Details

analyze119.0ms (0.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
0%	0%	50%	0.1%	0%	50%	0%	3
0%	0%	50%	0.1%	0%	50%	0%	4
25%	12.5%	37.5%	0.1%	0%	50%	0%	5
26.7%	12.5%	34.3%	0.1%	0%	53.1%	0%	6
37%	15.6%	26.5%	0.1%	1.6%	54.6%	1.6%	7
40.8%	15.6%	22.6%	0.1%	2.3%	57%	2.3%	8
49.4%	17.2%	17.6%	0.1%	3.5%	58.1%	3.5%	9
53.3%	17.2%	15%	0.1%	4.1%	59.5%	4.1%	10
59.5%	18%	12.2%	0.1%	4.8%	60.2%	4.8%	11
62.5%	18%	10.8%	0.1%	5.1%	60.9%	5.1%	12

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample2.9s (22.3%)

Results

1.4s	8256×	body	256	valid
794.0ms	1407×	body	1024	invalid
266.0ms	650×	body	512	invalid
224.0ms	1626×	body	256	invalid
87.0ms	473×	body	256	infinite
58.0ms	249×	body	256	unsamplable

Bogosity

preprocess31.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

1576×	`rational.json-simplify-5`
1540×	`rational.json-simplify-4`
1060×	`rational.json-simplify-2`
1040×	`rational.json-simplify-3`
1000×	`rational.json-simplify-12`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	98
1	56	98
2	147	86
3	413	86
4	1562	86
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (/.f64 k -2) 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 k (*.f64 2 (PI.f64))) (/.f64 (-.f64 n 1) -2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 k (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 n 2))))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 n 2))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 2 (.f64 k (PI.f64))) (+.f64 1/2 (/.f64 n -2))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 k 2)) (/.f64 (-.f64 n 1) -2)) (sqrt.f64 n))

Compiler

Compiled 20 to 17 computations (15% saved)

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

786×	`rational.json-simplify-5`
776×	`rational.json-simplify-4`
654×	`rational.json-simplify-37`
626×	`rational.json-simplify-21`
532×	`rational.json-simplify-2`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	37	49
2	88	43
3	228	43
4	820	43
5	5103	43

Stop Event

1×	node limit

Counts

1 → 6

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (+.f64 k -1) -1/2)) (sqrt.f64 k))

eval2.0ms (0%)

Compiler: Compiled 92 to 62 computations (32.6% saved)

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	4	2	6
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	5	2	7

Error

0.6b

Counts

7 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.7b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 k))
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
✓	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2))

Compiler

Compiled 57 to 39 computations (31.6% saved)

series56.0ms (0.4%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
24.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2))
17.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2))
7.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2))
2.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))

rewrite80.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

786×	`rational.json-simplify-23`
780×	`rational.json-1`
780×	`rational.json-2`
778×	`rational.json-4`
778×	`rational.json-3`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	108
1	114	102
2	359	102
3	1775	102

Stop Event

1×	node limit

Counts

4 → 261

Calls

Call 1

Inputs
(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2))
(.f64 (.f64 2 (PI.f64)) n)
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
(/.f64 1 (sqrt.f64 k))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (.f64 -1 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) 2) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 3) 1/2) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/2 (+.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (/.f64 1 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (/.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 3) (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (.f64 (PI.f64) n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (PI.f64) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 n n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (PI.f64) (-.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 (-.f64 n n) (.f64 (PI.f64) 0)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 (.f64 (PI.f64) 0) (-.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1 (-.f64 (-.f64 n n) (.f64 (PI.f64) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1 (-.f64 (.f64 (PI.f64) 0) (-.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (.f64 (PI.f64) n) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) 0) (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 n n) (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (PI.f64) n) 4) (.f64 n (.f64 (PI.f64) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (-.f64 n n)) (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (-.f64 n n) (.f64 (PI.f64) 0)) (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 (PI.f64) 0) (-.f64 n n)) (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 0 (+.f64 n n)) (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 0 (PI.f64)) (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.f64 n n) 2) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 -1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 -1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (.f64 -2 (/.f64 1/2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 (/.f64 2 (sqrt.f64 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 -1 (sqrt.f64 k)) (.f64 -1 (/.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 2 (/.f64 2 (sqrt.f64 k))) (.f64 (/.f64 1/2 (sqrt.f64 k)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (.f64 (/.f64 1/2 (sqrt.f64 k)) 6) 1/2) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -2 (neg.f64 (/.f64 1/2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -2 (/.f64 1/2 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -2 (.f64 1 (neg.f64 (/.f64 1/2 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -2 (.f64 1 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/2 (+.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/2 (.f64 2 (/.f64 -1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 -1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (.f64 2 (neg.f64 (/.f64 1/2 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (.f64 2 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (/.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (sqrt.f64 k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 2 (sqrt.f64 k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (/.f64 (/.f64 2 (sqrt.f64 k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (/.f64 1/2 (sqrt.f64 k))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1 (sqrt.f64 k)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (.f64 (/.f64 1 (sqrt.f64 k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (sqrt.f64 k))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 -1 (sqrt.f64 k)))))))

simplify103.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

906×	`rational.json-simplify-24`
826×	`rational.json-simplify-13`
752×	`rational.json-simplify-28`
736×	`rational.json-simplify-43`
616×	`rational.json-simplify-27`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	549	10165
1	1901	9877

Stop Event

1×	node limit

Counts

309 → 333

Calls

Call 1

Inputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) 0)
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(+.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)))
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(-.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) 0)
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(-.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 3) 1/2) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) 1/2))
(.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 1)
(.f64 -1/2 (+.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)))))
(.f64 -1 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))))
(.f64 1/2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) -1)
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) 1/2)
(.f64 (+.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)))) -1/2)
(/.f64 1 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) 1)
(/.f64 -1 (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 -1 (/.f64 1 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 1/2 (/.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) -1)
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) -1)
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 3) (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) 2)) -1)
(/.f64 (-.f64 (+.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)))) -1)
(neg.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(+.f64 (.f64 2 (.f64 (PI.f64) n)) 0)
(+.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (PI.f64) 0))
(+.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 n n))
(+.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (PI.f64) (-.f64 n n)))
(+.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 (-.f64 n n) (*.f64 (PI.f64) 0)))
(+.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 (*.f64 (PI.f64) 0) (-.f64 n n)))
(+.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1 (-.f64 (-.f64 n n) (.f64 (PI.f64) 0))))
(+.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 1 (-.f64 (.f64 (PI.f64) 0) (-.f64 n n))))
(+.f64 0 (.f64 2 (.f64 (PI.f64) n)))
(+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (.f64 (PI.f64) n) 4))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(+.f64 (.f64 (PI.f64) 0) (.f64 2 (*.f64 (PI.f64) n)))
(+.f64 (-.f64 n n) (.f64 2 (.f64 (PI.f64) n)))
(+.f64 (.f64 (.f64 (PI.f64) n) 4) (.f64 n (.f64 (PI.f64) -2)))
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(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) (sqrt.f64 k)) 1)
(/.f64 -1/2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 -1 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 -1 (/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 1/2 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) (/.f64 2 (sqrt.f64 k))))
(/.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 1/2 (/.f64 (.f64 (sqrt.f64 k) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))))
(/.f64 1/2 (/.f64 (/.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) (/.f64 1 (sqrt.f64 k))))
(/.f64 1/2 (.f64 (.f64 (sqrt.f64 k) 1/2) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 1/2 (/.f64 1 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)))))
(/.f64 1/2 (/.f64 -1 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))))
(/.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 1/2)
(/.f64 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k))) 2)
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) 1/2))
(/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) (*.f64 2 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) -1/2) (*.f64 (neg.f64 (sqrt.f64 k)) 1/2))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (*.f64 (sqrt.f64 k) 1/2))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) -1/2) 1/2) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 1/2) 1/2) (sqrt.f64 k))
(/.f64 (-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (-.f64 (.f64 (/.f64 1/2 (sqrt.f64 k)) 6) (.f64 2 (/.f64 2 (sqrt.f64 k)))) (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 0 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) (sqrt.f64 k))) -1)
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)) 3) (.f64 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) (sqrt.f64 k))) 2)) -1)
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 3) (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) 2)) (neg.f64 (sqrt.f64 k)))
(/.f64 (-.f64 0 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k)))) -1/2)
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k)))) -1/2)
(/.f64 (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) 1/2) (/.f64 (sqrt.f64 k) 1/4))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k)))) -1)
(neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))
(+.f64 (/.f64 1 (sqrt.f64 k)) 0)
(+.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(+.f64 0 (/.f64 1 (sqrt.f64 k)))
(+.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k)))
(+.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k)))
(+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(+.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 -1 (sqrt.f64 k)))
(-.f64 (/.f64 1 (sqrt.f64 k)) 0)
(-.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(-.f64 0 (/.f64 -1 (sqrt.f64 k)))
(-.f64 0 (*.f64 -2 (/.f64 1/2 (sqrt.f64 k))))
(-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(-.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 (/.f64 2 (sqrt.f64 k)) -1))
(-.f64 (/.f64 -1 (sqrt.f64 k)) (*.f64 -1 (/.f64 2 (sqrt.f64 k))))
(-.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(-.f64 (.f64 2 (/.f64 2 (sqrt.f64 k))) (.f64 (/.f64 1/2 (sqrt.f64 k)) 6))
(-.f64 (.f64 (.f64 (/.f64 1/2 (sqrt.f64 k)) 6) 1/2) (/.f64 1/2 (sqrt.f64 k)))
(*.f64 2 (/.f64 1/2 (sqrt.f64 k)))
(*.f64 1 (/.f64 1 (sqrt.f64 k)))
(*.f64 -2 (neg.f64 (/.f64 1/2 (sqrt.f64 k))))
(*.f64 -2 (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(.f64 -2 (.f64 1 (neg.f64 (/.f64 1/2 (sqrt.f64 k)))))
(.f64 -2 (.f64 1 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) 1)
(*.f64 -1/2 (+.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (sqrt.f64 k))))
(.f64 -1/2 (.f64 2 (/.f64 -1 (sqrt.f64 k))))
(*.f64 -1 (/.f64 -1 (sqrt.f64 k)))
(.f64 -1 (.f64 2 (neg.f64 (/.f64 1/2 (sqrt.f64 k)))))
(.f64 -1 (.f64 2 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(*.f64 1/2 (/.f64 2 (sqrt.f64 k)))
(*.f64 (/.f64 1/2 (sqrt.f64 k)) 2)
(*.f64 (/.f64 -1 (sqrt.f64 k)) -1)
(*.f64 (/.f64 2 (sqrt.f64 k)) 1/2)
(*.f64 1/4 (/.f64 (/.f64 2 (sqrt.f64 k)) 1/2))
(*.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 k))) -2)
(.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 1/4) 4)
(.f64 4 (.f64 (/.f64 1 (sqrt.f64 k)) 1/4))
(*.f64 (+.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (sqrt.f64 k))) -1/2)
(*.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) -2)
(neg.f64 (/.f64 -1 (sqrt.f64 k)))

Outputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 -1/2 (+.f64 k -1))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 3))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2))))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/48 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
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(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 3) (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) 2)) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 0 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k)))) -1/2)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 0) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k)))) -1/2)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) 1/2) (/.f64 (sqrt.f64 k) 1/4))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 -1 (/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 -1/2 k))))))
(.f64 2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 -1/2 k))) (+.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k)))) -1)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 1 (sqrt.f64 k)) 0)
(/.f64 1 (sqrt.f64 k))
(+.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(+.f64 0 (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(+.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(+.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(+.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 -1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(-.f64 (/.f64 1 (sqrt.f64 k)) 0)
(/.f64 1 (sqrt.f64 k))
(-.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(-.f64 0 (/.f64 -1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(-.f64 0 (*.f64 -2 (/.f64 1/2 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 -1/2 (sqrt.f64 k)))
(-.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 (/.f64 2 (sqrt.f64 k)) -1))
(/.f64 1 (sqrt.f64 k))
(-.f64 (/.f64 -1 (sqrt.f64 k)) (*.f64 -1 (/.f64 2 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(-.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(-.f64 (.f64 2 (/.f64 2 (sqrt.f64 k))) (.f64 (/.f64 1/2 (sqrt.f64 k)) 6))
(/.f64 1 (sqrt.f64 k))
(-.f64 (.f64 (.f64 (/.f64 1/2 (sqrt.f64 k)) 6) 1/2) (/.f64 1/2 (sqrt.f64 k)))
(-.f64 (.f64 1/2 (.f64 6 (/.f64 1/2 (sqrt.f64 k)))) (/.f64 1/2 (sqrt.f64 k)))
(-.f64 (*.f64 1/2 (/.f64 3 (sqrt.f64 k))) (/.f64 1/2 (sqrt.f64 k)))
(*.f64 2 (/.f64 1/2 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(*.f64 1 (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(*.f64 -2 (neg.f64 (/.f64 1/2 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(*.f64 -2 (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(.f64 -2 (.f64 1 (neg.f64 (/.f64 1/2 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(.f64 -2 (.f64 1 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) 1)
(/.f64 1 (sqrt.f64 k))
(*.f64 -1/2 (+.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(.f64 -1/2 (.f64 2 (/.f64 -1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(*.f64 -1 (/.f64 -1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(.f64 -1 (.f64 2 (neg.f64 (/.f64 1/2 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(.f64 -1 (.f64 2 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 1/2 (/.f64 2 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1/2 (sqrt.f64 k)) 2)
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 -1 (sqrt.f64 k)) -1)
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 2 (sqrt.f64 k)) 1/2)
(/.f64 1 (sqrt.f64 k))
(*.f64 1/4 (/.f64 (/.f64 2 (sqrt.f64 k)) 1/2))
(/.f64 1 (sqrt.f64 k))
(*.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 k))) -2)
(/.f64 1 (sqrt.f64 k))
(.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 1/4) 4)
(/.f64 1 (sqrt.f64 k))
(.f64 4 (.f64 (/.f64 1 (sqrt.f64 k)) 1/4))
(/.f64 1 (sqrt.f64 k))
(*.f64 (+.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (sqrt.f64 k))) -1/2)
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) -2)
(/.f64 1 (sqrt.f64 k))
(neg.f64 (/.f64 -1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.2b	(*.f64 (PI.f64) n)
✓	0.5b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))

