f64 (PI.f64) -2)) (-.f64 -1 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4)))) -2)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (-.f64 -1 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4))) (-.f64 -1 (*.f64 (PI.f64) -2))) -2)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(.f64 2 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1/2))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(.f64 1/2 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 8)))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)) 1)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(.f64 1 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4) (PI.f64)) -1)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 8)) 1/2)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(.f64 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 4) 1/4)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(.f64 1/4 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 4))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(/.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64)) -1)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(/.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 8)) 2)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(/.f64 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)) 4) 4)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(/.f64 (+.f64 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 4) (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 4)) 8)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(/.f64 (+.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 16)) 4)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(/.f64 (-.f64 (.f64 (PI.f64) 4) (.f64 2 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)))) 2)
(/.f64 (-.f64 (.f64 (PI.f64) 4) (.f64 2 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4)))) 2)
(-.f64 (/.f64 (.f64 (PI.f64) 4) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4)))
(+.f64 (-.f64 (/.f64 (.f64 (PI.f64) 4) 2) (PI.f64)) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(/.f64 (-.f64 (.f64 (PI.f64) 8) (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) 4)) 4)
(/.f64 (-.f64 (.f64 (PI.f64) 4) (.f64 2 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4)))) 2)
(-.f64 (/.f64 (.f64 (PI.f64) 4) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4)))
(+.f64 (-.f64 (/.f64 (.f64 (PI.f64) 4) 2) (PI.f64)) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(pow.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1)
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(neg.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (PI.f64)))
(+.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 0)
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(+.f64 0 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(+.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2))
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(-.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 0)
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(-.f64 (.f64 2 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(-.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) (/.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 2))
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1/2))
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(.f64 1/2 (.f64 2 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 1)
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(.f64 1 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(.f64 (.f64 2 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 1/2)
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 4) 1/4)
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(.f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 4))
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(*.f64 (sqrt.f64 (+.f64 1/2 (+.f64 1/2 (neg.f64 x)))) (sqrt.f64 1/2))
(sqrt.f64 (*.f64 (+.f64 (neg.f64 x) 1) 1/2))
(sqrt.f64 (*.f64 1/2 (+.f64 1 (neg.f64 x))))
(sqrt.f64 (*.f64 1/2 (-.f64 1 x)))
(*.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1/2 (+.f64 1/2 (neg.f64 x)))))
(sqrt.f64 (*.f64 (+.f64 (neg.f64 x) 1) 1/2))
(sqrt.f64 (*.f64 1/2 (+.f64 1 (neg.f64 x))))
(sqrt.f64 (*.f64 1/2 (-.f64 1 x)))
(/.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1)
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(/.f64 (.f64 2 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 2)
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(/.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4) 4)
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(/.f64 (+.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4) (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4)) 8)
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))
(pow.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1)
(sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))

eval627.0ms (0.9%)

Compiler: Compiled 6647 to 5673 computations (14.7% saved)

prune228.0ms (0.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	309	4	313
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	310	6	316

Error

56.8b

Counts

316 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	58.3b	(/.f64 (/.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (+.f64 (.f64 (PI.f64) 3) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))) 2) 2)
▶	57.3b	(/.f64 (+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3)) 2)
▶	57.3b	(/.f64 (+.f64 (/.f64 (PI.f64) -2) (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))) 2)
▶	57.3b	(/.f64 (+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1)) 2)
✓	58.2b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
✓	61.5b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))

Compiler

Compiled 124 to 113 computations (8.9% saved)

localize231.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))
✓	0.0b	(-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4))
✓	0.9b	(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
✓	5.7b	(+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1))

Compiler

Compiled 85 to 73 computations (14.1% saved)

series3.0ms (0%)

Counts

4 → 40

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1))
0.0ms	x	@	inf	(+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1))
0.0ms	x	@	-inf	(+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))
0.0ms	x	@	-inf	(sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))

rewrite254.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1602×	`rational_best-simplify-56`
1050×	`rational_best-4`
1050×	`rational_best-2`
1050×	`rational_best-3`
1050×	`rational_best-1`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	118
1	125	118
2	217	116
3	582	106
4	2527	106

Stop Event

1×	node limit

Counts

4 → 161

Calls

Call 1

Inputs
(+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
(-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4))
(sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))

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

simplify466.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1350×	`rational_best-simplify-47`
1228×	`rational_best-simplify-57`
932×	`rational_best-simplify-48`
860×	`rational_best-simplify-52`
784×	`rational_best-simplify-51`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	379	6865
1	920	6709
2	2222	6643

Stop Event

1×	node limit

Counts

201 → 210

Calls

Call 1

Inputs
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/4 (/.f64 x (sqrt.f64 1/2))))
(+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/4 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))) (*.f64 -1/4 (/.f64 x (sqrt.f64 1/2))))))
(-.f64 -1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (-.f64 -1 (PI.f64))))
(-.f64 -1 (+.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (PI.f64))))
(-.f64 -1 (+.f64 (+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (neg.f64 (PI.f64))))
(-.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (-.f64 -1 (PI.f64)))
(-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4))
(-.f64 (PI.f64) (+.f64 -1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) 1)))
(-.f64 (PI.f64) (-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (PI.f64)) (PI.f64)))
(-.f64 1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (+.f64 -1 (PI.f64))))
(-.f64 (+.f64 (PI.f64) 1) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) 1))
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(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 8) -2) -2)
(/.f64 (.f64 (-.f64 (neg.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 8)) 2) 4) 8)
(/.f64 (/.f64 (neg.f64 (.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)) 4)) -1) 4)
(pow.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1)
(neg.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) 1))
(+.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 0)
(+.f64 0 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2))
(-.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 0)
(-.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) -2))
(.f64 1/2 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 2))
(.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 1)
(.f64 1 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))
(.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1/2))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 2) 1/2)
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 4) 1/4)
(.f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 4))
(.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4)) 1/8)
(*.f64 (sqrt.f64 (+.f64 1/2 (+.f64 1/2 (neg.f64 x)))) (sqrt.f64 1/2))
(*.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1/2 (+.f64 1/2 (neg.f64 x)))))
(/.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1)
(/.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) 2)
(/.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 4)) 8)
(pow.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1)

