Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	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)

sample4.8s (56%)

Results

3.0s	4199×	body	1024	valid
953.0ms	2025×	body	512	valid
512.0ms	440×	body	2048	valid
324.0ms	1592×	body	256	valid
1.0ms	5×	body	256	invalid

Bogosity

preprocess4.0ms (0%)

Algorithm

2×	egg-herbie

Rules

2×	`rational_best-simplify-2`
2×	`rational_best-simplify-53`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	20	41
0	1	1

Stop Event

1×	saturated
1×	saturated

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)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`rational_best-simplify-2`
2×	`rational_best-simplify-53`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	20	41

Stop Event

1×

saturated

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)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

60.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	60.0b	(-.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)

localize27.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))
✓	5.5b	(-.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)

series2.0ms (0%)

Counts

2 → 24

Calls

6 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)))))
0.0ms	x	@	inf	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
0.0ms	x	@	-inf	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
0.0ms	x	@	-inf	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))
0.0ms	x	@	0	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))

rewrite138.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1554×	`rational_best-4`
1554×	`rational_best-2`
1554×	`rational_best-3`
1554×	`rational_best-1`
1188×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	62
1	96	62
2	152	62
3	206	62
4	328	62
5	566	62
6	1027	62
7	2116	62
8	3539	62
9	5036	62
10	7301	62

Stop Event

1×	node limit

Counts

2 → 161

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)))

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

simplify595.0ms (7%)

Algorithm

1×	egg-herbie

Rules

1884×	`rational_best-simplify-1`
1530×	`rational_best-simplify-2`
1044×	`rational_best-simplify-47`
988×	`rational_best-simplify-43`
960×	`rational_best-simplify-46`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	459	14925
1	1003	13679
2	2251	12749
3	2865	12121
4	4061	11597
5	4329	11597
6	4570	11597
7	4787	11537
8	5588	11537
9	5919	11497
10	7277	11493

Stop Event

1×	node limit

Counts

185 → 279

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

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

eval361.0ms (4.2%)

Compiler: Compiled 11169 to 9495 computations (15% saved)

prune202.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	276	3	279
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	276	4	280

Error

58.2b

Counts

280 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	60.0b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
▶	59.1b	(+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -2) (*.f64 (PI.f64) -1/2)) (PI.f64))
▶	60.0b	(+.f64 (+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4))
▶	60.0b	(+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (+.f64 (.f64 (PI.f64) 3/2) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4) (neg.f64 (PI.f64)))))

Compiler

Compiled 81 to 73 computations (9.9% saved)

localize52.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -4) (neg.f64 (PI.f64)))
✓	0.0b	(+.f64 (.f64 (PI.f64) 3/2) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4) (neg.f64 (PI.f64))))
✓	1.0b	(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
✓	60.3b	(+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (+.f64 (.f64 (PI.f64) 3/2) (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4) (neg.f64 (PI.f64)))))

Compiler

Compiled 106 to 85 computations (19.8% saved)

series4.0ms (0%)

Counts

4 → 48

Calls

12 calls:

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

rewrite98.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

88×	`rational_best-simplify-1`
64×	`rational_best-simplify-2`
54×	`rational_best-4`
54×	`rational_best-2`
54×	`rational_best-3`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	198
1	150	198
2	225	174
3	266	142
4	312	142
5	332	142
6	333	142

Stop Event

1×

saturated

Counts

4 → 22

Calls

Call 1

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

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

simplify221.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

46×	`rational_best-simplify-1`
42×	`rational_best-simplify-2`
14×	`rational_best-simplify-43`
8×	`rational_best-simplify-5`
8×	`rational_best-simplify-4`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	81	2984
1	120	2600
2	142	2600
3	155	2600
4	158	2600

Stop Event

1×

saturated

Counts

70 → 41

Calls

Call 1

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

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

localize46.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))))
	1.0b	(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
✓	5.5b	(+.f64 (+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4))