Compiler

Compiled 50 to 30 computations (40% saved)

series6.0ms (0%)

Counts

3 → 48

Calls

15 calls:

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

rewrite77.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1236×	`rational.json-simplify-6`
1002×	`rational.json-simplify-3`
772×	`rational.json-simplify-12`
602×	`rational.json-simplify-2`
594×	`rational.json-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	85
1	96	85
2	288	85
3	1382	85

Stop Event

1×	node limit

Counts

3 → 202

Calls

Call 1

Inputs
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))
(*.f64 (PI.f64) n)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (+.f64 0 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) 0)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))))))) 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simplify125.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1546×	`rational.json-simplify-67`
1258×	`rational.json-simplify-63`
1228×	`rational.json-simplify-1`
702×	`rational.json-simplify-24`
420×	`rational.json-simplify-50`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	435	8890
1	1296	8652
2	6087	8652

Stop Event

1×	node limit

Counts

250 → 262

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
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(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (-.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (/.f64 -1 (/.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (.f64 1 (neg.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))))))
(.f64 (/.f64 1/2 (.f64 2 (sqrt.f64 k))) (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))))
(.f64 (/.f64 1/2 (.f64 2 (sqrt.f64 k))) (/.f64 2 (/.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 1/2 (sqrt.f64 k))) 2)
(.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (/.f64 1/2 (.f64 2 (sqrt.f64 k))))
(.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (.f64 (/.f64 1/2 (sqrt.f64 k)) 1/2))
(.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (.f64 1 (/.f64 1/2 (*.f64 2 (sqrt.f64 k)))))
(.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (.f64 2 (sqrt.f64 k)))))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 1 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (/.f64 1 (sqrt.f64 k)) -1/2))
(.f64 (-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) -1/2)
(neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))

Outputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
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(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
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(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))))
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(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/48 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 3))))))))
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(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (*.f64 1/2 k)))
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(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k)))
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(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (*.f64 1/2 k)))
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(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))
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(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2)))
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(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2)))
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(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))
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(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2)))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k)))))
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(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (neg.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (neg.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (.f64 1 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (neg.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 -1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (neg.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (-.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (/.f64 -1 (/.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (.f64 1 (neg.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (.f64 2 (sqrt.f64 k))) (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (.f64 2 (sqrt.f64 k))) (/.f64 2 (/.f64 1/2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 1/2 (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (/.f64 1/2 (.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (.f64 (/.f64 1/2 (sqrt.f64 k)) 1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (.f64 1 (/.f64 1/2 (*.f64 2 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (.f64 2 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 1 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (/.f64 1 (sqrt.f64 k)) -1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) -1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))

eval229.0ms (1.8%)

Compiler: Compiled 14695 to 9419 computations (35.9% saved)

prune154.0ms (1.2%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	562	33	595
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	563	34	597

Error

0.1b

Counts

597 → 34

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.7b	(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
	0.9b	(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (.f64 (PI.f64) n) 4) (.f64 (PI.f64) (+.f64 n (+.f64 n n))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (.f64 2 (-.f64 n (-.f64 n (.f64 n (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (*.f64 n (PI.f64)) 3))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.7b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.f64 (/.f64 1 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))) (sqrt.f64 k))
	0.7b	(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
	21.6b	(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (.f64 (pow.f64 k 3) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n))) 3))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) -1/48)) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n))))))) (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n))) 2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8))))) (sqrt.f64 k))
	21.7b	(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n))))))) (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n))) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 1/8)))) (sqrt.f64 k))
	21.8b	(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 k (*.f64 (sqrt.f64 2) (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n)))))))) (sqrt.f64 k))
	22.1b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	3.6b	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
	0.8b	(/.f64 2 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) (/.f64 1/2 (sqrt.f64 k))))
	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
	1.2b	(-.f64 (/.f64 (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) 2) (sqrt.f64 k)) (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) 3) (sqrt.f64 k)))
	1.2b	(-.f64 (/.f64 (.f64 2 (/.f64 2 (sqrt.f64 k))) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))) (/.f64 (.f64 (/.f64 1/2 (sqrt.f64 k)) 6) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))
	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (-.f64 (.f64 n 3) (*.f64 n 4)) (neg.f64 (/.f64 1/2 (PI.f64)))) (/.f64 (-.f64 k 1) -2)))
	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))
▶	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 2 (/.f64 (/.f64 1 (PI.f64)) n)) (/.f64 (-.f64 k 1) -2)))
	0.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) 4) (/.f64 1 n)) (/.f64 (.f64 (PI.f64) 6) (/.f64 1 n))) (/.f64 (-.f64 k 1) -2)))
	0.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 (/.f64 (.f64 n 4) (/.f64 1/2 (PI.f64))) (/.f64 (*.f64 n 3) (/.f64 1/2 (PI.f64)))) (/.f64 (-.f64 k 1) -2)))
	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 (/.f64 (.f64 n 3) (/.f64 1 (PI.f64))) (*.f64 (PI.f64) n)) (/.f64 (-.f64 k 1) -2)))
	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 (.f64 (.f64 (PI.f64) 3) n) (.f64 (PI.f64) n)) (/.f64 (-.f64 k 1) -2)))
▶	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 n (.f64 2 (*.f64 n (PI.f64))))) (/.f64 (-.f64 k 1) -2)))
	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (-.f64 (*.f64 n 3) n)) (/.f64 (-.f64 k 1) -2)))
	0.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (-.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 3) 1/2) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 1/2)))
	21.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	3.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	0.9b	(.f64 (-.f64 (.f64 (.f64 (/.f64 1/2 (sqrt.f64 k)) 6) 1/2) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
	0.9b	(.f64 (-.f64 (.f64 2 (/.f64 2 (sqrt.f64 k))) (.f64 (/.f64 1/2 (sqrt.f64 k)) 6)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
	0.9b	(.f64 (-.f64 (.f64 1/2 (/.f64 3 (sqrt.f64 k))) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
▶	3.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))

Compiler

Compiled 1800 to 1405 computations (21.9% saved)

localize25.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
✓	0.3b	(/.f64 (PI.f64) (/.f64 1/2 n))
✓	0.5b	(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k)))

Compiler

Compiled 49 to 33 computations (32.7% saved)

series3.0ms (0%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
0.0ms	k	@	-inf	(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
0.0ms	k	@	inf	(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
0.0ms	k	@	0	(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k)))
0.0ms	n	@	0	(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k)))

rewrite74.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1190×	`rational.json-simplify-6`
930×	`rational.json-simplify-13`
904×	`rational.json-simplify-3`
734×	`rational.json-simplify-14`
728×	`rational.json-simplify-12`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	91
1	92	91
2	315	91
3	1570	91

Stop Event

1×	node limit

Counts

3 → 230

Calls

Call 1

Inputs
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k)))
(/.f64 (PI.f64) (/.f64 1/2 n))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))

Outputs

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

simplify139.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1502×	`rational.json-simplify-1`
1354×	`rational.json-simplify-63`
874×	`rational.json-simplify-61`
596×	`rational.json-simplify-24`
502×	`rational.json-simplify-50`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	483	9366
1	1405	9300
2	5976	9300

Stop Event

1×	node limit

Counts

278 → 276

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
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(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
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(-.f64 (+.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2))
(.f64 1/2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2))
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(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) 1/2)
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(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) -1)
(.f64 -1/2 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)))
(.f64 -1/2 (.f64 1 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2))))
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(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) -1/2)
(/.f64 1/2 (/.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 1)
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(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2) 2)
(/.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) -1)
(/.f64 (-.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))) -1)
(neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
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(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
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(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) 0))
(-.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
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(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2) (neg.f64 (sqrt.f64 k))))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) -1))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(-.f64 (/.f64 0 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(-.f64 (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)))
(-.f64 (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))) (-.f64 (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) 0) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(-.f64 (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))) (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))))
(-.f64 (+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(-.f64 (+.f64 (/.f64 0 (sqrt.f64 k)) (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)))) (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))))
(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (.f64 (sqrt.f64 k) 2)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 1/2 (sqrt.f64 k))))
(-.f64 (/.f64 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (sqrt.f64 k)) (/.f64 (+.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2)) (sqrt.f64 k)))
(-.f64 (/.f64 0 (/.f64 (sqrt.f64 k) -1/2)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 1/2 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2))))
(.f64 -1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(.f64 -1 (.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k)))))
(.f64 -1 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2) (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(.f64 -1 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 -1 (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) -1)
(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))
(.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 1/2 (sqrt.f64 k))))
(.f64 2 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (/.f64 1/2 (.f64 (sqrt.f64 k) 2))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) 1/2)
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (*.f64 1 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (.f64 1 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2))))
(.f64 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (/.f64 1/2 (.f64 (sqrt.f64 k) 2)))
(.f64 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (.f64 1 (/.f64 1/2 (*.f64 (sqrt.f64 k) 2))))
(.f64 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (.f64 (/.f64 1/2 (sqrt.f64 k)) 1/2))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 1 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (/.f64 1 (sqrt.f64 k)) -1/2))
(.f64 (-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) -1/2)
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))

Outputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 n 2))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 (sqrt.f64 2) k)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (.f64 n 2))))))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2)))))))
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(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 1/2 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 -1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 -1 (.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 -1 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2) (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 -1 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 -1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 2 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (/.f64 1/2 (.f64 (sqrt.f64 k) 2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (*.f64 1 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (neg.f64 (sqrt.f64 k))) (.f64 1 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (/.f64 1/2 (.f64 (sqrt.f64 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (.f64 1 (/.f64 1/2 (*.f64 (sqrt.f64 k) 2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)) (.f64 (/.f64 1/2 (sqrt.f64 k)) 1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1/2 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 1 (/.f64 1/2 (neg.f64 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (/.f64 1 (sqrt.f64 k)) -1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) -1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (sqrt.f64 k))
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
✓	0.4b	(/.f64 n (/.f64 1/2 (PI.f64)))
✓	0.5b	(pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2))

Compiler

Compiled 57 to 39 computations (31.6% saved)

series3.0ms (0%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
0.0ms	k	@	-inf	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
0.0ms	k	@	inf	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
0.0ms	k	@	0	(pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2))
0.0ms	n	@	0	(pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2))

rewrite69.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

994×	`rational.json-simplify-13`
868×	`rational.json-simplify-24`
858×	`rational.json-1`
858×	`rational.json-2`
856×	`rational.json-3`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	97
1	121	91
2	410	91
3	2032	91

Stop Event

1×	node limit

Counts

3 → 196

Calls

Call 1

Inputs
(pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2))
(/.f64 n (/.f64 1/2 (PI.f64)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))

Outputs

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

simplify121.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1090×	`rational.json-simplify-63`
832×	`rational.json-simplify-24`
814×	`rational.json-simplify-1`
556×	`rational.json-simplify-50`
426×	`rational.json-simplify-13`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	427	8718
1	1275	8616
2	6352	8616