Outputs
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
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(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))))
(.f64 -1 (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) 1))
(neg.f64 (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) 1))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))))
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(neg.f64 (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) 1))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
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(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 -1 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/4 (/.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (*.f64 x (/.f64 -1/4 (sqrt.f64 1/2))))
(+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/4 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (.f64 x (/.f64 -1/4 (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (.f64 (pow.f64 x 2) (/.f64 -1/32 (sqrt.f64 1/8)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 x (/.f64 -1/4 (sqrt.f64 1/2))) (.f64 (pow.f64 x 2) (/.f64 -1/32 (sqrt.f64 1/8)))))
(+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))) (*.f64 -1/4 (/.f64 x (sqrt.f64 1/2))))))
(+.f64 (+.f64 (.f64 x (/.f64 -1/4 (sqrt.f64 1/2))) (.f64 (pow.f64 x 3) (/.f64 -1/128 (sqrt.f64 1/32)))) (+.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 2) (/.f64 -1/32 (sqrt.f64 1/8)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 (pow.f64 x 2) (/.f64 -1/32 (sqrt.f64 1/8))) (+.f64 (.f64 x (/.f64 -1/4 (sqrt.f64 1/2))) (*.f64 (pow.f64 x 3) (/.f64 -1/128 (sqrt.f64 1/32))))))
(-.f64 -1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (-.f64 -1 (PI.f64))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
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(-.f64 -1 (+.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (PI.f64))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
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(-.f64 -1 (+.f64 (+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (neg.f64 (PI.f64))))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
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(-.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (-.f64 -1 (PI.f64)))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4))
(-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
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(-.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4)) 0)
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(+.f64 (/.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) -2) 2) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -1/2))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 -1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4) 1))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 1/2 (-.f64 (neg.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 8)) 2))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)) 1)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 1 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4) 1) -1)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 2 (.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1/2))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 (-.f64 (neg.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 8)) 2) 1/2)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 (.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 4) 1/4)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 1/4 (.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 4))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(.f64 (.f64 (-.f64 (neg.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 8)) 2) 4) 1/8)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(/.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(/.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) 1) -1)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(/.f64 (-.f64 (neg.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 8)) 2) 2)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(/.f64 (.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)) 4) 4)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(/.f64 (neg.f64 (.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)) 4)) -4)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 8) -2) -2)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(/.f64 (.f64 (-.f64 (neg.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 8)) 2) 4) 8)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(/.f64 (/.f64 (neg.f64 (.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 4)) 4)) -1) 4)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(pow.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) 1)
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(neg.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) 1))
(neg.f64 (+.f64 1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 -1 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -4))
(+.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 0)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(+.f64 0 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(+.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2))
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(-.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 0)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(-.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) -2))
(-.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))) 2) (/.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))) -2))
(.f64 1/2 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 2))
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 1)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(.f64 1 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1/2))
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 2) 1/2)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(.f64 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 4) 1/4)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(.f64 1/4 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 4))
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4)) 1/8)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(*.f64 (sqrt.f64 (+.f64 1/2 (+.f64 1/2 (neg.f64 x)))) (sqrt.f64 1/2))
(sqrt.f64 (*.f64 (+.f64 (neg.f64 x) 1) 1/2))
(sqrt.f64 (*.f64 1/2 (+.f64 1 (neg.f64 x))))
(sqrt.f64 (*.f64 1/2 (-.f64 1 x)))
(*.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1/2 (+.f64 1/2 (neg.f64 x)))))
(sqrt.f64 (*.f64 (+.f64 (neg.f64 x) 1) 1/2))
(sqrt.f64 (*.f64 1/2 (+.f64 1 (neg.f64 x))))
(sqrt.f64 (*.f64 1/2 (-.f64 1 x)))
(/.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(/.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 2) 2)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(/.f64 (.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))) 4) 4)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 4)) 8)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))
(pow.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))) 1)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))

localize434.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
✓	0.1b	(+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))
✓	0.9b	(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
✓	58.4b	(+.f64 (/.f64 (PI.f64) -2) (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))))

Compiler

Compiled 158 to 131 computations (17.1% saved)

series32.0ms (0%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
24.0ms	x	@	-inf	(+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))
3.0ms	x	@	-inf	(+.f64 (/.f64 (PI.f64) -2) (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))))
2.0ms	x	@	0	(+.f64 (/.f64 (PI.f64) -2) (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))))
1.0ms	x	@	inf	(+.f64 (/.f64 (PI.f64) -2) (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))))
0.0ms	x	@	inf	(+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))

rewrite655.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1642×	`rational_best-4`
1642×	`rational_best-2`
1642×	`rational_best-3`
1642×	`rational_best-1`
1642×	`exponential-1`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	21	238
1	140	238
2	271	238
3	783	222
4	3874	210

Stop Event

1×	node limit

Counts

4 → 189

Calls

Call 1

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

Outputs
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simplify862.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1362×	`rational_best-simplify-3`
1018×	`rational_best-simplify-56`
558×	`rational_best-simplify-75`
556×	`rational_best-simplify-57`
540×	`rational_best-simplify-76`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	394	16843
1	999	16281
2	3089	12283

Stop Event

1×	node limit

Counts

237 → 265

Calls

Call 1

Inputs
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x)))))) (.f64 -1 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x)))))) (.f64 -1 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x)))))) (.f64 -1 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x)))))) (.f64 -1 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (.f64 -1/2 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (.f64 (PI.f64) -1/2) (+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))))
(-.f64 (.f64 (PI.f64) -1/2) (+.f64 (+.f64 (.f64 (PI.f64) 1/2) (.f64 -2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))
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(-.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 -2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (-.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
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(-.f64 (.f64 2 (-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (.f64 (PI.f64) 1/2))
(-.f64 (-.f64 (+.f64 (.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64))) (.f64 (PI.f64) -1/4)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) (/.f64 (PI.f64) 4))
(-.f64 (-.f64 (.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64))) (+.f64 (.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64))) (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 (PI.f64) 1/2)))) (.f64 -2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(-.f64 (-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (/.f64 (PI.f64) 4)) (-.f64 (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (/.f64 (PI.f64) 4)) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))
(-.f64 (-.f64 (-.f64 (.f64 (PI.f64) -1/4) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 -2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (neg.f64 (-.f64 (.f64 (PI.f64) -1/4) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))
(-.f64 (+.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (neg.f64 (PI.f64))) (-.f64 (-.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(-.f64 (+.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (+.f64 (.f64 (PI.f64) -1/4) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (-.f64 (/.f64 (PI.f64) 4) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(.f64 1/2 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))))
(.f64 (+.f64 (.f64 2 (-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (*.f64 (PI.f64) -1/2)) 1)
(.f64 1 (+.f64 (.f64 2 (-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (*.f64 (PI.f64) -1/2)))
(.f64 (+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))) -1)
(.f64 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))) 1/2)
(.f64 -1 (+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))))
(.f64 (.f64 2 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4)))) 1/4)
(.f64 1/4 (.f64 2 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4)))))
(.f64 (+.f64 (.f64 2 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4)))) (.f64 2 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))))) 1/8)
(/.f64 (+.f64 (.f64 2 (-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (.f64 (PI.f64) -1/2)) 1)
(/.f64 (+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))) -1)
(/.f64 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))) 2)
(/.f64 (.f64 2 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))) 4)
(/.f64 (+.f64 (.f64 2 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4)))) (.f64 2 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))))) 8)
(pow.f64 (+.f64 (.f64 2 (-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (.f64 (PI.f64) -1/2)) 1)
(neg.f64 (+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) 0)
(+.f64 0 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(+.f64 (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (neg.f64 (PI.f64))) (*.f64 (PI.f64) 1/2))
(+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (*.f64 (PI.f64) -1/2))
(+.f64 (neg.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (/.f64 (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (neg.f64 (PI.f64))) 2))
(+.f64 (.f64 (PI.f64) -1/4) (+.f64 (.f64 (PI.f64) -1/4) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))
(+.f64 (-.f64 (.f64 (PI.f64) -1/4) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (-.f64 (.f64 (PI.f64) -1/4) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(+.f64 (+.f64 (.f64 (PI.f64) -1/4) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (.f64 (PI.f64) -1/4))
(+.f64 (+.f64 (.f64 (PI.f64) -1/4) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) (neg.f64 (/.f64 (PI.f64) 4)))
(+.f64 (-.f64 (.f64 (PI.f64) -1/2) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 1/2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))
(.f64 1/2 (-.f64 (.f64 (PI.f64) -2) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4) (neg.f64 (PI.f64)))))
(.f64 1/2 (-.f64 (.f64 (PI.f64) -2) (+.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))))
(.f64 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) 1)
(.f64 1 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))
(.f64 (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 (PI.f64) 1/2)) -1)
(.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)) 1/2)
(.f64 -1 (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 (PI.f64) 1/2)))
(.f64 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))) 1/4)
(.f64 1/4 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))))
(.f64 (+.f64 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))) (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))) 1/8)
(/.f64 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) 1)
(/.f64 (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (*.f64 (PI.f64) 1/2)) -1)
(/.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4)) 2)
(/.f64 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))) 4)
(/.f64 (+.f64 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))) (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4)))) 8)
(pow.f64 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) 1)
(neg.f64 (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (*.f64 (PI.f64) 1/2)))