New

Error

Program

✓

0.0b

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

1.0b

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

✓

5.5b

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

Compiler

Compiled 85 to 72 computations (15.3% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite16.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

44×	`rational_best-simplify-2`
44×	`rational_best-simplify-1`
34×	`rational_best-4`
34×	`rational_best-2`
34×	`rational_best-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	114
1	123	114
2	167	82
3	191	82
4	200	82
5	201	82

Stop Event

1×

saturated

Counts

2 → 10

Calls

Call 1

Inputs

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

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

Outputs

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

((#(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 -1/2)))))) 0)))) (#(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 -1/2)))))) 1)))) (#(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 -1/2)))))))))) (#(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 -1/2)))))) 1)))) (#(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 -1/2)))))) 1)))))

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

34×	`rational_best-simplify-1`
28×	`rational_best-simplify-2`
10×	`rational_best-simplify-43`
4×	`rational_best-simplify-5`
4×	`rational_best-simplify-4`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	1938
1	97	1394
2	108	1394
3	111	1394

Stop Event

1×

saturated

Counts

34 → 22

Calls

Call 1

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

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

localize34.0ms (0.4%)

Local error

Found 3 expressions with local error:

New

Error

Program

✓

0.0b

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

1.0b

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

✓

5.5b

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

Compiler

Compiled 67 to 55 computations (17.9% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite15.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

42×	`rational_best-simplify-1`
40×	`rational_best-simplify-2`
32×	`rational_best-4`
32×	`rational_best-2`
32×	`rational_best-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	90
1	110	90
2	152	82
3	173	82
4	177	82
5	178	82

Stop Event

1×

saturated

Counts

2 → 10

Calls

Call 1

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

Outputs

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

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

simplify25.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

32×	`rational_best-simplify-1`
20×	`rational_best-simplify-2`
12×	`rational_best-simplify-43`
4×	`rational_best-simplify-5`
4×	`rational_best-simplify-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	1490
1	73	1490
2	84	1490
3	86	1490

Stop Event

1×

saturated

Counts

34 → 18

Calls

Call 1

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

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

eval54.0ms (0.6%)

Compiler: Compiled 2642 to 2237 computations (15.3% saved)

prune22.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	121	4	125

Error

58.2b

Counts

125 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	60.0b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
✓	59.1b	(+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -2) (*.f64 (PI.f64) -1/2)) (PI.f64))
✓	60.0b	(+.f64 (+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4))
▶	60.0b	(+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (+.f64 (.f64 (PI.f64) 3/2) (-.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64))))

Compiler

Compiled 80 to 72 computations (10% saved)

localize161.0ms (1.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (PI.f64) 3/2) (-.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64)))
	1.0b	(asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2))))
✓	1.0b	(asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))
✓	60.3b	(+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (+.f64 (.f64 (PI.f64) 3/2) (-.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64))))

Compiler

Compiled 122 to 101 computations (17.2% saved)

series1.0ms (0%)

Counts

3 → 28

Calls

9 calls:

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

rewrite321.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1454×	`rational_best-4`
1454×	`rational_best-2`
1454×	`rational_best-3`
1454×	`rational_best-1`
1454×	`exponential-1`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	25	151
1	162	151
2	232	151
3	296	151
4	401	151
5	631	135
6	1079	103
7	1935	103
8	3384	103
9	4794	103
10	6308	103

Stop Event

1×	node limit

Counts

3 → 49

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

simplify1.2s (14.2%)