Stop Event

1×	node limit

Counts

244 → 259

Calls

Call 1

Inputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
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(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 0)
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(+.f64 0 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))
(+.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2))
(+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 0) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))
(+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))))
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(-.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 0)
(-.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 0))
(-.f64 0 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 -1 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)))
(-.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 3))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 3) 1/2) (.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))))
(.f64 1/2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2))
(.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 1)
(.f64 -1 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) -1)
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) 1/2)
(.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) -1) -1/2)
(/.f64 1/2 (/.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 1 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 1)
(/.f64 -1 (/.f64 -1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 -1 (/.f64 1 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))))
(/.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) -1)
(/.f64 (-.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) -1) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))) -1)
(neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(+.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
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(+.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (.f64 (PI.f64) 0)))
(+.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (-.f64 n n)))
(+.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 n (*.f64 (PI.f64) 0)))
(+.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 (-.f64 n n) (.f64 (PI.f64) 0)))
(+.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 (.f64 (PI.f64) 0) (-.f64 n n)))
(+.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1 (neg.f64 (*.f64 (PI.f64) 0))))
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(-.f64 (-.f64 n n) (*.f64 n (/.f64 (PI.f64) -1/2)))
(-.f64 (.f64 n (.f64 (PI.f64) 4)) (*.f64 (PI.f64) (+.f64 n n)))
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(-.f64 (*.f64 0 (neg.f64 (PI.f64))) (/.f64 n (/.f64 -1/2 (PI.f64))))
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(-.f64 (*.f64 0 (neg.f64 n)) (/.f64 n (/.f64 -1/2 (PI.f64))))
(-.f64 (.f64 (.f64 (PI.f64) 3) n) (*.f64 n (PI.f64)))
(-.f64 (.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) 3) 1/2) (.f64 n (PI.f64)))
(-.f64 (.f64 (.f64 n 3) (PI.f64)) (*.f64 n (PI.f64)))
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(-.f64 (.f64 (.f64 (PI.f64) 0) -1) (/.f64 n (/.f64 -1/2 (PI.f64))))
(-.f64 (*.f64 (-.f64 n n) -1) (/.f64 n (/.f64 -1/2 (PI.f64))))
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(*.f64 (PI.f64) (+.f64 n n))
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(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 0 (sqrt.f64 k))))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (.f64 0 (-.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (-.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 0) (/.f64 0 (sqrt.f64 k))))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 0)))
(-.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
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(-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(-.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 2 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (.f64 (/.f64 -1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 2 (sqrt.f64 k))))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (.f64 -1 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 2 (sqrt.f64 k)))))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 2 (sqrt.f64 k))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))) 1/2) (.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(-.f64 (.f64 (/.f64 4 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))))
(-.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) 2) (/.f64 1 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 0) -1) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(-.f64 (.f64 (/.f64 0 (sqrt.f64 k)) -1) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
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(/.f64 1/2 (/.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 2 (sqrt.f64 k))))
(/.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2)))
(/.f64 1/2 (/.f64 (.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))))
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(/.f64 1/2 (/.f64 -1 (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
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(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) 1)
(/.f64 -1/2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2)))
(/.f64 2 (/.f64 (.f64 (sqrt.f64 k) 2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))))
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(/.f64 -1 (/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2)))
(/.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
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(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 2 (sqrt.f64 k))) 2)
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) 1/2))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (sqrt.f64 k) 2))
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(/.f64 (.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 1/2 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) 1/2) (.f64 (*.f64 (sqrt.f64 k) 2) 2))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k)))) -1)
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 0) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 3) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2) 2)) (neg.f64 (sqrt.f64 k)))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))

Outputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
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(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 2 (/.f64 (sqrt.f64 k) (.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) -1/2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 2 (/.f64 1 (.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 -1 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 -1 (/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 1 (/.f64 -1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 2 (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) 1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (.f64 (sqrt.f64 k) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 1/2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) 1/2) (.f64 (*.f64 (sqrt.f64 k) 2) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k)))) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 0) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 3) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2) 2)) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 n (.f64 2 (*.f64 n (PI.f64))))) (/.f64 (-.f64 k 1) -2)))
✓	0.2b	(*.f64 n (PI.f64))
✓	0.3b	(-.f64 n (.f64 2 (.f64 n (PI.f64))))
✓	0.5b	(pow.f64 (-.f64 n (-.f64 n (.f64 2 (.f64 n (PI.f64))))) (/.f64 (-.f64 k 1) -2))

Compiler

Compiled 81 to 46 computations (43.2% saved)

series3.0ms (0%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 n (.f64 2 (*.f64 n (PI.f64))))) (/.f64 (-.f64 k 1) -2)))
0.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 n (.f64 2 (*.f64 n (PI.f64))))) (/.f64 (-.f64 k 1) -2)))
0.0ms	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 n (.f64 2 (*.f64 n (PI.f64))))) (/.f64 (-.f64 k 1) -2)))
0.0ms	n	@	inf	(-.f64 n (.f64 2 (.f64 n (PI.f64))))
0.0ms	k	@	0	(pow.f64 (-.f64 n (-.f64 n (.f64 2 (.f64 n (PI.f64))))) (/.f64 (-.f64 k 1) -2))

rewrite119.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

992×	`rational.json-1`
992×	`rational.json-2`
990×	`rational.json-4`
990×	`rational.json-3`
882×	`rational.json-simplify-24`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	136
1	133	130
2	451	106
3	2353	106

Stop Event

1×	node limit

Counts

4 → 237

Calls

Call 1

Inputs
(pow.f64 (-.f64 n (-.f64 n (.f64 2 (.f64 n (PI.f64))))) (/.f64 (-.f64 k 1) -2))
(-.f64 n (.f64 2 (.f64 n (PI.f64))))
(*.f64 n (PI.f64))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 n (.f64 2 (*.f64 n (PI.f64))))) (/.f64 (-.f64 k 1) -2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (.f64 -1 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k 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simplify103.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

852×	`rational.json-simplify-24`
664×	`rational.json-simplify-50`
614×	`rational.json-simplify-63`
578×	`rational.json-simplify-13`
546×	`rational.json-simplify-28`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	546	11097
1	1803	10075

Stop Event

1×	node limit

Counts

285 → 328

Calls

Call 1

Inputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 n (-.f64 1 (.f64 2 (PI.f64))))
(.f64 n (-.f64 1 (.f64 2 (PI.f64))))
(.f64 n (-.f64 1 (.f64 2 (PI.f64))))
(.f64 n (-.f64 1 (.f64 2 (PI.f64))))
(.f64 n (-.f64 1 (.f64 2 (PI.f64))))
(.f64 n (-.f64 1 (.f64 2 (PI.f64))))
(.f64 n (-.f64 1 (.f64 2 (PI.f64))))
(.f64 n (-.f64 1 (.f64 2 (PI.f64))))
(.f64 (+.f64 1 (.f64 -2 (PI.f64))) n)
(.f64 (+.f64 1 (.f64 -2 (PI.f64))) n)
(.f64 (+.f64 1 (.f64 -2 (PI.f64))) n)
(.f64 (+.f64 1 (.f64 -2 (PI.f64))) n)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) 0)
(+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) 0))
(+.f64 0 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)))
(+.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)))
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(+.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2))
(-.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) 0)
(-.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) 0))
(-.f64 0 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(-.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (.f64 -1 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))
(-.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)))
(-.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))) (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)))))
(-.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))) (.f64 1 (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))))))
(-.f64 (.f64 (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))) 1/2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2))
(.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1)
(.f64 -1 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))))
(.f64 1/2 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) -1)
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) 1/2)
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(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)) (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0)))
(-.f64 0 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (.f64 (/.f64 -1 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) (/.f64 2 (sqrt.f64 k))))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (.f64 -1 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)))))
(-.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))
(-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))
(-.f64 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (sqrt.f64 k)))
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k))) (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)))) (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)) (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (sqrt.f64 k)))))
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k))) (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)))) (.f64 1 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)) (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k))))))
(-.f64 (.f64 (+.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (+.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k)))))
(-.f64 (.f64 (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))) (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0) -1) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))
(-.f64 (.f64 (/.f64 0 (sqrt.f64 k)) -1) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))
(-.f64 (.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)) (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)))) 1/2) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k))))
(-.f64 (.f64 (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))) (/.f64 1/2 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 2 (/.f64 (.f64 (sqrt.f64 k) 2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))))
(/.f64 2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) -1/2)))
(/.f64 2 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2)))
(/.f64 2 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 2 (/.f64 1 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (sqrt.f64 k))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (sqrt.f64 k)) 1)
(/.f64 -1/2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 -1 (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 -1 (/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 1/2 (/.f64 (.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))))
(/.f64 1/2 (/.f64 (/.f64 1/2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) (/.f64 1 (sqrt.f64 k))))
(/.f64 1/2 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) (/.f64 2 (sqrt.f64 k))))
(/.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 1/2 (.f64 (.f64 1/2 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 1/2 (/.f64 1 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)))))
(/.f64 1/2 (/.f64 -1 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))))
(/.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 1/2)
(/.f64 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k))) 2)
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) 1/2))
(/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (*.f64 (sqrt.f64 k) 2))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) -1/2) (*.f64 (neg.f64 (sqrt.f64 k)) 1/2))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (*.f64 1/2 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (*.f64 (sqrt.f64 k) 1/2))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) -1/2) 1/2) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2) 1/2) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) 1/2) (/.f64 (sqrt.f64 k) 1/4))
(/.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k)))) -1)
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (-.f64 (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))) (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))) (neg.f64 (sqrt.f64 k)))
(neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))

Outputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 -1/2 (+.f64 k -1))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
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(/.f64 -1/2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 -1 (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 -1 (/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (/.f64 1/2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) (/.f64 1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) (/.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (.f64 (.f64 1/2 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 1 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 -1 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 1/2)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) 1/2))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (*.f64 (sqrt.f64 k) 2))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) -1/2) (*.f64 (neg.f64 (sqrt.f64 k)) 1/2))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (*.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (*.f64 (sqrt.f64 k) 1/2))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) -1/2) 1/2) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 1/2) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) 1/2) (/.f64 (sqrt.f64 k) 1/4))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k)))) -1)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (+.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2)))) (+.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 k -1/2) 1/2))) (.f64 2 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 n (PI.f64))
✓	0.3b	(.f64 (.f64 n (PI.f64)) 3)
✓	0.5b	(pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (*.f64 n (PI.f64)) 3))) (-.f64 1/2 (/.f64 k 2)))
✓	1.1b	(+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (.f64 n (PI.f64)) 3))

Compiler

Compiled 100 to 63 computations (37% saved)

series56.0ms (0.4%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
31.0ms	n	@	-inf	(pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (*.f64 n (PI.f64)) 3))) (-.f64 1/2 (/.f64 k 2)))
14.0ms	n	@	0	(pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (*.f64 n (PI.f64)) 3))) (-.f64 1/2 (/.f64 k 2)))
7.0ms	n	@	inf	(pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (*.f64 n (PI.f64)) 3))) (-.f64 1/2 (/.f64 k 2)))
1.0ms	k	@	0	(pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (*.f64 n (PI.f64)) 3))) (-.f64 1/2 (/.f64 k 2)))
1.0ms	n	@	0	(+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (.f64 n (PI.f64)) 3))

rewrite66.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1008×	`rational.json-simplify-29`
952×	`rational.json-simplify-42`
716×	`rational.json-simplify-47`
660×	`rational.json-1`
660×	`rational.json-2`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	109
1	115	109
2	326	57
3	1659	57

Stop Event

1×	node limit

Counts

3 → 253

Calls

Call 1

Inputs

(+.f64 (*.f64 n (*.f64 (PI.f64) -2)) (*.f64 (*.f64 n (PI.f64)) 3))

(pow.f64 (*.f64 2 (+.f64 (*.f64 n (*.f64 (PI.f64) -2)) (*.f64 (*.f64 n (PI.f64)) 3))) (-.f64 1/2 (/.f64 k 2)))

(*.f64 (*.f64 n (PI.f64)) 3)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (PI.f64)) (-.f64 n n))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (PI.f64)) (*.f64 (PI.f64) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (PI.f64)) (*.f64 n (*.f64 (PI.f64) 0)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (PI.f64)) (*.f64 0 (-.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (PI.f64)) (*.f64 0 (-.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (PI.f64)) (*.f64 1/2 (*.f64 -2 (-.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 n) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (*.f64 (PI.f64) 2)) (*.f64 n (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 n (neg.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (neg.f64 (PI.f64))) (*.f64 n (*.f64 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simplify113.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1288×	`rational.json-simplify-24`
786×	`rational.json-simplify-50`
618×	`rational.json-simplify-43`
520×	`rational.json-simplify-63`
402×	`rational.json-simplify-44`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	538	9251
1	1776	5963