Outputs
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (neg.f64 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))) (PI.f64))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (neg.f64 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))) (PI.f64))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (neg.f64 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))) (PI.f64))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (neg.f64 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))) (PI.f64))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x)))))) (.f64 -1 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (neg.f64 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(-.f64 (-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x)))))) (.f64 -1 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (neg.f64 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(-.f64 (-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x)))))) (.f64 -1 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (neg.f64 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(-.f64 (-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x)))))) (.f64 -1 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (neg.f64 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(-.f64 (-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (neg.f64 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))) (PI.f64))
(-.f64 (+.f64 (.f64 -1 (PI.f64)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (neg.f64 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))) (PI.f64))
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(/.f64 (.f64 2 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))) 4)
(pow.f64 (+.f64 (.f64 2 (-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (.f64 (PI.f64) -1/2)) 1)
(-.f64 (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (.f64 (PI.f64) -1/2)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))))
(neg.f64 (+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))))
(+.f64 (.f64 (PI.f64) -1/2) (/.f64 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) 1/2))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(+.f64 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) 0)
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(+.f64 0 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(+.f64 (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (neg.f64 (PI.f64))) (*.f64 (PI.f64) 1/2))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (*.f64 (PI.f64) -1/2))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(+.f64 (neg.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (/.f64 (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (neg.f64 (PI.f64))) 2))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(+.f64 (.f64 (PI.f64) -1/4) (+.f64 (.f64 (PI.f64) -1/4) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(+.f64 (-.f64 (.f64 (PI.f64) -1/4) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (-.f64 (.f64 (PI.f64) -1/4) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(+.f64 (+.f64 (.f64 (PI.f64) -1/4) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (.f64 (PI.f64) -1/4))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(+.f64 (+.f64 (.f64 (PI.f64) -1/4) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) (neg.f64 (/.f64 (PI.f64) 4)))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(+.f64 (-.f64 (.f64 (PI.f64) -1/2) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(.f64 1/2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))
(.f64 1/2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))
(.f64 1/2 (-.f64 (.f64 (PI.f64) -2) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4) (neg.f64 (PI.f64)))))
(.f64 1/2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))
(.f64 1/2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))
(.f64 1/2 (-.f64 (.f64 (PI.f64) -2) (+.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))))
(.f64 1/2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))
(.f64 1/2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))
(.f64 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) 1)
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(.f64 1 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(.f64 (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 (PI.f64) 1/2)) -1)
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)) 1/2)
(.f64 1/2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))
(.f64 1/2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 (PI.f64) 1/2)))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(.f64 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))) 1/4)
(.f64 1/2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))
(.f64 1/2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))
(.f64 1/4 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))))
(.f64 1/2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))
(.f64 1/2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))
(.f64 (+.f64 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))) (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))) 1/8)
(.f64 1/2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))
(.f64 1/2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))
(/.f64 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) 1)
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(/.f64 (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (*.f64 (PI.f64) 1/2)) -1)
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(/.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4)) 2)
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(/.f64 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))) 4)
(/.f64 (.f64 2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))) 4)
(/.f64 (+.f64 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))) (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4)))) 8)
(/.f64 (.f64 2 (-.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))) 4)
(/.f64 (.f64 2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))) 4)
(pow.f64 (+.f64 (.f64 (PI.f64) -1/2) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) 1)
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))
(neg.f64 (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (*.f64 (PI.f64) 1/2)))
(-.f64 (.f64 (PI.f64) -1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 (PI.f64) -1/2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))

localize500.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))))
	0.0b	(sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))
	0.9b	(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
✓	5.7b	(+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3))

Compiler

Compiled 100 to 83 computations (17% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3))
1.0ms	x	@	inf	(+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3))
1.0ms	x	@	-inf	(+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3))
0.0ms	x	@	0	(+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))))
0.0ms	x	@	-inf	(+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))))

rewrite420.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1416×	`rational_best-4`
1416×	`rational_best-2`
1416×	`rational_best-3`
1416×	`rational_best-1`
1416×	`exponential-1`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	90
1	135	90
2	278	90
3	779	90
4	3878	70

Stop Event

1×	node limit

Counts

2 → 103

Calls

Call 1

Inputs
(+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3))
(+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))))

Outputs

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simplify562.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1276×	`rational_best-simplify-3`
1112×	`rational_best-simplify-55`
924×	`rational_best-simplify-63`
658×	`rational_best-simplify-1`
578×	`rational_best-simplify-51`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	247	6007
1	584	6007
2	1402	5609
3	5403	4755

Stop Event

1×	node limit

Counts

127 → 123

Calls

Call 1

Inputs
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(.f64 (.f64 2 (.f64 2 (+.f64 (PI.f64) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -1/4)))) 1/4)
(.f64 (.f64 2 (+.f64 (PI.f64) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -1/4))) 1/2)
(.f64 1/4 (.f64 2 (.f64 2 (+.f64 (PI.f64) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -1/4)))))
(.f64 (+.f64 (.f64 2 (.f64 2 (+.f64 (PI.f64) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -1/4)))) (.f64 2 (.f64 2 (+.f64 (PI.f64) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -1/4))))) 1/8)
(/.f64 (+.f64 (PI.f64) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -1/4)) 1)
(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4) (PI.f64)) -1)
(/.f64 (.f64 2 (.f64 2 (+.f64 (PI.f64) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -1/4)))) 4)
(/.f64 (.f64 2 (+.f64 (PI.f64) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -1/4))) 2)
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(-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -2))
(-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) (+.f64 (neg.f64 (PI.f64)) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))))
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(-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) (/.f64 (/.f64 (+.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) -1/2) 2))
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(-.f64 (+.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))))
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(.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))) 1)
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(.f64 1 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))))
(.f64 (.f64 (+.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) (/.f64 (PI.f64) 2)) 4) 1/2)
(.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -2) (PI.f64)))
(.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -2) (PI.f64)) -1)
(.f64 (.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -4) -1/4)
(.f64 (.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) 4) 1/4)
(.f64 -2 (-.f64 (neg.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (/.f64 (PI.f64) 2)))
(.f64 (.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -8) -1/8)
(.f64 (neg.f64 (.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -8)) 1/8)
(.f64 (+.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) (/.f64 (PI.f64) 2)) 2)
(.f64 (-.f64 (neg.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (/.f64 (PI.f64) 2)) -2)
(.f64 (/.f64 (.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) 4) 1/2) 1/8)
(.f64 1/4 (.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) 4))
(/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) 1)
(/.f64 (+.f64 (.f64 (PI.f64) -2) (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -1/4)) -2)
(/.f64 (.f64 (+.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) (/.f64 (PI.f64) 2)) 4) 2)
(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -2) (PI.f64)) -1)
(/.f64 (.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))) -4) -4)
(/.f64 (.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))) 4) 4)
(/.f64 (neg.f64 (.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))) -8)) 8)
(/.f64 (+.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) (/.f64 (PI.f64) 2)) 1/2)
(/.f64 (-.f64 (neg.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))) (/.f64 (PI.f64) 2)) -1/2)
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(neg.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -2) (PI.f64)))

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

localize460.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64))
✓	0.1b	(+.f64 (.f64 (PI.f64) 3) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))
	0.9b	(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
✓	58.4b	(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (+.f64 (.f64 (PI.f64) 3) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))))

Compiler

Compiled 148 to 124 computations (16.2% saved)

series22.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
15.0ms	x	@	inf	(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (+.f64 (.f64 (PI.f64) 3) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))))
3.0ms	x	@	0	(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (+.f64 (.f64 (PI.f64) 3) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))))
1.0ms	x	@	-inf	(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (+.f64 (.f64 (PI.f64) 3) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))))
1.0ms	x	@	inf	(+.f64 (.f64 (PI.f64) 3) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))
0.0ms	x	@	-inf	(+.f64 (.f64 (PI.f64) 3) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))

rewrite474.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1434×	`rational_best-simplify-56`
1178×	`rational_best-4`
1178×	`rational_best-2`
1178×	`rational_best-3`
1178×	`rational_best-1`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	165
1	124	165
2	224	165
3	618	133
4	2746	117