Algorithm

1×	egg-herbie

Rules

30176×	`rational_best-simplify-43`
2598×	`rational_best-simplify-1`
1572×	`rational_best-simplify-2`
1396×	`rational_best-simplify-51`
436×	`rational_best-simplify-44`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	115	4137
1	165	3377
2	213	3377
3	273	3377
4	323	3377
5	427	3217
6	583	3217
7	930	3217
8	1266	3217
9	1632	3217
10	1967	3217
11	2133	3217
12	2191	3217
13	2236	3217
14	2266	3217
15	2424	3217
16	2546	3217
17	2602	3217
18	2637	3217
19	2681	3217
20	2719	3217
21	2747	3217
22	2771	3217
23	4683	3217
24	4687	3217
25	4689	3217
26	4689	3217
27	5571	3217
28	5669	3217
29	5669	3217
30	6174	3217
31	6512	3217
32	6539	3217
33	6577	3217
34	6593	3217
35	6601	3217
36	6619	3217
37	6627	3217
38	6627	3217
39	6627	3217
40	6638	3217
41	6701	3217
42	6740	3217
43	6740	3217
44	6740	3217
45	6740	3217

Stop Event

1×	node limit

Counts

77 → 69

Calls

Call 1

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

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

eval42.0ms (0.5%)

Compiler: Compiled 1958 to 1668 computations (14.8% saved)

prune12.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	79	4	83

Error

58.2b

Counts

83 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	60.0b	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
✓	59.1b	(+.f64 (+.f64 (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))) -2) (*.f64 (PI.f64) -1/2)) (PI.f64))
✓	60.0b	(+.f64 (+.f64 (.f64 (PI.f64) 1/2) (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2)))))) (.f64 (asin.f64 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) -4))
✓	60.0b	(+.f64 (.f64 2 (asin.f64 (sqrt.f64 (+.f64 1/2 (.f64 x -1/2))))) (+.f64 (.f64 (PI.f64) 3/2) (-.f64 (.f64 -4 (asin.f64 (sqrt.f64 (-.f64 1/2 (*.f64 1/2 x))))) (PI.f64))))

Compiler

Compiled 80 to 72 computations (10% saved)

regimes20.0ms (0.2%)

Accuracy

Total -1.9b remaining (-3.2%)

Threshold costs -1.9b (-3.2%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

7 calls:

4.0ms	x
3.0ms	(/.f64 (-.f64 1 x) 2)
2.0ms	(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))
2.0ms	(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))
2.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))

Results

Error	Segments	Branch
59.1b	1	`x`
59.1b	1	`(-.f64 (/.f64 (PI.f64) 2) (*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))))`
59.1b	1	`(*.f64 2 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2))))`
59.1b	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 x) 2)))`
59.1b	1	`(sqrt.f64 (/.f64 (-.f64 1 x) 2))`
59.1b	1	`(/.f64 (-.f64 1 x) 2)`
59.1b	1	`(-.f64 1 x)`

Compiler

Compiled 154 to 132 computations (14.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	90

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 30 to 27 computations (10% saved)

soundness0.0ms (0%)

end26.0ms (0.3%)

Compiler: Compiled 29 to 25 computations (13.8% saved)

Details

analyze5.0ms (0.1%)

sample4.8s (56%)

preprocess4.0ms (0%)

simplify9.0ms (0.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize27.0ms (0.3%)

series2.0ms (0%)

rewrite138.0ms (1.6%)

simplify595.0ms (7%)

eval361.0ms (4.2%)

prune202.0ms (2.4%)

localize52.0ms (0.6%)

series4.0ms (0%)

rewrite98.0ms (1.1%)

simplify221.0ms (2.6%)

localize46.0ms (0.5%)

series1.0ms (0%)

rewrite16.0ms (0.2%)

simplify26.0ms (0.3%)

localize34.0ms (0.4%)

series2.0ms (0%)

rewrite15.0ms (0.2%)

simplify25.0ms (0.3%)

eval54.0ms (0.6%)

prune22.0ms (0.3%)

localize161.0ms (1.9%)

series1.0ms (0%)

rewrite321.0ms (3.8%)

simplify1.2s (14.2%)

eval42.0ms (0.5%)

prune12.0ms (0.1%)

regimes20.0ms (0.2%)

simplify2.0ms (0%)

soundness0.0ms (0%)

end26.0ms (0.3%)

Profiling