Stop Event

1×	node limit

Counts

301 → 300

Calls

Call 1

Inputs
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
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(+.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 1 (.f64 3 (*.f64 (PI.f64) 0))))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 (.f64 (PI.f64) 3) 0))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 (.f64 n 3) 0))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 (*.f64 0 (-.f64 (PI.f64) n)) 1/3))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 (*.f64 0 (-.f64 n (PI.f64))) 1/3))
(+.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 n (PI.f64)))
(+.f64 0 (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (.f64 (.f64 n (PI.f64)) -3) (.f64 (.f64 n (PI.f64)) 6))
(+.f64 (-.f64 n n) (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (.f64 (PI.f64) 0) (.f64 n (*.f64 (PI.f64) 3)))
(+.f64 (.f64 (.f64 n (PI.f64)) 6) (.f64 (.f64 n (PI.f64)) -3))
(+.f64 (.f64 n (.f64 (PI.f64) 0)) (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (.f64 (.f64 n (PI.f64)) 9) (.f64 3 (.f64 n (*.f64 (PI.f64) -2))))
(+.f64 (.f64 n (.f64 (PI.f64) -6)) (.f64 (.f64 n (PI.f64)) 9))
(+.f64 (.f64 3 (-.f64 n n)) (.f64 n (*.f64 (PI.f64) 3)))
(+.f64 (.f64 3 (.f64 (PI.f64) 0)) (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (/.f64 (-.f64 n n) 1/3) (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (/.f64 (.f64 (PI.f64) 0) 1/3) (.f64 n (*.f64 (PI.f64) 3)))
(+.f64 (/.f64 (.f64 n (.f64 (PI.f64) 3)) 1/3) (/.f64 (.f64 n (.f64 (PI.f64) -2)) 1/3))
(+.f64 (/.f64 (.f64 n (.f64 (PI.f64) -2)) 1/3) (/.f64 (.f64 n (.f64 (PI.f64) 3)) 1/3))
(+.f64 (.f64 (-.f64 n n) 3) (.f64 n (*.f64 (PI.f64) 3)))
(+.f64 (.f64 (.f64 (.f64 n (PI.f64)) 6) 3) (.f64 3 (.f64 (.f64 n (PI.f64)) -5)))
(+.f64 (.f64 (.f64 n (.f64 (PI.f64) -4)) 3) (.f64 3 (.f64 (.f64 n (PI.f64)) 5)))
(+.f64 (.f64 (.f64 n (.f64 (PI.f64) 3)) 1/2) (/.f64 (.f64 n (PI.f64)) 2/3))
(+.f64 (.f64 (.f64 (PI.f64) 0) 3) (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (.f64 0 (.f64 (PI.f64) 3)) (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (.f64 (+.f64 n n) (.f64 (PI.f64) 3)) (.f64 (.f64 n (PI.f64)) -3))
(+.f64 (.f64 0 (.f64 n 3)) (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (.f64 (.f64 (PI.f64) 2) (.f64 n 3)) (.f64 (*.f64 n (PI.f64)) -3))
(+.f64 (/.f64 (.f64 (.f64 n (PI.f64)) 6) 1/3) (/.f64 (.f64 (.f64 n (PI.f64)) -5) 1/3))
(+.f64 (/.f64 (.f64 n (.f64 (PI.f64) -4)) 1/3) (/.f64 (.f64 (.f64 n (PI.f64)) 5) 1/3))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) 0)
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (-.f64 n n))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (*.f64 (PI.f64) 0))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 n (.f64 (PI.f64) 0)))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (*.f64 3 (-.f64 n n)))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 3 (.f64 (PI.f64) 0)))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 (-.f64 n n) 1/3))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 (*.f64 (PI.f64) 0) 1/3))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 1 (.f64 3 (-.f64 n n))))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 1 (.f64 3 (*.f64 (PI.f64) 0))))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 (.f64 (PI.f64) 3) 0))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 (.f64 n 3) 0))
(-.f64 0 (.f64 (.f64 n (PI.f64)) -3))
(-.f64 0 (.f64 -1 (.f64 n (*.f64 (PI.f64) 3))))
(-.f64 (.f64 (.f64 n (PI.f64)) -3) (.f64 n (.f64 (PI.f64) -6)))
(-.f64 (.f64 (.f64 n (PI.f64)) -3) (.f64 -1 (.f64 (*.f64 n (PI.f64)) 6)))
(-.f64 (.f64 (.f64 n (PI.f64)) -3) (.f64 -3 (.f64 n (*.f64 (PI.f64) 2))))
(-.f64 (.f64 (.f64 n (PI.f64)) 6) (.f64 n (.f64 (PI.f64) 3)))
(-.f64 (.f64 (.f64 n (PI.f64)) 12) (.f64 (.f64 n (PI.f64)) 9))
(-.f64 (/.f64 (-.f64 n n) 1/3) (.f64 (.f64 n (PI.f64)) -3))
(-.f64 (/.f64 (.f64 (PI.f64) 0) 1/3) (.f64 (*.f64 n (PI.f64)) -3))
(-.f64 (/.f64 (.f64 (.f64 n (PI.f64)) 4) 1/3) (/.f64 (.f64 n (.f64 (PI.f64) 3)) 1/3))
(-.f64 (/.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -4))) 1/3) (/.f64 (.f64 n (*.f64 (PI.f64) -2)) 1/3))
(-.f64 (/.f64 (.f64 (.f64 (PI.f64) 2) 3) (/.f64 1 n)) (.f64 n (.f64 (PI.f64) 3)))
(-.f64 (/.f64 (.f64 (+.f64 n n) 3) (/.f64 1 (PI.f64))) (.f64 n (*.f64 (PI.f64) 3)))
(-.f64 (.f64 (-.f64 n n) 3) (.f64 (*.f64 n (PI.f64)) -3))
(-.f64 (.f64 (-.f64 n n) -3) (.f64 (*.f64 n (PI.f64)) -3))
(-.f64 (.f64 (.f64 (PI.f64) 0) -3) (.f64 (.f64 n (PI.f64)) -3))
(-.f64 (.f64 (.f64 (.f64 n (PI.f64)) 4) 3) (.f64 (*.f64 n (PI.f64)) 9))
(-.f64 (.f64 (.f64 (PI.f64) 0) 3) (.f64 (.f64 n (PI.f64)) -3))
(-.f64 (.f64 0 (.f64 (PI.f64) 3)) (.f64 (.f64 n (PI.f64)) -3))
(-.f64 (.f64 (+.f64 n n) (.f64 (PI.f64) 3)) (.f64 n (.f64 (PI.f64) 3)))
(-.f64 (.f64 0 (.f64 n 3)) (.f64 (.f64 n (PI.f64)) -3))
(-.f64 (.f64 (.f64 (PI.f64) 2) (.f64 n 3)) (.f64 n (*.f64 (PI.f64) 3)))
(-.f64 (.f64 (.f64 (.f64 (PI.f64) 2) 3) n) (.f64 n (*.f64 (PI.f64) 3)))
(-.f64 (.f64 (.f64 (+.f64 n n) 3) (PI.f64)) (.f64 n (.f64 (PI.f64) 3)))
(-.f64 (.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -4))) 3) (.f64 3 (.f64 n (*.f64 (PI.f64) -2))))
(-.f64 (.f64 (.f64 (.f64 n (PI.f64)) 9) 1/2) (/.f64 (.f64 n (PI.f64)) 2/3))
(-.f64 (.f64 (.f64 (+.f64 n n) 2) (.f64 (PI.f64) 3)) (.f64 (.f64 (PI.f64) 3) (.f64 n 3)))
(-.f64 (.f64 (-.f64 0 (.f64 (PI.f64) -4)) (.f64 n 3)) (.f64 (.f64 n 3) (.f64 (PI.f64) 3)))
(/.f64 n (/.f64 (/.f64 1 (PI.f64)) 3))
(/.f64 n (/.f64 1 (*.f64 (PI.f64) 3)))
(/.f64 n (*.f64 (/.f64 1 (PI.f64)) 1/3))
(/.f64 n (/.f64 -1 (*.f64 -3 (PI.f64))))
(/.f64 (PI.f64) (/.f64 (/.f64 1 n) 3))
(/.f64 (PI.f64) (/.f64 1 (*.f64 n 3)))
(/.f64 (PI.f64) (*.f64 (/.f64 1 n) 1/3))
(/.f64 (PI.f64) (/.f64 -1 (*.f64 -3 n)))
(/.f64 (*.f64 n (PI.f64)) 1/3)
(/.f64 3 (/.f64 1 (*.f64 n (PI.f64))))
(/.f64 (.f64 n (.f64 (PI.f64) 3)) 1)
(/.f64 1/2 (/.f64 1/6 (*.f64 n (PI.f64))))
(/.f64 1 (/.f64 1/3 (*.f64 n (PI.f64))))
(/.f64 -1 (/.f64 1 (.f64 (.f64 n (PI.f64)) -3)))
(/.f64 (*.f64 n (neg.f64 (PI.f64))) -1/3)
(/.f64 (neg.f64 n) (/.f64 (/.f64 -1 (PI.f64)) 3))
(/.f64 (neg.f64 n) (/.f64 -1 (*.f64 (PI.f64) 3)))
(/.f64 (neg.f64 n) (*.f64 (/.f64 -1 (PI.f64)) 1/3))
(/.f64 (.f64 (.f64 n (PI.f64)) -3) -1)
(/.f64 (neg.f64 (PI.f64)) (/.f64 (/.f64 -1 n) 3))
(/.f64 (neg.f64 (PI.f64)) (/.f64 -1 (*.f64 n 3)))
(/.f64 (neg.f64 (PI.f64)) (*.f64 (/.f64 -1 n) 1/3))
(/.f64 6 (/.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2))
(/.f64 (*.f64 (PI.f64) 3) (/.f64 1 n))
(/.f64 (*.f64 n 3) (/.f64 1 (PI.f64)))
(/.f64 -3 (/.f64 1 (*.f64 n (neg.f64 (PI.f64)))))
(/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64)))
(/.f64 (*.f64 -3 n) (/.f64 -1 (PI.f64)))
(/.f64 (*.f64 -3 (PI.f64)) (/.f64 -1 n))
(/.f64 (/.f64 (*.f64 -3 n) (/.f64 1 (PI.f64))) -1)
(/.f64 (/.f64 (*.f64 -3 (PI.f64)) (/.f64 1 n)) -1)
(/.f64 (/.f64 (neg.f64 n) 1/3) (/.f64 -1 (PI.f64)))
(/.f64 (/.f64 (neg.f64 (PI.f64)) 1/3) (/.f64 -1 n))
(/.f64 (-.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -4)))) -1/3)
(/.f64 (-.f64 (.f64 n 3) (.f64 (+.f64 n n) 3)) (/.f64 -1 (PI.f64)))
(/.f64 (-.f64 (.f64 (PI.f64) 3) (.f64 (*.f64 (PI.f64) 2) 3)) (/.f64 -1 n))
(/.f64 (-.f64 (.f64 3 (-.f64 n n)) (.f64 n (*.f64 (PI.f64) 3))) -1)
(/.f64 (-.f64 (.f64 3 (.f64 (PI.f64) 0)) (.f64 n (.f64 (PI.f64) 3))) -1)
(/.f64 (-.f64 (.f64 (.f64 n (PI.f64)) 9) (.f64 (.f64 n (PI.f64)) 12)) -1)
(/.f64 (/.f64 (*.f64 (PI.f64) 3) 2) (/.f64 1/2 n))
(/.f64 (/.f64 (*.f64 n 3) 2) (/.f64 1/2 (PI.f64)))
(/.f64 (-.f64 (+.f64 (.f64 (.f64 n (PI.f64)) -3) (.f64 (.f64 n (PI.f64)) -3)) (.f64 (.f64 n (PI.f64)) -3)) -1)
(/.f64 (-.f64 (.f64 (.f64 (.f64 n (PI.f64)) -3) 2) (.f64 (*.f64 n (PI.f64)) -3)) -1)
(/.f64 (+.f64 (.f64 n (neg.f64 (PI.f64))) (.f64 n (*.f64 (PI.f64) -2))) -1)
(/.f64 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (*.f64 n (neg.f64 (PI.f64)))) -1)
(/.f64 (-.f64 (.f64 n (.f64 (PI.f64) 0)) (*.f64 n (PI.f64))) -1/3)
(/.f64 (-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 (.f64 n (PI.f64)) 4)) -1/3)
(/.f64 (-.f64 (.f64 n (.f64 (PI.f64) 0)) (.f64 n (.f64 (PI.f64) 3))) -1)
(neg.f64 (.f64 (.f64 n (PI.f64)) -3))

Outputs
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (.f64 (PI.f64) 1))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (.f64 (PI.f64) 1))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (.f64 (PI.f64) 1))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (.f64 (PI.f64) 1))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (.f64 (PI.f64) 1))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (.f64 (PI.f64) 1))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (.f64 (PI.f64) 1))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (.f64 (PI.f64) 1))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (neg.f64 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (neg.f64 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (neg.f64 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2)))))))
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(.f64 n (.f64 (PI.f64) 3))
(/.f64 (-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 (.f64 n (PI.f64)) 4)) -1/3)
(.f64 n (.f64 (PI.f64) 3))
(/.f64 (-.f64 (.f64 n (.f64 (PI.f64) 0)) (.f64 n (.f64 (PI.f64) 3))) -1)
(.f64 n (.f64 (PI.f64) 3))
(neg.f64 (.f64 (.f64 n (PI.f64)) -3))
(.f64 n (.f64 (PI.f64) 3))

localize70.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
✓	0.4b	(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))
✓	1.0b	(log.f64 (*.f64 2 (PI.f64)))
✓	3.3b	(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))

Compiler

Compiled 85 to 60 computations (29.4% saved)

series49.0ms (0.4%)

Counts

4 → 44

Calls

15 calls:

Time	Variable		Point	Expression
22.0ms	n	@	0	(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
11.0ms	n	@	-inf	(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
8.0ms	n	@	inf	(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
2.0ms	k	@	-inf	(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
1.0ms	k	@	0	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))

rewrite72.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1440×	`rational.json-simplify-29`
932×	`rational.json-1`
932×	`rational.json-2`
932×	`rational.json-4`
932×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	142
1	123	142
2	378	142
3	2051	142

Stop Event

1×	node limit

Counts

4 → 145

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(log.f64 (*.f64 2 (PI.f64)))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))

Outputs
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simplify127.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1400×	`rational.json-simplify-37`
1092×	`rational.json-simplify-61`
1072×	`rational.json-simplify-67`
634×	`rational.json-simplify-1`
606×	`rational.json-simplify-69`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	305	8987
1	796	8933
2	4003	8933