Stop Event

1×	node limit

Counts

3 → 190

Calls

Call 1

Inputs

(+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (+.f64 (*.f64 (PI.f64) 3) (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))))

(+.f64 (*.f64 (PI.f64) 3) (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))

(-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (*.f64 (PI.f64) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) 3) (-.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) 3) (+.f64 (-.f64 (*.f64 (PI.f64) 3) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (*.f64 (PI.f64) 2))) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)) (+.f64 (*.f64 (PI.f64) -3) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (*.f64 (PI.f64) 2)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8) (*.f64 (PI.f64) -2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8) (*.f64 (PI.f64) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (*.f64 (PI.f64) -2)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (*.f64 (PI.f64) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 (-.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8)) (*.f64 (PI.f64) -3)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (*.f64 (PI.f64) 3)) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8) (PI.f64)) (*.f64 (PI.f64) -3))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (*.f64 (PI.f64) 2)) 2) (+.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (*.f64 (PI.f64) 2)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8) (+.f64 (+.f64 (*.f64 (PI.f64) -3) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8) (*.f64 (PI.f64) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (*.f64 (PI.f64) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8) (+.f64 (+.f64 (*.f64 (PI.f64) -3) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8) (+.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (*.f64 (PI.f64) -3)) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8) (+.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (+.f64 (PI.f64) (*.f64 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simplify1.5s (2.2%)

Algorithm

1×	egg-herbie

Rules

1466×	`rational_best-simplify-48`
1430×	`rational_best-simplify-57`
1416×	`rational_best-simplify-52`
1316×	`rational_best-simplify-51`
948×	`rational_best-simplify-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	397	16384
1	1003	14124
2	2603	12778

Stop Event

1×	node limit

Counts

226 → 331

Calls

Call 1

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

Outputs
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(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -16) (*.f64 (PI.f64) 4)) 4)
(/.f64 (/.f64 (-.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -16)) -1) 4)
(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -16) (*.f64 (PI.f64) 4)) 4)
(/.f64 (/.f64 (.f64 (-.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -8)) 2) -1) 4)
(/.f64 (.f64 2 (-.f64 (.f64 (PI.f64) 2) (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) -4)
(pow.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64)) 1)
(-.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
(neg.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4)))
(-.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))

eval7.6s (10.9%)

Compiler: Compiled 32393 to 27807 computations (14.2% saved)

prune3.0s (4.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	1060	8	1068
Fresh	0	0	0
Picked	1	0	1
Done	2	3	5
Total	1063	11	1074

Error

56.3b

Counts

1074 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	58.3b	(/.f64 (/.f64 (-.f64 (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4) (+.f64 (.f64 (PI.f64) -2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 6))) 2) 2)
▶	58.3b	(/.f64 (/.f64 (-.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2)) 2) 2)
	58.3b	(/.f64 (/.f64 (+.f64 (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -1/2) (-.f64 (+.f64 (-.f64 (.f64 3 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 4)) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4)) (PI.f64))) 2) 2)
	58.3b	(/.f64 (/.f64 (+.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 4) (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -12) (*.f64 (PI.f64) -3))) 2) 2)
▶	58.3b	(/.f64 (-.f64 (-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) 2)
▶	58.4b	(/.f64 (-.f64 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64))) (+.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 (PI.f64) 0))) 2)
▶	57.3b	(/.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))) 2)
✓	57.3b	(/.f64 (+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3)) 2)
▶	60.5b	(/.f64 (+.f64 (-.f64 -1 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) (+.f64 (PI.f64) 1)) 2)
✓	58.2b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
✓	61.5b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))

Compiler

Compiled 546 to 495 computations (9.3% saved)

localize436.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))
✓	0.1b	(-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
	0.9b	(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
✓	58.5b	(-.f64 (neg.f64 (PI.f64)) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))))

Compiler

Compiled 120 to 96 computations (20% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite414.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1160×	`rational_best-4`
1160×	`rational_best-2`
1160×	`rational_best-3`
1160×	`rational_best-1`
1160×	`exponential-1`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	157
1	117	157
2	226	125
3	655	117
4	2873	103

Stop Event

1×	node limit

Counts

3 → 160

Calls

Call 1

Inputs

(-.f64 (neg.f64 (PI.f64)) (*.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))))

(-.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))

(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (PI.f64) (*.f64 2 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (PI.f64)) (-.f64 (*.f64 (PI.f64) 2) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (PI.f64)) (+.f64 1 (+.f64 -1 (-.f64 (*.f64 (PI.f64) 2) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (neg.f64 (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)) (/.f64 (*.f64 2 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 (PI.f64) 2) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)) (neg.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 (PI.f64) 2) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)) (+.f64 1 (-.f64 -1 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) (neg.f64 (+.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) (PI.f64)) (*.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (PI.f64)) (+.f64 1 (-.f64 (*.f64 (PI.f64) 2) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (-.f64 (*.f64 (PI.f64) 2) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 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(*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (-.f64 (*.f64 (PI.f64) 2) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)) (/.f64 (PI.f64) 2)) (/.f64 (PI.f64) -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (+.f64 1 (-.f64 (*.f64 (PI.f64) 2) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))) 2) (/.f64 (-.f64 (-.f64 -1 (PI.f64)) (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 1 (PI.f64)) 2) (/.f64 (-.f64 -1 (-.f64 (*.f64 2 (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (PI.f64))) (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 2 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)) 2) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 (-.f64 -1 (PI.f64)) (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (PI.f64))) 2) (/.f64 (+.f64 1 (-.f64 (*.f64 (PI.f64) 2) (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 -1 (-.f64 (*.f64 2 (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (PI.f64))) (PI.f64))) 2) (/.f64 (-.f64 1 (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (/.f64 (PI.f64) -2) (+.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) (PI.f64)) (*.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))) (-.f64 (/.f64 (PI.f64) -2) (-.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (/.f64 (PI.f64) -2) (-.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) (PI.f64))) (-.f64 (/.f64 (PI.f64) -2) (+.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) (PI.f64)) (*.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 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simplify1.2s (1.7%)

Algorithm

1×	egg-herbie

Rules

1432×	`rational_best-simplify-75`
888×	`rational_best-simplify-1`
528×	`rational_best-simplify-47`
524×	`rational_best-simplify-50`
514×	`rational_best-simplify-108`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	8928
1	707	8780
2	1653	8660
3	5531	7532

Stop Event

1×	node limit

Counts

196 → 210

Calls

Call 1

Inputs
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(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (PI.f64))) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (PI.f64))) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (PI.f64))) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))) (PI.f64)))
(.f64 -1 (+.f64 (.f64 2 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))) (PI.f64)))
(-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
(-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (PI.f64))
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(-.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (PI.f64))
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(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))
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(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))
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(+.f64 (/.f64 (+.f64 1 (-.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))) 2) (/.f64 (-.f64 (-.f64 -1 (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (PI.f64))) 2))
(+.f64 (/.f64 (-.f64 1 (PI.f64)) 2) (/.f64 (-.f64 -1 (-.f64 (.f64 2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4) (PI.f64))) (PI.f64))) 2))
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(+.f64 (/.f64 (-.f64 (-.f64 -1 (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4) (PI.f64))) 2) (/.f64 (+.f64 1 (-.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))) 2))
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(.f64 1/4 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) 4))
(.f64 (.f64 2 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4)) 1/8)
(/.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) 1)
(/.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) (PI.f64)) -1)
(/.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) 2)
(/.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) 4)
(/.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) -2) -2)
(/.f64 (neg.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4)) -4)
(/.f64 (.f64 2 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) 4)) 8)
(/.f64 (+.f64 (.f64 (PI.f64) -4) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4)) -4)
(/.f64 (.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) -2) 2) -4)
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(neg.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) (PI.f64)))