Stop Event

1×	node limit

Counts

189 → 187

Calls

Call 1

Inputs
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(/.f64 (neg.f64 (sqrt.f64 (/.f64 1 k))) (.f64 1 (/.f64 -1 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))))))
(/.f64 (neg.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))) (/.f64 -1 (sqrt.f64 (/.f64 1 k))))
(/.f64 (neg.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))) (/.f64 1 (neg.f64 (sqrt.f64 (/.f64 1 k)))))
(/.f64 (neg.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))) (*.f64 1 (/.f64 -1 (sqrt.f64 (/.f64 1 k)))))
(/.f64 (.f64 2 (sqrt.f64 (/.f64 1 k))) (/.f64 (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2))))) 1/2))
(/.f64 (.f64 2 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 (/.f64 1 (sqrt.f64 (/.f64 1 k))) 1/2))
(/.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 k))) (/.f64 1/2 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2))))))
(/.f64 (.f64 1/2 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 1/2 (sqrt.f64 (/.f64 1 k))))
(/.f64 (-.f64 (+.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k)))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k))))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k))))) -1)
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Outputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
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(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
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(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (+.f64 (log.f64 -1) (log.f64 (.f64 2 (PI.f64))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 -1)))))
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(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 -1)))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (+.f64 (log.f64 -1) (log.f64 (.f64 2 (PI.f64))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 -1)))))
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(exp.f64 (.f64 1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
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(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
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(-.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) 0) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(-.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 0) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(-.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (sqrt.f64 (/.f64 1 k)))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(-.f64 (.f64 0 (neg.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(-.f64 (.f64 0 (neg.f64 (sqrt.f64 (/.f64 1 k)))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(-.f64 (.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (sqrt.f64 (/.f64 1 k)))) 2) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 (/.f64 1 k)) 3)))
(-.f64 (.f64 2 (.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))) (.f64 2 (sqrt.f64 (/.f64 1 k))))) (.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))) (*.f64 3 (sqrt.f64 (/.f64 1 k)))))
(-.f64 (.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))) (.f64 (sqrt.f64 (/.f64 1 k)) 4)) (.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))) (.f64 3 (sqrt.f64 (/.f64 1 k)))))
(/.f64 1/2 (/.f64 (/.f64 1/2 (sqrt.f64 (/.f64 1 k))) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 1/2 (/.f64 (/.f64 1/2 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))) (sqrt.f64 (/.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 1/2 (/.f64 (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))) (*.f64 2 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 1/2 (/.f64 (/.f64 1 (sqrt.f64 (/.f64 1 k))) (.f64 2 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 1/2 (/.f64 1 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (sqrt.f64 (/.f64 1 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 1/2 (/.f64 -1 (+.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k)))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 1 (sqrt.f64 (/.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 1 (/.f64 1 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) 1)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 -1 (/.f64 1 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k)))) -1)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 1 k))) (/.f64 -1 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 1 k))) (/.f64 1 (neg.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 1 k))) (.f64 1 (/.f64 -1 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (neg.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))) (/.f64 -1 (sqrt.f64 (/.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (neg.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))) (/.f64 1 (neg.f64 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (neg.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2))))) (*.f64 1 (/.f64 -1 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (.f64 2 (sqrt.f64 (/.f64 1 k))) (/.f64 (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2))))) 1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (.f64 2 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 (/.f64 1 (sqrt.f64 (/.f64 1 k))) 1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 k))) (/.f64 1/2 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (.f64 1/2 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 1/2 (sqrt.f64 (/.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(/.f64 (-.f64 (+.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k)))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k))))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k))))) -1)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))
(neg.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (log.f64 n)) (+.f64 1/2 (*.f64 k -1/2)))) (neg.f64 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (*.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))))

eval630.0ms (4.9%)

Compiler: Compiled 39411 to 25100 computations (36.3% saved)

prune483.0ms (3.7%)

Pruning

40 alts after pruning (36 fresh and 4 done)

	Pruned	Kept	Total
New	1468	26	1494
Fresh	18	10	28
Picked	0	1	1
Done	2	3	5
Total	1488	40	1528

Error

0.1b

Counts

1528 → 40

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.7b	(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
	0.9b	(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (.f64 n (PI.f64)) 4) (.f64 n (*.f64 (PI.f64) 3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (.f64 2 (-.f64 n (-.f64 n (.f64 n (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (.f64 n (PI.f64)) 1/3))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.9b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (PI.f64) (.f64 (/.f64 1 n) 1/3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.2b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (-.f64 (.f64 (.f64 n (PI.f64)) 12) (.f64 (*.f64 n (PI.f64)) 9)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.9b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (/.f64 (.f64 (.f64 n (PI.f64)) 6) 1/3) (/.f64 (.f64 (*.f64 n (PI.f64)) -5) 1/3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (.f64 (.f64 n (PI.f64)) 6) 3) (.f64 3 (.f64 (*.f64 n (PI.f64)) -5))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.6b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (PI.f64) (.f64 3 (.f64 n -4))) (.f64 (.f64 n (PI.f64)) 15)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (/.f64 n (/.f64 1 (PI.f64))) 3))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 n 3) (.f64 (+.f64 n n) 2)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.7b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.f64 (/.f64 1 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))) (sqrt.f64 k))
	0.7b	(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
	21.7b	(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 1/8)))) (sqrt.f64 k))
	21.8b	(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k))))) (sqrt.f64 k))
	22.1b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	0.8b	(/.f64 2 (/.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 1/2 (sqrt.f64 k))))
▶	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
	1.2b	(-.f64 (.f64 (/.f64 4 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))))
	3.6b	(-.f64 (.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))) (.f64 (sqrt.f64 (/.f64 1 k)) 4)) (.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))) (.f64 3 (sqrt.f64 (/.f64 1 k)))))
	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (-.f64 (.f64 n 3) (*.f64 n 4)) (neg.f64 (/.f64 1/2 (PI.f64)))) (/.f64 (-.f64 k 1) -2)))
▶	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))
✓	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 2 (/.f64 (/.f64 1 (PI.f64)) n)) (/.f64 (-.f64 k 1) -2)))
	0.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) 4) (/.f64 1 n)) (/.f64 (.f64 (PI.f64) 6) (/.f64 1 n))) (/.f64 (-.f64 k 1) -2)))
	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (.f64 n -2))) (/.f64 (-.f64 k 1) -2)))
▶	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (neg.f64 n) (.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2)))
	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (+.f64 (-.f64 n (+.f64 (.f64 2 (*.f64 n (PI.f64))) (+.f64 n n))) (+.f64 n n))) (/.f64 (-.f64 k 1) -2)))
	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (-.f64 (*.f64 n 3) n)) (/.f64 (-.f64 k 1) -2)))
	21.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	3.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	0.9b	(.f64 (-.f64 (.f64 2 (/.f64 2 (sqrt.f64 k))) (*.f64 (/.f64 1/2 (sqrt.f64 k)) 6)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
	0.9b	(.f64 (-.f64 (.f64 1/2 (/.f64 3 (sqrt.f64 k))) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
	4.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (.f64 2 (log.f64 n))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
✓	3.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
▶	25.0b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))

Compiler

Compiled 1985 to 1525 computations (23.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (sqrt.f64 k))
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))
	0.3b	(/.f64 (PI.f64) (/.f64 1/2 n))
✓	0.5b	(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2))

Compiler

Compiled 57 to 39 computations (31.6% saved)

series13.0ms (0.1%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
11.0ms	k	@	inf	(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2))
0.0ms	k	@	0	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))
0.0ms	k	@	-inf	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))
0.0ms	k	@	inf	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))
0.0ms	k	@	0	(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2))

rewrite59.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

998×	`rational.json-simplify-13`
870×	`rational.json-simplify-24`
858×	`rational.json-1`
858×	`rational.json-2`
856×	`rational.json-3`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	82
1	121	76
2	410	76
3	2028	76

Stop Event

1×	node limit

Counts

2 → 106

Calls

Call 1

Inputs
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 0 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (-.f64 (/.f64 0 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) 0)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (-.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) 0) (/.f64 0 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (*.f64 1 (-.f64 (/.f64 0 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (*.f64 1 (-.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) 0) (/.f64 0 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (*.f64 2 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) 0)))))) (#(struct:change #<rule 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simplify130.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1346×	`rational.json-simplify-67`
1284×	`rational.json-simplify-63`
906×	`rational.json-simplify-40`
710×	`rational.json-simplify-1`
600×	`rational.json-simplify-57`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	272	6596
1	846	6556
2	4509	6556
3	6638	6556

Stop Event

1×	node limit

Counts

142 → 139

Calls

Call 1

Inputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
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(/.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1 (/.f64 -1 (sqrt.f64 k))))
(/.f64 (.f64 1/2 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) 1/2)
(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 2 (sqrt.f64 k))) 2)
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 (/.f64 1 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))) 1/2))
(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 2) (*.f64 (sqrt.f64 k) 2))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2)))) (*.f64 1/2 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 2) 1/2) (.f64 (.f64 (sqrt.f64 k) 2) 2))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k)))) -1)
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 0) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 3) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) 2) 2)) (neg.f64 (sqrt.f64 k)))
(neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))

Outputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))))))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 3))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))) (.f64 -1/48 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 3))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 1/2 (+.f64 1 (neg.f64 k)))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 1/2 (+.f64 1 (neg.f64 k)))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 1/2 (+.f64 1 (neg.f64 k)))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 1/2 (+.f64 1 (neg.f64 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))) (sqrt.f64 (/.f64 1 k)))
(+.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) 0)
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(-.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))) 1/2) (.f64 1/2 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (.f64 (/.f64 4 (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 2) 2) (/.f64 1 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 0) -1) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (.f64 (/.f64 0 (sqrt.f64 k)) -1) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 3) (/.f64 1/2 (sqrt.f64 k))) (.f64 1/2 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (/.f64 1 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 2)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (/.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 1 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 2 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 -1 (+.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 -1/2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 2)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 2 (/.f64 (.f64 (sqrt.f64 k) 2) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 2 (/.f64 (/.f64 1 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 2 (/.f64 (sqrt.f64 k) (.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) -1/2)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 2 (/.f64 1 (.f64 1/2 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 -1 (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 -1 (/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 2)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1 (/.f64 -1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 1/2 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) 1/2)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 2 (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 (/.f64 1 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))) 1/2))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 2) (*.f64 (sqrt.f64 k) 2))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2)))) (*.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 2) 1/2) (.f64 (.f64 (sqrt.f64 k) 2) 2))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k)))) -1)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 0) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (.f64 k -1/2))) 3) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) 2) 2)) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
✓	0.2b	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))
✓	0.2b	(*.f64 (PI.f64) (+.f64 n n))
✓	0.5b	(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))

Compiler

Compiled 67 to 34 computations (49.3% saved)

series13.0ms (0.1%)

Counts

4 → 60

Calls

21 calls:

Time	Variable		Point	Expression
4.0ms	k	@	0	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))
1.0ms	n	@	0	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))
1.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))
1.0ms	n	@	inf	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))
1.0ms	n	@	-inf	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))

rewrite102.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1180×	`rational.json-simplify-6`
938×	`rational.json-simplify-3`
872×	`rational.json-simplify-13`
744×	`rational.json-simplify-12`
704×	`rational.json-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	134
1	106	134
2	320	134
3	1576	134

Stop Event

1×	node limit

Counts

4 → 371

Calls

Call 1

Inputs
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))
(*.f64 (PI.f64) (+.f64 n n))
(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (-.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (+.f64 0 (-.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (.f64 1 (-.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (.f64 1/2 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simplify156.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1040×	`rational.json-simplify-2`
936×	`rational.json-simplify-13`
890×	`rational.json-simplify-3`
808×	`rational.json-simplify-24`
782×	`rational.json-simplify-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	749	19413
1	2317	18813

Stop Event

1×	node limit

Counts

431 → 471

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
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(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))) (.f64 (/.f64 1 (sqrt.f64 k)) -1/2))
(.f64 (-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) -1/2)
(.f64 (+.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))))
(.f64 (+.f64 (.f64 1/2 (/.f64 1/2 (sqrt.f64 k))) (.f64 1/2 (/.f64 1/2 (sqrt.f64 k)))) (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (neg.f64 (sqrt.f64 k))))

Outputs
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (sqrt.f64 2) k)) (.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
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(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 3))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (sqrt.f64 2) k)) (.f64 -1/2 (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2))) (.f64 1/8 (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/48 (.f64 (pow.f64 k 3) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 3))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))))
(/.f64 (sqrt.f64 k) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
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(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) 2)) (.f64 (sqrt.f64 k) 2)) (.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) (.f64 1/2 (/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))))
(+.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) (.f64 (-.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k)))) (/.f64 1/4 (sqrt.f64 k))))
(-.f64 (/.f64 (+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) 2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) 2)) (sqrt.f64 k)) (/.f64 (+.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) 2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 1/2 (.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) 1/4)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 -1/2 (.f64 2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (neg.f64 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 2 (.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 -1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 -1 (.f64 2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (/.f64 (sqrt.f64 k) -1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) -1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 -1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (.f64 1/2 (/.f64 1/2 (sqrt.f64 k))) (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) 2)))
(.f64 (/.f64 1/4 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) 4))
(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (*.f64 (/.f64 1/4 (sqrt.f64 k)) 4))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (.f64 1/2 (sqrt.f64 k))) 1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) 2) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 -2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) (/.f64 (sqrt.f64 k) -1/2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 -2 (.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (/.f64 (sqrt.f64 k) -1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 4 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) 1/4))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k)))) (neg.f64 (/.f64 1/2 (sqrt.f64 k))))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 -1/2 (sqrt.f64 k)))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))) (.f64 1 (neg.f64 (/.f64 1/2 (sqrt.f64 k)))))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k)))) (neg.f64 (/.f64 1/2 (sqrt.f64 k))))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 -1/2 (sqrt.f64 k)))
(.f64 (-.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))) (.f64 (/.f64 1 (sqrt.f64 k)) -1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) -1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (+.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 1/2 (/.f64 1/2 (sqrt.f64 k))) (.f64 1/2 (/.f64 1/2 (sqrt.f64 k)))) (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 2 (.f64 (+.f64 (/.f64 1/4 (sqrt.f64 k)) (/.f64 1/4 (sqrt.f64 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 2 (.f64 (+.f64 (/.f64 1/4 (sqrt.f64 k)) (/.f64 1/4 (sqrt.f64 k))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (neg.f64 n) (.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2)))
✓	0.2b	(-.f64 (neg.f64 n) (*.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))
✓	0.4b	(*.f64 (+.f64 n n) (+.f64 (PI.f64) -1))
✓	0.5b	(pow.f64 (-.f64 n (-.f64 (neg.f64 n) (*.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2))

Compiler

Compiled 100 to 54 computations (46% saved)

series85.0ms (0.7%)

Counts

4 → 60

Calls

18 calls:

Time	Variable		Point	Expression
50.0ms	n	@	-inf	(pow.f64 (-.f64 n (-.f64 (neg.f64 n) (*.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2))
17.0ms	n	@	0	(pow.f64 (-.f64 n (-.f64 (neg.f64 n) (*.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2))
7.0ms	n	@	inf	(pow.f64 (-.f64 n (-.f64 (neg.f64 n) (*.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2))
5.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (neg.f64 n) (.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2)))
3.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (neg.f64 n) (.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2)))

rewrite84.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1250×	`rational.json-simplify-29`
1238×	`rational.json-1`
1238×	`rational.json-2`
1236×	`rational.json-4`
1236×	`rational.json-3`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	178
1	148	172
2	522	142
3	2971	118

Stop Event

1×	node limit

Counts

4 → 261

Calls

Call 1

Inputs
(pow.f64 (-.f64 n (-.f64 (neg.f64 n) (*.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2))
(*.f64 (+.f64 n n) (+.f64 (PI.f64) -1))
(-.f64 (neg.f64 n) (*.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (neg.f64 n) (.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2)))

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

simplify122.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

730×	`rational.json-simplify-50`
724×	`rational.json-simplify-24`
650×	`rational.json-simplify-13`
626×	`rational.json-simplify-28`
546×	`rational.json-simplify-43`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	577	13665
1	1931	11893

Stop Event

1×	node limit

Counts

321 → 373

Calls

Call 1

Inputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (+.f64 2 (*.f64 2 (-.f64 (PI.f64) 1)))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (+.f64 2 (*.f64 2 (-.f64 (PI.f64) 1)))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (+.f64 2 (*.f64 2 (-.f64 (PI.f64) 1)))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (+.f64 2 (*.f64 2 (-.f64 (PI.f64) 1)))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (+.f64 2 (.f64 2 (-.f64 (PI.f64) 1))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (+.f64 2 (.f64 2 (-.f64 (PI.f64) 1))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (+.f64 2 (.f64 2 (-.f64 (PI.f64) 1))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (+.f64 2 (.f64 2 (-.f64 (PI.f64) 1))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (.f64 -2 (-.f64 (PI.f64) 1)) 2))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (.f64 -2 (-.f64 (PI.f64) 1)) 2))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (.f64 -2 (-.f64 (PI.f64) 1)) 2))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (.f64 -2 (-.f64 (PI.f64) 1)) 2))))))
(sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (*.f64 n (-.f64 (PI.f64) 1)))))
(+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1)))))) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))))))
(+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) 2)) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))))) (+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1)))))) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (*.f64 n (-.f64 (PI.f64) 1)))))))))
(+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) 2)) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))))) (+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) (+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1)))))) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))))) (.f64 -1/48 (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) 3)) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))))))))
(exp.f64 (.f64 -1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (*.f64 2 n))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (*.f64 2 n))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (*.f64 2 n))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (*.f64 2 n))) (-.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (.f64 2 n))) (+.f64 1 (.f64 -1 k)))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (.f64 2 n))) (+.f64 1 (.f64 -1 k)))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (.f64 2 n))) (+.f64 1 (.f64 -1 k)))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (.f64 2 n))) (+.f64 1 (.f64 -1 k)))))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
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(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 2) (.f64 (sqrt.f64 k) 2))
(/.f64 (.f64 -1/2 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))) (.f64 (neg.f64 (sqrt.f64 k)) 1/2))
(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (.f64 1/2 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (.f64 (sqrt.f64 k) 1/2))
(/.f64 (/.f64 (.f64 -1/2 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2))) 1/2) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) 1/2) 1/2) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) 2) 1/2) (/.f64 (sqrt.f64 k) 1/4))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (-.f64 (+.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 2)) (+.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 2) (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) 2))) (neg.f64 (sqrt.f64 k)))
(neg.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))

Outputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (+.f64 2 (*.f64 2 (-.f64 (PI.f64) 1)))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (+.f64 2 (*.f64 -2 (-.f64 1 (PI.f64))))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (+.f64 (*.f64 2 (PI.f64)) 0)) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (+.f64 2 (*.f64 2 (-.f64 (PI.f64) 1)))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (+.f64 2 (*.f64 -2 (-.f64 1 (PI.f64))))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (+.f64 (*.f64 2 (PI.f64)) 0)) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (+.f64 2 (*.f64 2 (-.f64 (PI.f64) 1)))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (+.f64 2 (*.f64 -2 (-.f64 1 (PI.f64))))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (+.f64 (*.f64 2 (PI.f64)) 0)) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (+.f64 2 (*.f64 2 (-.f64 (PI.f64) 1)))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (+.f64 2 (*.f64 -2 (-.f64 1 (PI.f64))))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (+.f64 (*.f64 2 (PI.f64)) 0)) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (+.f64 2 (.f64 2 (-.f64 (PI.f64) 1))))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (+.f64 2 (.f64 -2 (-.f64 1 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (+.f64 (*.f64 2 (PI.f64)) 0)) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (+.f64 2 (.f64 2 (-.f64 (PI.f64) 1))))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (+.f64 2 (.f64 -2 (-.f64 1 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (+.f64 (*.f64 2 (PI.f64)) 0)) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (+.f64 2 (.f64 2 (-.f64 (PI.f64) 1))))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (+.f64 2 (.f64 -2 (-.f64 1 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (+.f64 (*.f64 2 (PI.f64)) 0)) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (+.f64 2 (.f64 2 (-.f64 (PI.f64) 1))))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (+.f64 2 (.f64 -2 (-.f64 1 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (+.f64 (log.f64 (+.f64 (*.f64 2 (PI.f64)) 0)) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (.f64 -2 (-.f64 (PI.f64) 1)) 2))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (-.f64 (.f64 (PI.f64) -2) -2) 2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (-.f64 (.f64 (PI.f64) -2) 2) -2))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (.f64 -2 (-.f64 (PI.f64) 1)) 2))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (-.f64 (.f64 (PI.f64) -2) -2) 2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (-.f64 (.f64 (PI.f64) -2) 2) -2))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (.f64 -2 (-.f64 (PI.f64) 1)) 2))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (-.f64 (.f64 (PI.f64) -2) -2) 2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (-.f64 (.f64 (PI.f64) -2) 2) -2))) (*.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (.f64 -2 (-.f64 (PI.f64) 1)) 2))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (-.f64 (.f64 (PI.f64) -2) -2) 2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 (-.f64 (.f64 (PI.f64) -2) 2) -2))) (*.f64 -1/2 (+.f64 k -1))))
(sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (*.f64 n (-.f64 (PI.f64) 1)))))
(sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (*.f64 -2 (-.f64 1 (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))
(+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1)))))) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))))))
(+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 -1/2 (.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64))))))))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
(+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) 2)) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))))) (+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1)))))) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (*.f64 n (-.f64 (PI.f64) 1)))))))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 -1/2 (.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))))))) (.f64 1/8 (.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 n (*.f64 -2 (-.f64 1 (PI.f64)))))) 2)))))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (+.f64 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1/8)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) 2)) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))))) (+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) (+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1)))))) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))))) (.f64 -1/48 (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))) 3)) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 2 (.f64 n (-.f64 (PI.f64) 1))))))))))
(+.f64 (.f64 1/8 (.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) 2)))) (+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64))))))))) (.f64 -1/48 (.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) 3)))))))
(+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (+.f64 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1/8)) (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 -1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 3)))))))
(exp.f64 (.f64 -1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (*.f64 2 n))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (log.f64 (+.f64 (.f64 2 n) (.f64 n (*.f64 -2 (-.f64 1 (PI.f64)))))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 -1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (*.f64 2 n))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (log.f64 (+.f64 (.f64 2 n) (.f64 n (*.f64 -2 (-.f64 1 (PI.f64)))))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 -1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (*.f64 2 n))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (log.f64 (+.f64 (.f64 2 n) (.f64 n (*.f64 -2 (-.f64 1 (PI.f64)))))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 -1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (*.f64 2 n))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (log.f64 (+.f64 (.f64 2 n) (.f64 n (*.f64 -2 (-.f64 1 (PI.f64)))))))))
(exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (.f64 2 n))) (+.f64 1 (.f64 -1 k)))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 1/2 (+.f64 1 (.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 1/2 (.f64 1/2 (neg.f64 k)))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (.f64 2 n))) (+.f64 1 (.f64 -1 k)))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 1/2 (+.f64 1 (.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 1/2 (.f64 1/2 (neg.f64 k)))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (.f64 2 n))) (+.f64 1 (.f64 -1 k)))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 1/2 (+.f64 1 (.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 1/2 (.f64 1/2 (neg.f64 k)))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (+.f64 (.f64 2 (.f64 (-.f64 (PI.f64) 1) n)) (.f64 2 n))) (+.f64 1 (.f64 -1 k)))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 1/2 (+.f64 1 (.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 1/2 (.f64 1/2 (neg.f64 k)))))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 2 (.f64 n (-.f64 (PI.f64) 1)))
(.f64 n (.f64 -2 (-.f64 1 (PI.f64))))
(.f64 2 (-.f64 (.f64 (PI.f64) n) n))
(.f64 -1 (.f64 n (+.f64 1 (*.f64 2 (-.f64 (PI.f64) 1)))))
(.f64 n (.f64 -1 (+.f64 1 (*.f64 -2 (-.f64 1 (PI.f64))))))
(-.f64 n (.f64 (PI.f64) (.f64 2 n)))
(.f64 -1 (.f64 n (+.f64 1 (*.f64 2 (-.f64 (PI.f64) 1)))))
(.f64 n (.f64 -1 (+.f64 1 (*.f64 -2 (-.f64 1 (PI.f64))))))
(-.f64 n (.f64 (PI.f64) (.f64 2 n)))
(.f64 -1 (.f64 n (+.f64 1 (*.f64 2 (-.f64 (PI.f64) 1)))))
(.f64 n (.f64 -1 (+.f64 1 (*.f64 -2 (-.f64 1 (PI.f64))))))
(-.f64 n (.f64 (PI.f64) (.f64 2 n)))
(.f64 -1 (.f64 n (+.f64 1 (*.f64 2 (-.f64 (PI.f64) 1)))))
(.f64 n (.f64 -1 (+.f64 1 (*.f64 -2 (-.f64 1 (PI.f64))))))
(-.f64 n (.f64 (PI.f64) (.f64 2 n)))
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(.f64 n (.f64 -1 (+.f64 1 (*.f64 -2 (-.f64 1 (PI.f64))))))
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(-.f64 (.f64 0 (neg.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)))) (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))
(+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) 0) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 -1/2 (+.f64 k -1))) (-.f64 (/.f64 1 (sqrt.f64 k)) 0))
(-.f64 (+.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 2 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (/.f64 2 (sqrt.f64 k)))) (+.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) (/.f64 2 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 -1 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 -1 (/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) 2)))
(/.f64 -1 (/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 -1/2 k))))))
(.f64 2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 -1/2 (+.f64 k -1))) (+.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 -1 (.f64 (/.f64 1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 -1/2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 2 (/.f64 (.f64 (sqrt.f64 k) 2) (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 2 (/.f64 (/.f64 1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 -1/2 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 2 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) 1/2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 2 (.f64 (/.f64 1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))) (.f64 (sqrt.f64 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 2 (/.f64 1 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (.f64 1/2 (sqrt.f64 k)) (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (/.f64 1/2 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))) (/.f64 1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (/.f64 1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))) (/.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 1/2 (.f64 (.f64 1/2 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 1 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) (/.f64 2 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 -1 (+.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (.f64 1 (/.f64 -1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) (/.f64 1/2 (sqrt.f64 k))) 1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 (/.f64 1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))) 1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) (/.f64 2 (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 2) (.f64 (sqrt.f64 k) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (.f64 -1/2 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))) (.f64 (neg.f64 (sqrt.f64 k)) 1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 1/2) (.f64 (sqrt.f64 k) 1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 -1/2 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2))) 1/2) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) 1/2) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 -1 (/.f64 (+.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 -1/2 k))))))
(.f64 2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 -1/2 (+.f64 k -1))) (+.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) 2) 1/2) (/.f64 (sqrt.f64 k) 1/4))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 0) (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(/.f64 (-.f64 (+.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 2)) (+.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) 2) (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (*.f64 k -1/2) 1/2)) 2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 (+.f64 k -1))) (sqrt.f64 k))

localize42.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 n (PI.f64))
✓	0.4b	(/.f64 (*.f64 n (PI.f64)) 1/3)
✓	0.5b	(pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (.f64 n (PI.f64)) 1/3))) (-.f64 1/2 (/.f64 k 2)))
✓	1.1b	(+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (*.f64 n (PI.f64)) 1/3))