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

localize115.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
	1.0b	(asin.f64 (sqrt.f64 1/2))

Compiler

Compiled 51 to 48 computations (5.9% saved)

localize1.3s (1.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2)))))
✓	0.1b	(-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (PI.f64))
✓	0.9b	(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))
✓	58.4b	(-.f64 (-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))))

Compiler

Compiled 116 to 95 computations (18.1% saved)

series28.0ms (0%)

Counts

4 → 48

Calls

12 calls:

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

rewrite1.2s (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1410×	`rational_best-4`
1410×	`rational_best-2`
1410×	`rational_best-3`
1410×	`rational_best-1`
1410×	`exponential-1`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	168
1	111	162
2	223	142
3	676	142
4	3285	120

Stop Event

1×	node limit

Counts

4 → 193

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) (-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))) (+.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))) (-.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))) (-.f64 (neg.f64 (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) 4)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) (PI.f64)) (.f64 2 (-.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) (-.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) (/.f64 (+.f64 (neg.f64 (PI.f64)) (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)) 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) 4)) (neg.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (neg.f64 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) (PI.f64))) (-.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) 4) (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)) 2) (+.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2) (/.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)) 2) (-.f64 (/.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) -2)) 2) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) 4)) 2) (/.f64 (-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) 4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) (PI.f64))) (+.f64 1 (.f64 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simplify907.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

902×	`rational_best-simplify-50`
776×	`rational_best-simplify-48`
750×	`rational_best-simplify-52`
710×	`rational_best-simplify-64`
694×	`rational_best-simplify-57`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	11479
1	712	10209
2	1970	8695

Stop Event

1×	node limit

Counts

241 → 235

Calls

Call 1

Inputs
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(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) 4) (*.f64 (PI.f64) 4)) -4)
(/.f64 (.f64 -1 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2)))) 4)) -4)
(/.f64 (/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) 4) (*.f64 (PI.f64) 4)) -1) 4)
(/.f64 (/.f64 (.f64 -1 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2)))) 4)) -1) 4)
(pow.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2)))) 1)
(neg.f64 (-.f64 (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2))) (PI.f64)))

Outputs
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(-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x)))))) (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x)))))))
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(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(.f64 -1 (-.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) (PI.f64)))
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(.f64 1/4 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2)))) 4))
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2)))) 8) 1/8)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(.f64 (.f64 2 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) 8)) 1/16)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2)))) 1)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))) 2)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (-.f64 (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2))) (PI.f64)) -1)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) 4) 4)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) (PI.f64))) -2)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) 8) 8)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (.f64 2 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2)))) 8)) 16)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) 4) (*.f64 (PI.f64) 4)) -4)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (.f64 -1 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2)))) 4)) -4)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))) 4) (*.f64 (PI.f64) 4)) -1) 4)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(/.f64 (/.f64 (.f64 -1 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2)))) 4)) -1) 4)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(pow.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2)))) 1)
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))
(neg.f64 (-.f64 (asin.f64 (sqrt.f64 (-.f64 (*.f64 x -1/2) -1/2))) (PI.f64)))
(-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))))

localize533.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) 4))
✓	0.1b	(+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) 4)))
✓	0.9b	(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
✓	58.4b	(-.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2))

Compiler

Compiled 222 to 195 computations (12.2% saved)

series10.0ms (0%)

Counts

4 → 44

Calls

12 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	(-.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2))
1.0ms	x	@	inf	(-.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2))
1.0ms	x	@	-inf	(-.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2))
0.0ms	x	@	-inf	(+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) 4)))
0.0ms	x	@	inf	(+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) 4)))

rewrite441.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1498×	`rational_best-4`
1498×	`rational_best-2`
1498×	`rational_best-3`
1498×	`rational_best-1`
1498×	`exponential-1`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	258
1	162	258
2	296	258
3	833	188
4	3653	138

Stop Event

1×	node limit

Counts

4 → 156

Calls

Call 1

Inputs
(-.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2))
(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))
(+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) 4)))
(+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))) 4))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 (PI.f64) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2) (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6)) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 (PI.f64) 2)) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 1/4) (/.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2) (+.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -12))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 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(+.f64 1/2 (.f64 -1/2 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64))))))))

simplify683.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1192×	`rational_best-simplify-48`
1188×	`rational_best-simplify-52`
920×	`rational_best-simplify-57`
876×	`rational_best-simplify-51`
752×	`rational_best-simplify-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	307	9718
1	729	9656
2	2086	7814

Stop Event

1×	node limit

Counts

200 → 195

Calls

Call 1

Inputs
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
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(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (*.f64 (PI.f64) 2)))
(+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) -8))
(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (*.f64 (PI.f64) 2))
(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2) (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) -6)))
(+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6))
(+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6)) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) -2))
(+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) -8)) 0)
(+.f64 0 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) -8)))
(+.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 (PI.f64) 2)) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6) (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(+.f64 (.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 1/4) (/.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2) (+.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -12))) 2))
(+.f64 (.f64 1/2 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6)) (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -5)))
(+.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -5)) (.f64 1/2 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6)))
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(.f64 (+.f64 (.f64 2 (+.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -12))) (.f64 2 (+.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) -12)))) 1/8)
(/.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) -6)) 1)
(/.f64 (+.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) -12)) 2)
(/.f64 (+.f64 (.f64 (PI.f64) -2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 6)) -1)
(/.f64 (.f64 2 (+.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -12))) 4)
(/.f64 (+.f64 (.f64 2 (+.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -12))) (.f64 2 (+.f64 (.f64 (PI.f64) 4) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -12)))) 8)
(pow.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) -6)) 1)
(neg.f64 (+.f64 (.f64 (PI.f64) -2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 6)))
(neg.f64 (-.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(-.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2) (*.f64 (PI.f64) -2)))
(-.f64 (PI.f64) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 2) (neg.f64 (PI.f64))))
(-.f64 (PI.f64) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 2) (PI.f64)))
(-.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2))
(-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2) (*.f64 (PI.f64) -2))
(-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))) 0)
(-.f64 0 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64))))
(-.f64 (.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 1/4) (+.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (*.f64 (PI.f64) -2)))
(-.f64 (.f64 (PI.f64) 4) (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 2)))
(-.f64 (-.f64 (.f64 (PI.f64) 2) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))
(-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64)))
(-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (/.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) (PI.f64))) 2))
(-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (-.f64 (neg.f64 (PI.f64)) (.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 1/4)))
(-.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2)) (neg.f64 (PI.f64)))
(-.f64 (-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 2)) (neg.f64 (PI.f64)))
(-.f64 (-.f64 (.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 1/4) (.f64 (PI.f64) -2)) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))
(.f64 1/2 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 (PI.f64) 4)))
(.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))) 1)
(.f64 1 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) (PI.f64))) -1)
(.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 (PI.f64) 4)) 1/2)
(.f64 1/4 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (*.f64 (PI.f64) 4))))
(.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (*.f64 (PI.f64) 4))) 1/4)
(.f64 (+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (.f64 (PI.f64) 4))) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (*.f64 (PI.f64) 4)))) 1/8)
(/.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))) 1)
(/.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64))) -1)
(/.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (*.f64 (PI.f64) 4)) 2)
(/.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (.f64 (PI.f64) 4))) 4)
(/.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) (PI.f64)) -1/2)
(/.f64 (+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (.f64 (PI.f64) 4))) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (.f64 (PI.f64) 4)))) 8)
(/.f64 (neg.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) (PI.f64))) 1/2)
(pow.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))) 1)
(neg.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64))))