Compiler

Compiled 100 to 63 computations (37% saved)

series2.0ms (0%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (.f64 n (PI.f64)) 1/3))) (-.f64 1/2 (/.f64 k 2)))
0.0ms	n	@	0	(+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (*.f64 n (PI.f64)) 1/3))
0.0ms	n	@	-inf	(pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (.f64 n (PI.f64)) 1/3))) (-.f64 1/2 (/.f64 k 2)))
0.0ms	n	@	inf	(pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (.f64 n (PI.f64)) 1/3))) (-.f64 1/2 (/.f64 k 2)))
0.0ms	n	@	0	(pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (.f64 n (PI.f64)) 1/3))) (-.f64 1/2 (/.f64 k 2)))

rewrite64.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

872×	`rational.json-simplify-29`
858×	`rational.json-simplify-42`
752×	`rational.json-1`
752×	`rational.json-2`
752×	`rational.json-4`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	109
1	120	109
2	352	93
3	1716	93

Stop Event

1×	node limit

Counts

3 → 186

Calls

Call 1

Inputs

(+.f64 (*.f64 n (*.f64 (PI.f64) -2)) (/.f64 (*.f64 n (PI.f64)) 1/3))

(pow.f64 (*.f64 2 (+.f64 (*.f64 n (*.f64 (PI.f64) -2)) (/.f64 (*.f64 n (PI.f64)) 1/3))) (-.f64 1/2 (/.f64 k 2)))

(/.f64 (*.f64 n (PI.f64)) 1/3)

Outputs

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simplify109.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1350×	`rational.json-simplify-37`
1342×	`rational.json-simplify-33`
978×	`rational.json-simplify-1`
628×	`rational.json-simplify-24`
616×	`rational.json-simplify-50`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	430	7452
1	1314	5712
2	5328	5004

Stop Event

1×	node limit

Counts

234 → 239

Calls

Call 1

Inputs
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
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(/.f64 (-.f64 (+.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 (.f64 n -2) (.f64 n 3))) 2) (+.f64 1/2 (.f64 k -1/2))) (.f64 2 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 (.f64 n -2) (.f64 n 3))) 2) (+.f64 1/2 (.f64 k -1/2))))) (+.f64 (.f64 2 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 (.f64 n -2) (.f64 n 3))) 2) (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 (.f64 n -2) (.f64 n 3))) 2) (+.f64 1/2 (*.f64 k -1/2)))))) -1)
(/.f64 (-.f64 (+.f64 (neg.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 (.f64 n -2) (.f64 n 3))) 2) (+.f64 1/2 (.f64 k -1/2)))) (neg.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 (.f64 n -2) (.f64 n 3))) 2) (+.f64 1/2 (.f64 k -1/2))))) (neg.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 (.f64 n -2) (.f64 n 3))) 2) (+.f64 1/2 (*.f64 k -1/2))))) -1)
(neg.f64 (neg.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 (.f64 n -2) (.f64 n 3))) 2) (+.f64 1/2 (*.f64 k -1/2)))))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) 0)
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (-.f64 n n))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (*.f64 (PI.f64) 0))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (*.f64 (PI.f64) (-.f64 n n)))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 0 (/.f64 1/3 (PI.f64))))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 0 (*.f64 (/.f64 1 (PI.f64)) 1/3)))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 (*.f64 0 (neg.f64 n)) 1/3))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 0 (/.f64 1/3 (neg.f64 n))))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 (.f64 (PI.f64) 3) 0))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 (.f64 n -3) 0))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 (*.f64 0 (-.f64 (PI.f64) n)) 1/3))
(+.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 (*.f64 0 (-.f64 n (PI.f64))) 1/3))
(+.f64 0 (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (.f64 (PI.f64) (.f64 n -3)) (*.f64 n (/.f64 (PI.f64) 1/6)))
(+.f64 (-.f64 n n) (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (.f64 (PI.f64) 0) (.f64 n (*.f64 (PI.f64) 3)))
(+.f64 (.f64 n (/.f64 (PI.f64) 1/6)) (.f64 (PI.f64) (*.f64 n -3)))
(+.f64 (.f64 (PI.f64) (-.f64 n n)) (.f64 n (*.f64 (PI.f64) 3)))
(+.f64 (.f64 (.f64 n (PI.f64)) 3/2) (.f64 (.f64 n (PI.f64)) 3/2))
(+.f64 (.f64 (.f64 n (PI.f64)) 3/2) (.f64 1 (.f64 (*.f64 n (PI.f64)) 3/2)))
(+.f64 (/.f64 0 (/.f64 1/3 (PI.f64))) (.f64 n (.f64 (PI.f64) 3)))
(+.f64 (/.f64 0 (.f64 (/.f64 1 (PI.f64)) 1/3)) (.f64 n (*.f64 (PI.f64) 3)))
(+.f64 (.f64 (.f64 n (.f64 (PI.f64) 3)) 1/2) (.f64 (*.f64 n (PI.f64)) 3/2))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) 0)
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (-.f64 n n))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (*.f64 (PI.f64) 0))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (*.f64 (PI.f64) (-.f64 n n)))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 0 (/.f64 1/3 (PI.f64))))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 0 (*.f64 (/.f64 1 (PI.f64)) 1/3)))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (/.f64 0 (/.f64 1/3 (neg.f64 n))))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (*.f64 3/2 (-.f64 n n)))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 3/2 (.f64 (PI.f64) 0)))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 (.f64 (PI.f64) 3) 0))
(-.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 (.f64 n -3) 0))
(-.f64 0 (.f64 (PI.f64) (.f64 n -3)))
(-.f64 0 (.f64 1/2 (neg.f64 (.f64 n (/.f64 (PI.f64) 1/6)))))
(-.f64 (.f64 (PI.f64) (.f64 n -3)) (/.f64 (*.f64 n (/.f64 (PI.f64) 1/6)) -1))
(-.f64 (.f64 (PI.f64) (.f64 n -3)) (/.f64 (.f64 n (.f64 (PI.f64) 2)) -1/3))
(-.f64 (.f64 (PI.f64) (.f64 n -3)) (/.f64 (*.f64 (PI.f64) 2) (/.f64 1/3 (neg.f64 n))))
(-.f64 (.f64 (PI.f64) (.f64 n -3)) (.f64 -1 (.f64 n (/.f64 (PI.f64) 1/6))))
(-.f64 (.f64 (PI.f64) (.f64 n -3)) (.f64 (.f64 n -3) (*.f64 (PI.f64) 2)))
(-.f64 (-.f64 n n) (.f64 (PI.f64) (.f64 n -3)))
(-.f64 (.f64 (PI.f64) 0) (.f64 (PI.f64) (*.f64 n -3)))
(-.f64 (.f64 n (/.f64 (PI.f64) 1/6)) (.f64 n (*.f64 (PI.f64) 3)))
(-.f64 (+.f64 (.f64 n (/.f64 (PI.f64) 1/6)) (.f64 n (/.f64 (PI.f64) 1/6))) (+.f64 (.f64 n (.f64 (PI.f64) 3)) (*.f64 n (/.f64 (PI.f64) 1/6))))
(-.f64 (+.f64 (.f64 n (/.f64 (PI.f64) 1/6)) (.f64 n (/.f64 (PI.f64) 1/6))) (.f64 1 (+.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 n (/.f64 (PI.f64) 1/6)))))
(-.f64 (/.f64 0 (/.f64 1/3 (PI.f64))) (.f64 (PI.f64) (.f64 n -3)))
(-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64))))
(-.f64 (/.f64 0 (.f64 (/.f64 1 (PI.f64)) 1/3)) (.f64 (PI.f64) (*.f64 n -3)))
(-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (.f64 (/.f64 1 (PI.f64)) 1/3)) (/.f64 (+.f64 n (+.f64 n n)) (.f64 (/.f64 1 (PI.f64)) 1/3)))
(-.f64 (/.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (PI.f64) 2)) (/.f64 1/3 n)) (/.f64 (+.f64 (PI.f64) (*.f64 (PI.f64) 2)) (/.f64 1/3 n)))
(-.f64 (/.f64 (.f64 0 (neg.f64 n)) 1/3) (.f64 (PI.f64) (*.f64 n -3)))
(-.f64 (/.f64 (.f64 2 (.f64 n (.f64 (PI.f64) 2))) 1/3) (/.f64 (+.f64 (.f64 n (PI.f64)) (.f64 n (.f64 (PI.f64) 2))) 1/3))
(-.f64 (/.f64 (-.f64 n n) -1/3) (.f64 (PI.f64) (.f64 n -3)))
(-.f64 (/.f64 0 (/.f64 1/3 (neg.f64 n))) (.f64 (PI.f64) (.f64 n -3)))
(-.f64 (.f64 0 (.f64 n -3)) (.f64 (PI.f64) (.f64 n -3)))
(-.f64 (.f64 (+.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 n (/.f64 (PI.f64) 1/6))) 1/2) (.f64 (.f64 n (PI.f64)) 3/2))
(-.f64 (.f64 (.f64 (.f64 n (/.f64 (PI.f64) 1/6)) 2) 1/2) (.f64 n (*.f64 (PI.f64) 3)))
(-.f64 (.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (PI.f64) 2)) (.f64 n 3)) (.f64 (.f64 n 3) (+.f64 (PI.f64) (*.f64 (PI.f64) 2))))
(-.f64 (.f64 (+.f64 (.f64 n (PI.f64)) (.f64 n (.f64 (PI.f64) 2))) 3/2) (.f64 (.f64 n (PI.f64)) 3/2))
(-.f64 (.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (.f64 (PI.f64) 3)) (.f64 (.f64 (PI.f64) 3) (+.f64 n (+.f64 n n))))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (PI.f64) (.f64 n 3))
(.f64 (.f64 n (*.f64 (PI.f64) -2)) -3/2)
(.f64 (.f64 n (PI.f64)) 3)
(.f64 (.f64 n (*.f64 (PI.f64) 3)) 1)
(.f64 1/2 (.f64 n (/.f64 (PI.f64) 1/6)))
(.f64 1 (.f64 n (*.f64 (PI.f64) 3)))
(.f64 (.f64 n 3) (PI.f64))
(.f64 3/2 (.f64 n (*.f64 (PI.f64) 2)))
(.f64 -1 (.f64 (PI.f64) (*.f64 n -3)))
(.f64 (.f64 n (neg.f64 (PI.f64))) -3)
(*.f64 (neg.f64 n) (/.f64 (PI.f64) -1/3))
(*.f64 (neg.f64 n) (/.f64 -1 (/.f64 1/3 (PI.f64))))
(.f64 (neg.f64 n) (/.f64 -1 (.f64 (/.f64 1 (PI.f64)) 1/3)))
(.f64 (.f64 (PI.f64) (*.f64 n -3)) -1)
(.f64 (.f64 n (*.f64 (PI.f64) 2)) 3/2)
(.f64 (neg.f64 (PI.f64)) (.f64 n -3))
(*.f64 (neg.f64 (PI.f64)) (/.f64 -1 (/.f64 1/3 n)))
(.f64 (.f64 (PI.f64) 2) (.f64 (.f64 n 3) 1/2))
(.f64 (.f64 (PI.f64) 2) (/.f64 n 2/3))
(.f64 (.f64 (PI.f64) 2) (-.f64 (.f64 n 3) (.f64 (*.f64 n 3) 1/2)))
(.f64 (.f64 (PI.f64) 2) (-.f64 (*.f64 n 3) (/.f64 n 2/3)))
(.f64 (/.f64 n 1/6) (.f64 1/2 (PI.f64)))
(.f64 3 (.f64 n (PI.f64)))
(.f64 (.f64 (PI.f64) 3) n)
(.f64 (+.f64 n n) (.f64 (PI.f64) 3/2))
(*.f64 (+.f64 n n) (/.f64 1/2 (/.f64 1/3 (PI.f64))))
(.f64 (+.f64 n n) (/.f64 1/2 (.f64 (/.f64 1 (PI.f64)) 1/3)))
(*.f64 (+.f64 n n) (/.f64 3/2 (/.f64 1 (PI.f64))))
(.f64 (.f64 n (/.f64 (PI.f64) 1/6)) 1/2)
(.f64 -1/2 (+.f64 (.f64 (PI.f64) (.f64 n -3)) (.f64 (PI.f64) (*.f64 n -3))))
(.f64 -1/2 (/.f64 (+.f64 (.f64 n (neg.f64 (PI.f64))) (*.f64 n (neg.f64 (PI.f64)))) 1/3))
(*.f64 -1/2 (/.f64 (+.f64 (neg.f64 (PI.f64)) (neg.f64 (PI.f64))) (/.f64 1/3 n)))
(*.f64 -1/2 (/.f64 (+.f64 (neg.f64 n) (neg.f64 n)) (/.f64 1/3 (PI.f64))))
(.f64 -1/2 (/.f64 (+.f64 (neg.f64 n) (neg.f64 n)) (.f64 (/.f64 1 (PI.f64)) 1/3)))
(.f64 (.f64 n -3) (neg.f64 (PI.f64)))
(*.f64 (/.f64 (PI.f64) -1/3) (neg.f64 n))
(.f64 (.f64 n 1/2) (/.f64 (*.f64 (PI.f64) -2) -1/3))
(.f64 (.f64 (PI.f64) 1/2) (/.f64 n 1/6))
(.f64 (/.f64 (.f64 (PI.f64) -2) -1/3) (*.f64 1/2 n))
(.f64 (.f64 (PI.f64) 3/2) (+.f64 n n))
(.f64 (.f64 (.f64 n 3) 1/2) (.f64 (PI.f64) 2))
(.f64 (+.f64 (.f64 n (neg.f64 (PI.f64))) (*.f64 n (neg.f64 (PI.f64)))) -3/2)
(.f64 (+.f64 (.f64 (PI.f64) (.f64 n -3)) (.f64 (PI.f64) (*.f64 n -3))) -1/2)
(.f64 -3/2 (.f64 n (*.f64 (PI.f64) -2)))
(.f64 -3/2 (+.f64 (.f64 n (neg.f64 (PI.f64))) (*.f64 n (neg.f64 (PI.f64)))))
(*.f64 -3/2 (/.f64 (+.f64 (neg.f64 n) (neg.f64 n)) (/.f64 1 (PI.f64))))
(.f64 (.f64 1/2 n) (/.f64 (*.f64 (PI.f64) -2) -1/3))
(.f64 (/.f64 n 2/3) (.f64 (PI.f64) 2))
(.f64 (.f64 1/2 (PI.f64)) (/.f64 n 1/6))
(neg.f64 (.f64 (PI.f64) (.f64 n -3)))