Outputs
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -6)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -6)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -6)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -6)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))) -6) (.f64 2 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))))
(-.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))) -6) (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))) (*.f64 (PI.f64) -2)))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))) -6) (.f64 2 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))))
(-.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))) -6) (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))) (*.f64 (PI.f64) -2)))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))) -6) (.f64 2 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))))
(-.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))) -6) (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))) (*.f64 (PI.f64) -2)))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))))
(-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))) -6) (.f64 2 (PI.f64))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))))
(-.f64 (.f64 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))) -6) (+.f64 (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2))))) (*.f64 (PI.f64) -2)))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
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(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -6)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -6)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8))
(-.f64 (+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x))))))
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(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -8))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
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(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
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(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 x 1/2))))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -6))
(-.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 6))
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(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -6))
(-.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 6))
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(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -6))
(-.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 6))
(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -6))
(-.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 6))
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(+.f64 (.f64 2 (PI.f64)) (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -6))
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(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -6))
(-.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 6))
(neg.f64 (-.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -6))
(-.f64 (.f64 2 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 6))
(-.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2) (*.f64 (PI.f64) -2)))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (PI.f64) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 2) (neg.f64 (PI.f64))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (PI.f64) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 2) (PI.f64)))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2) (*.f64 (PI.f64) -2))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))) 0)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 0 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 1/4) (+.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (*.f64 (PI.f64) -2)))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (.f64 (PI.f64) 4) (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 2)))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (-.f64 (.f64 (PI.f64) 2) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64)))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (/.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) (PI.f64))) 2))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (-.f64 (neg.f64 (PI.f64)) (.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 1/4)))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -2)) (neg.f64 (PI.f64)))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 2)) (neg.f64 (PI.f64)))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(-.f64 (-.f64 (.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 1/4) (.f64 (PI.f64) -2)) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(.f64 1/2 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 (PI.f64) 4)))
(.f64 1/2 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 (PI.f64) 4)))
(.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))) 1)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(.f64 1 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) (PI.f64))) -1)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (.f64 (PI.f64) 4)) 1/2)
(.f64 1/2 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 (PI.f64) 4)))
(.f64 1/4 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (*.f64 (PI.f64) 4))))
(.f64 1/4 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -8) (.f64 2 (*.f64 (PI.f64) 4))))
(.f64 1/4 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -8) (.f64 (PI.f64) 8)))
(.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (*.f64 (PI.f64) 4))) 1/4)
(.f64 1/4 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -8) (.f64 2 (*.f64 (PI.f64) 4))))
(.f64 1/4 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -8) (.f64 (PI.f64) 8)))
(.f64 (+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (.f64 (PI.f64) 4))) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (*.f64 (PI.f64) 4)))) 1/8)
(.f64 1/8 (+.f64 (.f64 2 (.f64 (PI.f64) 4)) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -8) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -8) (.f64 2 (*.f64 (PI.f64) 4))))))
(.f64 1/8 (+.f64 (.f64 (PI.f64) 8) (+.f64 (.f64 (PI.f64) 8) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -16))))
(.f64 1/8 (+.f64 (.f64 (PI.f64) 8) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -16) (*.f64 (PI.f64) 8))))
(/.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))) 1)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(/.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64))) -1)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(/.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (*.f64 (PI.f64) 4)) 2)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(/.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (.f64 (PI.f64) 4))) 4)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(/.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) (PI.f64)) -1/2)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(/.f64 (+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (.f64 (PI.f64) 4))) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -8) (.f64 2 (.f64 (PI.f64) 4)))) 8)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(/.f64 (neg.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) (PI.f64))) 1/2)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(pow.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))))) 1)
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))
(neg.f64 (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) (PI.f64))))
(+.f64 (.f64 2 (PI.f64)) (.f64 -2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))
(.f64 -2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)))

localize749.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))
✓	0.1b	(+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64)))
	0.9b	(asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))
✓	58.5b	(-.f64 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64))) (+.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 (PI.f64) 0)))

Compiler

Compiled 230 to 191 computations (17% saved)

series10.0ms (0%)

Counts

3 → 32

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(-.f64 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64))) (+.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 (PI.f64) 0)))
2.0ms	x	@	-inf	(-.f64 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64))) (+.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 (PI.f64) 0)))
1.0ms	x	@	inf	(-.f64 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64))) (+.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 (PI.f64) 0)))
0.0ms	x	@	0	(+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64)))
0.0ms	x	@	inf	(+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64)))

rewrite617.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1524×	`rational_best-simplify-97`
1182×	`rational_best-simplify-86`
916×	`rational_best-simplify-62`
642×	`rational_best-simplify-55`
386×	`rational_best-simplify-1`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	245
1	178	231
2	336	231
3	918	231
4	4894	145

Stop Event

1×	node limit

Counts

3 → 197

Calls

Call 1

Inputs

(-.f64 (+.f64 (*.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) 4) (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64))) (+.f64 (*.f64 2 (-.f64 (PI.f64) (*.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))) (*.f64 (PI.f64) 0)))

(+.f64 (*.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))) 4) (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))

(-.f64 (PI.f64) (*.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))

Outputs

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simplify3.0s (4.3%)

Algorithm

1×	egg-herbie

Rules

1322×	`rational_best-simplify-57`
994×	`rational_best-simplify-51`
898×	`rational_best-simplify-52`
780×	`rational_best-simplify-48`
686×	`rational_best-simplify-59`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	489	20439
1	1140	19975
2	2845	18415

Stop Event

1×	node limit

Counts

229 → 434

Calls

Call 1

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

Outputs
(-.f64 (+.f64 (.f64 4 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (+.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))) (PI.f64)))
(-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (.f64 4 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (+.f64 (PI.f64) (.f64 2 (-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 2)))))
(-.f64 (.f64 4 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (.f64 2 (-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2))) (-.f64 (/.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -1/4) (PI.f64))))
(-.f64 (+.f64 (.f64 4 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (+.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))) (PI.f64)))
(-.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (.f64 4 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (+.f64 (PI.f64) (.f64 2 (-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 2)))))
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(+.f64 (-.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2) (PI.f64))) 1)
(-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2))
(+.f64 (-.f64 -1 (+.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4) (PI.f64)))) (-.f64 1 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))))
(+.f64 (-.f64 1 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))) (-.f64 -1 (+.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (PI.f64)))))
(+.f64 (-.f64 1 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))) (-.f64 -1 (-.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (+.f64 (PI.f64) (PI.f64)))))
(+.f64 (-.f64 (PI.f64) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 -2 (+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2) -1) -1)))
(+.f64 (-.f64 -1 (-.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2) (PI.f64)) (/.f64 (PI.f64) 2))) (-.f64 1 (/.f64 (PI.f64) 2)))
(+.f64 (-.f64 1 (/.f64 (PI.f64) 2)) (-.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2) (+.f64 (/.f64 (PI.f64) 2) (PI.f64)))))
(-.f64 2 (+.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2) (+.f64 -1 (PI.f64))) 1))
(+.f64 (-.f64 2 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2) (+.f64 (PI.f64) -1))) -1)
(+.f64 (-.f64 -1 (+.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2) (PI.f64)))) (-.f64 1 (PI.f64)))
(+.f64 (-.f64 1 (PI.f64)) (-.f64 -1 (+.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2) (PI.f64)))))
(+.f64 (-.f64 1 (PI.f64)) (-.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2) (+.f64 (PI.f64) (PI.f64)))))
(+.f64 (-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2)) (+.f64 (+.f64 (PI.f64) -1) (-.f64 1 (PI.f64))))
(.f64 1/2 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4)))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(.f64 1/2 (-.f64 (.f64 4 (PI.f64)) (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 4))))
(.f64 1/2 (-.f64 (.f64 4 (PI.f64)) (+.f64 (.f64 (PI.f64) 2) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2)))))))
(.f64 1/2 (+.f64 (.f64 (PI.f64) 2) (neg.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))))
(.f64 1/2 (+.f64 (.f64 (PI.f64) 2) (/.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -1/4)))
(.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)) 1)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4)) 1/2)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(.f64 1 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(.f64 (+.f64 (.f64 (PI.f64) -2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4)) -1/2)
(.f64 -1/2 (+.f64 (.f64 (PI.f64) -2) (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))
(.f64 -1/2 (+.f64 (.f64 4 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) (.f64 (PI.f64) -2)))
(.f64 -1 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 2) (PI.f64)))
(-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2))
(.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) 2) (PI.f64)) -1)
(-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2))
(.f64 (.f64 4 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))) 1/4)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(.f64 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2)) 8) 1/8)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(.f64 (/.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)) -1/4) -1/4)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(.f64 1/4 (.f64 4 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))))
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(.f64 (+.f64 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2)) 8) (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)) 8)) 1/16)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(/.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2)) 1)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(/.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4)) 2)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(/.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2) (PI.f64)) -1)
(-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2))
(/.f64 (.f64 4 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2))) 4)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(/.f64 (.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -2)) 8) 8)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(pow.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2)) 1)
(+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2))
(neg.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2) (PI.f64)))
(-.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2))

eval7.4s (10.6%)

Compiler: Compiled 48035 to 41258 computations (14.1% saved)

prune2.6s (3.8%)

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	1343	6	1349
Fresh	2	1	3
Picked	1	0	1
Done	2	5	7
Total	1348	12	1360

Error

56.3b

Counts

1360 → 12

Alt Table

Click to see full alt table

Status	Error	Program
	58.3b	(/.f64 (/.f64 (-.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6) (.f64 (PI.f64) -2)) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2)) 2) 2)
	58.3b	(/.f64 (/.f64 (+.f64 (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -1/2) (-.f64 (+.f64 (-.f64 (.f64 3 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 4)) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4)) (PI.f64))) 2) 2)
	58.3b	(/.f64 (-.f64 (+.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) (neg.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) 2)
✓	57.3b	(/.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))) 2)
✓	57.3b	(/.f64 (+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3)) 2)
	58.3b	(/.f64 (+.f64 (-.f64 (.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)) -2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2)) 2)
	58.3b	(/.f64 (+.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (PI.f64)) (.f64 2 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -3)))) 2)
✓	60.5b	(/.f64 (+.f64 (-.f64 -1 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) (+.f64 (PI.f64) 1)) 2)
	58.3b	(/.f64 (+.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2)) (/.f64 (+.f64 1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) -1)) 2)) 2)
	58.3b	(/.f64 (+.f64 (neg.f64 (+.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) 2)
✓	58.2b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
✓	61.5b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))

Compiler

Compiled 310 to 283 computations (8.7% saved)

regimes280.0ms (0.4%)

Counts

21 → 1

Calls

Call 1

Inputs
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
(/.f64 (+.f64 (-.f64 -1 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) (+.f64 (PI.f64) 1)) 2)
(/.f64 (+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1)) 2)
(/.f64 (-.f64 (.f64 (PI.f64) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4))) 2)
(/.f64 (+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3)) 2)
(/.f64 (/.f64 (-.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6) (.f64 (PI.f64) -2)) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2)) 2) 2)
(/.f64 (+.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2)) (/.f64 (+.f64 1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) -1)) 2)) 2)
(/.f64 (/.f64 (-.f64 (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4) (+.f64 (.f64 (PI.f64) -2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 6))) 2) 2)
(/.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))) 2)
(/.f64 (-.f64 (-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) 2)
(/.f64 (+.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (PI.f64)) (.f64 2 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -3)))) 2)
(/.f64 (/.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (+.f64 (.f64 (PI.f64) 3) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))) 2) 2)
(/.f64 (/.f64 (+.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 4) (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -12) (*.f64 (PI.f64) -3))) 2) 2)
(/.f64 (-.f64 (+.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) (neg.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) 2)
(/.f64 (+.f64 (neg.f64 (+.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) 2)
(/.f64 (+.f64 (/.f64 (PI.f64) -2) (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))) 2)
(/.f64 (/.f64 (-.f64 (+.f64 (.f64 -4 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) (+.f64 (.f64 (PI.f64) 2) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2)) 2) 2)
(/.f64 (+.f64 (-.f64 (.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)) -2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 4))) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) 2)) 2)
(/.f64 (/.f64 (+.f64 (/.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -1/2) (-.f64 (+.f64 (-.f64 (.f64 3 (PI.f64)) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 4)) (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4)) (PI.f64))) 2) 2)
(/.f64 (-.f64 (+.f64 (.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))) 4) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (PI.f64))) (+.f64 (.f64 2 (-.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (.f64 (PI.f64) 0))) 2)

Outputs

(/.f64 (+.f64 (/.f64 (PI.f64) -2) (+.f64 (*.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (*.f64 2 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))) 2)

Calls

7 calls:

83.0ms	x
45.0ms	(-.f64 1 x)
31.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))
28.0ms	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
7.0ms	(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))

Results

Error	Segments	Branch
57.3b	1	`x`
57.3b	1	`(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))`
57.3b	1	`(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))`
57.3b	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))`
57.3b	1	`(sqrt.f64 (/.f64 (-.f64 1 x) 2))`
57.3b	1	`(/.f64 (-.f64 1 x) 2)`
57.3b	1	`(-.f64 1 x)`

Compiler

Compiled 609 to 528 computations (13.3% saved)

regimes217.0ms (0.3%)

Counts

16 → 1

Calls

Call 1

Inputs
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
(/.f64 (+.f64 (-.f64 -1 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) (+.f64 (PI.f64) 1)) 2)
(/.f64 (+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1)) 2)
(/.f64 (-.f64 (.f64 (PI.f64) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4))) 2)
(/.f64 (+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3)) 2)
(/.f64 (/.f64 (-.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6) (.f64 (PI.f64) -2)) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2)) 2) 2)
(/.f64 (+.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2)) (/.f64 (+.f64 1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) -1)) 2)) 2)
(/.f64 (/.f64 (-.f64 (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4) (+.f64 (.f64 (PI.f64) -2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 6))) 2) 2)
(/.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))) 2)
(/.f64 (-.f64 (-.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) 2)
(/.f64 (+.f64 (-.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (PI.f64)) (.f64 2 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -3)))) 2)
(/.f64 (/.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) (+.f64 (.f64 (PI.f64) 3) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))) -4) (PI.f64)))) 2) 2)
(/.f64 (/.f64 (+.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) 4) (PI.f64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -12) (*.f64 (PI.f64) -3))) 2) 2)
(/.f64 (-.f64 (+.f64 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2)))) (neg.f64 (asin.f64 (sqrt.f64 (-.f64 (.f64 x -1/2) -1/2))))) (.f64 2 (asin.f64 (sqrt.f64 (-.f64 1/2 (.f64 x 1/2)))))) 2)
(/.f64 (+.f64 (neg.f64 (+.f64 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (PI.f64)) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2)))))) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) 2)

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

Calls

7 calls:

67.0ms	x
42.0ms	(-.f64 1 x)
33.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))
31.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) 2))
6.0ms	(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))

Results

Error	Segments	Branch
57.3b	1	`x`
57.3b	1	`(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))`
57.3b	1	`(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))`
57.3b	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))`
57.3b	1	`(sqrt.f64 (/.f64 (-.f64 1 x) 2))`
57.3b	1	`(/.f64 (-.f64 1 x) 2)`
57.3b	1	`(-.f64 1 x)`

Compiler

Compiled 420 to 365 computations (13.1% saved)

regimes121.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

Inputs
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
(/.f64 (+.f64 (-.f64 -1 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) (+.f64 (PI.f64) 1)) 2)
(/.f64 (+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1)) 2)
(/.f64 (-.f64 (.f64 (PI.f64) 2) (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (/.f64 x -2)))) 4))) 2)
(/.f64 (+.f64 (/.f64 (+.f64 (PI.f64) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) -1/2) (*.f64 (PI.f64) 3)) 2)
(/.f64 (/.f64 (-.f64 (-.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x)))) -6) (.f64 (PI.f64) -2)) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 2)) 2) 2)
(/.f64 (+.f64 (+.f64 (PI.f64) (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -2)) (/.f64 (+.f64 1 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) -4) -1)) 2)) 2)
(/.f64 (/.f64 (-.f64 (/.f64 (.f64 -8 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 -1/2 x))))) 4) (+.f64 (.f64 (PI.f64) -2) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 -1/2 x)))) 6))) 2) 2)

Outputs
(/.f64 (+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1)) 2)

Calls

7 calls:

41.0ms	x
13.0ms	(/.f64 (-.f64 1 x) 2)
5.0ms	(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))
5.0ms	(-.f64 1 x)
5.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) 2))

Results

Error	Segments	Branch
57.3b	1	`x`
57.3b	1	`(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))`
57.3b	1	`(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))`
57.3b	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))`
57.3b	1	`(sqrt.f64 (/.f64 (-.f64 1 x) 2))`
57.3b	1	`(/.f64 (-.f64 1 x) 2)`
57.3b	1	`(-.f64 1 x)`

Compiler

Compiled 225 to 198 computations (12% saved)

regimes189.0ms (0.3%)

Counts

3 → 3

Calls

Call 1

Inputs

(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))

(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))

(/.f64 (+.f64 (-.f64 -1 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) (+.f64 (PI.f64) 1)) 2)

Outputs

(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))

(/.f64 (+.f64 (-.f64 -1 (*.f64 (asin.f64 (sqrt.f64 1/2)) 4)) (+.f64 (PI.f64) 1)) 2)

(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))

Calls

7 calls:

69.0ms	x
32.0ms	(/.f64 (-.f64 1 x) 2)
29.0ms	(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))
21.0ms	(-.f64 1 x)
20.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) 2))

Results

Error	Segments	Branch
56.8b	3	`x`
58.2b	1	`(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))`
57.2b	3	`(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))`
57.2b	3	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))`
57.2b	3	`(sqrt.f64 (/.f64 (-.f64 1 x) 2))`
57.2b	3	`(/.f64 (-.f64 1 x) 2)`
57.2b	3	`(-.f64 1 x)`

Compiler

Compiled 87 to 77 computations (11.5% saved)

bsearch427.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
74.0ms	1.0576460330827338e-18	6.480003776551802e-14
353.0ms	-7.978761333065063e-160	-1.709897498714331e-166

Results

309.0ms	144×	body	1024	valid
56.0ms	128×	body	256	valid

Compiler

Compiled 528 to 509 computations (3.6% saved)

regimes80.0ms (0.1%)

Accuracy

Total -3.3b remaining (-5.6%)

Threshold costs -3.3b (-5.6%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))

Calls

7 calls:

22.0ms	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
20.0ms	(-.f64 1 x)
19.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) 2))
6.0ms	x
4.0ms	(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))

Results

Error	Segments	Branch
58.2b	1	`x`
58.2b	1	`(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))`
58.2b	1	`(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))`
58.2b	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))`
58.2b	1	`(sqrt.f64 (/.f64 (-.f64 1 x) 2))`
58.2b	1	`(/.f64 (-.f64 1 x) 2)`
58.2b	1	`(-.f64 1 x)`

Compiler

Compiled 74 to 65 computations (12.2% saved)

simplify28.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	444

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (+.f64 (/.f64 (PI.f64) -2) (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))) 2)
(/.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))) 2)
(/.f64 (+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1)) 2)
(if (<=.f64 x -3444422103075043/2026130648867672343023636652192949780767796011837127392576004555513014068072709055859231957493703024554784124321924213467966382361040905912054138102594708831572842677442143322112) (-.f64 (/.f64 (PI.f64) 2) (.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))) (if (<=.f64 x 8924260225606735/162259276829213363391578010288128) (/.f64 (+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 1/2)) 4)) (+.f64 (PI.f64) 1)) 2) (-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))))
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))

Outputs
(/.f64 (+.f64 (/.f64 (PI.f64) -2) (+.f64 (.f64 2 (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))) (-.f64 (/.f64 (PI.f64) -2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))))))) 2)
(/.f64 (-.f64 (neg.f64 (PI.f64)) (.f64 2 (-.f64 (asin.f64 (sqrt.f64 (+.f64 (.f64 -1/2 x) 1/2))) (-.f64 (PI.f64) (asin.f64 (sqrt.f64 (+.f64 (*.f64 -1/2 x) 1/2))))))) 2)
(/.f64 (+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) 4)) (+.f64 (PI.f64) 1)) 2)
(if (<=.f64 x -3444422103075043/2026130648867672343023636652192949780767796011837127392576004555513014068072709055859231957493703024554784124321924213467966382361040905912054138102594708831572842677442143322112) (-.f64 (/.f64 (PI.f64) 2) (.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))) (if (<=.f64 x 8924260225606735/162259276829213363391578010288128) (/.f64 (+.f64 (-.f64 -1 (.f64 (asin.f64 (sqrt.f64 1/2)) 4)) (+.f64 (PI.f64) 1)) 2) (-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))))
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 1/2))))

Compiler

Compiled 147 to 132 computations (10.2% saved)

soundness0.0ms (0%)

end637.0ms (0.9%)

Compiler: Compiled 142 to 122 computations (14.1% saved)

Details

analyze8.0ms (0%)

sample22.8s (32.6%)

preprocess311.0ms (0.4%)

simplify418.0ms (0.6%)

eval1.0ms (0%)

prune2.0ms (0%)

localize140.0ms (0.2%)

series6.0ms (0%)

rewrite321.0ms (0.5%)

simplify411.0ms (0.6%)

eval412.0ms (0.6%)

prune201.0ms (0.3%)

localize112.0ms (0.2%)

series0.0ms (0%)

rewrite567.0ms (0.8%)

simplify457.0ms (0.7%)

localize227.0ms (0.3%)

series75.0ms (0.1%)

rewrite509.0ms (0.7%)

simplify789.0ms (1.1%)

eval627.0ms (0.9%)

prune228.0ms (0.3%)

localize231.0ms (0.3%)

series3.0ms (0%)

rewrite254.0ms (0.4%)

simplify466.0ms (0.7%)

localize434.0ms (0.6%)

series32.0ms (0%)

rewrite655.0ms (0.9%)

simplify862.0ms (1.2%)

localize500.0ms (0.7%)

series4.0ms (0%)

rewrite420.0ms (0.6%)

simplify562.0ms (0.8%)

localize460.0ms (0.7%)

series22.0ms (0%)

rewrite474.0ms (0.7%)

simplify1.5s (2.2%)

eval7.6s (10.9%)

prune3.0s (4.4%)

localize436.0ms (0.6%)

series3.0ms (0%)

rewrite414.0ms (0.6%)

simplify1.2s (1.7%)

localize115.0ms (0.2%)

localize1.3s (1.9%)

series28.0ms (0%)

rewrite1.2s (1.8%)

simplify907.0ms (1.3%)

localize533.0ms (0.8%)

series10.0ms (0%)

rewrite441.0ms (0.6%)

simplify683.0ms (1%)

localize749.0ms (1.1%)

series10.0ms (0%)

rewrite617.0ms (0.9%)

simplify3.0s (4.3%)

eval7.4s (10.6%)

prune2.6s (3.8%)

regimes280.0ms (0.4%)

regimes217.0ms (0.3%)

regimes121.0ms (0.2%)

regimes189.0ms (0.3%)

bsearch427.0ms (0.6%)

regimes80.0ms (0.1%)

simplify28.0ms (0%)

soundness0.0ms (0%)

end637.0ms (0.9%)

Profiling