Outputs
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 n (.f64 (PI.f64) 1))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (.f64 (PI.f64) 1) 2)) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (.f64 (PI.f64) 1) 2)) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (.f64 (PI.f64) 1) 2)) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (.f64 (PI.f64) 1) 2)) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (.f64 (PI.f64) 1) 2)) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (.f64 (PI.f64) 1) 2)) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (.f64 (PI.f64) 1) 2)) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (neg.f64 (log.f64 (/.f64 1 n))))))
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(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
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(-.f64 (.f64 0 (.f64 n -3)) (.f64 (PI.f64) (.f64 n -3)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(-.f64 (.f64 (+.f64 (.f64 n (.f64 (PI.f64) 3)) (.f64 n (/.f64 (PI.f64) 1/6))) 1/2) (.f64 (.f64 n (PI.f64)) 3/2))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(-.f64 (.f64 (.f64 (.f64 n (/.f64 (PI.f64) 1/6)) 2) 1/2) (.f64 n (*.f64 (PI.f64) 3)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(-.f64 (.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (PI.f64) 2)) (.f64 n 3)) (.f64 (.f64 n 3) (+.f64 (PI.f64) (*.f64 (PI.f64) 2))))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(-.f64 (.f64 (+.f64 (.f64 n (PI.f64)) (.f64 n (.f64 (PI.f64) 2))) 3/2) (.f64 (.f64 n (PI.f64)) 3/2))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(-.f64 (.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (.f64 (PI.f64) 3)) (.f64 (.f64 (PI.f64) 3) (+.f64 n (+.f64 n n))))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (PI.f64) (.f64 n 3))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 n (*.f64 (PI.f64) -2)) -3/2)
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 n (PI.f64)) 3)
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 n (*.f64 (PI.f64) 3)) 1)
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 1/2 (.f64 n (/.f64 (PI.f64) 1/6)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 1 (.f64 n (*.f64 (PI.f64) 3)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 n 3) (PI.f64))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 3/2 (.f64 n (*.f64 (PI.f64) 2)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 -1 (.f64 (PI.f64) (*.f64 n -3)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 n (neg.f64 (PI.f64))) -3)
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(*.f64 (neg.f64 n) (/.f64 (PI.f64) -1/3))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(*.f64 (neg.f64 n) (/.f64 -1 (/.f64 1/3 (PI.f64))))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (neg.f64 n) (/.f64 -1 (.f64 (/.f64 1 (PI.f64)) 1/3)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 (PI.f64) (*.f64 n -3)) -1)
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 n (*.f64 (PI.f64) 2)) 3/2)
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (neg.f64 (PI.f64)) (.f64 n -3))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(*.f64 (neg.f64 (PI.f64)) (/.f64 -1 (/.f64 1/3 n)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 (PI.f64) 2) (.f64 (.f64 n 3) 1/2))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 (PI.f64) 2) (/.f64 n 2/3))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 (PI.f64) 2) (-.f64 (.f64 n 3) (.f64 (*.f64 n 3) 1/2)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 (PI.f64) 2) (-.f64 (*.f64 n 3) (/.f64 n 2/3)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (/.f64 n 1/6) (.f64 1/2 (PI.f64)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 3 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 (PI.f64) 3) n)
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (+.f64 n n) (.f64 (PI.f64) 3/2))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(*.f64 (+.f64 n n) (/.f64 1/2 (/.f64 1/3 (PI.f64))))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (+.f64 n n) (/.f64 1/2 (.f64 (/.f64 1 (PI.f64)) 1/3)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(*.f64 (+.f64 n n) (/.f64 3/2 (/.f64 1 (PI.f64))))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 n (/.f64 (PI.f64) 1/6)) 1/2)
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 -1/2 (+.f64 (.f64 (PI.f64) (.f64 n -3)) (.f64 (PI.f64) (*.f64 n -3))))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 -1/2 (/.f64 (+.f64 (.f64 n (neg.f64 (PI.f64))) (*.f64 n (neg.f64 (PI.f64)))) 1/3))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(*.f64 -1/2 (/.f64 (+.f64 (neg.f64 (PI.f64)) (neg.f64 (PI.f64))) (/.f64 1/3 n)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(*.f64 -1/2 (/.f64 (+.f64 (neg.f64 n) (neg.f64 n)) (/.f64 1/3 (PI.f64))))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 -1/2 (/.f64 (+.f64 (neg.f64 n) (neg.f64 n)) (.f64 (/.f64 1 (PI.f64)) 1/3)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 n -3) (neg.f64 (PI.f64)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(*.f64 (/.f64 (PI.f64) -1/3) (neg.f64 n))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 n 1/2) (/.f64 (*.f64 (PI.f64) -2) -1/3))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 (PI.f64) 1/2) (/.f64 n 1/6))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (/.f64 (.f64 (PI.f64) -2) -1/3) (*.f64 1/2 n))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 (PI.f64) 3/2) (+.f64 n n))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 (.f64 n 3) 1/2) (.f64 (PI.f64) 2))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (+.f64 (.f64 n (neg.f64 (PI.f64))) (*.f64 n (neg.f64 (PI.f64)))) -3/2)
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (+.f64 (.f64 (PI.f64) (.f64 n -3)) (.f64 (PI.f64) (*.f64 n -3))) -1/2)
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 -3/2 (.f64 n (*.f64 (PI.f64) -2)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 -3/2 (+.f64 (.f64 n (neg.f64 (PI.f64))) (*.f64 n (neg.f64 (PI.f64)))))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(*.f64 -3/2 (/.f64 (+.f64 (neg.f64 n) (neg.f64 n)) (/.f64 1 (PI.f64))))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 1/2 n) (/.f64 (*.f64 (PI.f64) -2) -1/3))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (/.f64 n 2/3) (.f64 (PI.f64) 2))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(.f64 (.f64 1/2 (PI.f64)) (/.f64 n 1/6))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))
(neg.f64 (.f64 (PI.f64) (.f64 n -3)))
(.f64 (PI.f64) (.f64 n 3))
(.f64 n (.f64 (PI.f64) 3))

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))
✓	0.4b	(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
	1.0b	(log.f64 (*.f64 2 (PI.f64)))
✓	4.8b	(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))

Compiler

Compiled 65 to 45 computations (30.8% saved)

series5.0ms (0%)

Counts

3 → 36

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))
0.0ms	k	@	0	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))
0.0ms	k	@	inf	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))
0.0ms	n	@	-inf	(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))
0.0ms	n	@	0	(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))

rewrite75.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

862×	`rational.json-simplify-6`
832×	`rational.json-simplify-3`
778×	`rational.json-simplify-4`
772×	`rational.json-simplify-5`
654×	`rational.json-simplify-12`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	105
1	103	105
2	267	105
3	1219	105

Stop Event

1×	node limit

Counts

3 → 188

Calls

Call 1

Inputs

(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2))

(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))

(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2))) (*.f64 2 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) 0) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 2 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2))) (neg.f64 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simplify124.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1756×	`rational.json-simplify-63`
1178×	`rational.json-simplify-50`
548×	`rational.json-simplify-24`
436×	`rational.json-simplify-5`
396×	`rational.json-simplify-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	381	9632
1	1200	9386
2	5848	9346

Stop Event

1×	node limit

Counts

224 → 250

Calls

Call 1

Inputs
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(exp.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(exp.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(exp.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (+.f64 (log.f64 -1) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (+.f64 (log.f64 -1) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (+.f64 (log.f64 -1) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (+.f64 (log.f64 -1) (log.f64 (*.f64 2 (PI.f64)))))))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))
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Outputs
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(exp.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
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(exp.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
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(exp.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))
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(-.f64 (.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)) (.f64 (sqrt.f64 (/.f64 1 k)) 3)) 1/2) (.f64 1/2 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) (sqrt.f64 (/.f64 1 k)))))
(.f64 1/2 (-.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) 3)) (.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 1/2 (.f64 (exp.f64 (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (-.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 3) (sqrt.f64 (/.f64 1 k)))))
(-.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 (/.f64 1 k))) 2) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)) (*.f64 (sqrt.f64 (/.f64 1 k)) 3)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(-.f64 (.f64 (.f64 (.f64 2 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))) 2) (sqrt.f64 (/.f64 1 k))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)) (*.f64 (sqrt.f64 (/.f64 1 k)) 3)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(-.f64 (.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)) 0) -1) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) (neg.f64 (sqrt.f64 (/.f64 1 k)))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 1/2 (/.f64 (/.f64 1/2 (sqrt.f64 (/.f64 1 k))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 1/2 (/.f64 (/.f64 1/2 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))) (sqrt.f64 (/.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 1/2 (/.f64 (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))) (*.f64 2 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 1/2 (/.f64 (/.f64 1 (sqrt.f64 (/.f64 1 k))) (.f64 2 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 1/2 (/.f64 1 (.f64 2 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)) (sqrt.f64 (/.f64 1 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 1/2 (/.f64 -1 (-.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)) (neg.f64 (sqrt.f64 (/.f64 1 k)))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)) (sqrt.f64 (/.f64 1 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)) (/.f64 1 (sqrt.f64 (/.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)) (neg.f64 (/.f64 -1 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (/.f64 1 k))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (neg.f64 (/.f64 -1 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) (sqrt.f64 (/.f64 1 k))) 1)
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(/.f64 -1 (/.f64 1 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) (neg.f64 (sqrt.f64 (/.f64 1 k))))))
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(/.f64 (neg.f64 (sqrt.f64 (/.f64 1 k))) (/.f64 -1 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))))
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(/.f64 (neg.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2))) (/.f64 -1 (sqrt.f64 (/.f64 1 k))))
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(/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) (neg.f64 (sqrt.f64 (/.f64 1 k)))) -1)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 (.f64 2 (sqrt.f64 (/.f64 1 k))) (/.f64 (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2))) 1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 (.f64 2 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2))) (/.f64 (/.f64 1 (sqrt.f64 (/.f64 1 k))) 1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 k))) (/.f64 1/2 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 (.f64 1/2 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2))) (/.f64 1/2 (sqrt.f64 (/.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 (.f64 (-.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) 1/2)) (neg.f64 (sqrt.f64 (/.f64 1 k)))) (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) (sqrt.f64 (/.f64 1 k)))) 1/2) -1)
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(neg.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)) (neg.f64 (sqrt.f64 (/.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))

eval760.0ms (5.9%)

Compiler: Compiled 48642 to 31281 computations (35.7% saved)

prune582.0ms (4.5%)

Pruning

41 alts after pruning (32 fresh and 9 done)

	Pruned	Kept	Total
New	1753	13	1766
Fresh	12	19	31
Picked	0	1	1
Done	0	8	8
Total	1765	41	1806

Error

0.1b

Counts

1806 → 41

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.7b	(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
▶	0.7b	(/.f64 (pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
	0.9b	(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (.f64 n (PI.f64)) 4) (.f64 n (*.f64 (PI.f64) 3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (.f64 2 (-.f64 n (-.f64 n (.f64 n (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (.f64 n (PI.f64)) 1/3))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.9b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (PI.f64) (.f64 (/.f64 1 n) 1/3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	1.4b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.2b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (-.f64 (.f64 (.f64 n (PI.f64)) 12) (.f64 (*.f64 n (PI.f64)) 9)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.2b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (-.f64 (.f64 (PI.f64) (.f64 n -3)) (/.f64 (.f64 (PI.f64) 2) (/.f64 1/3 (neg.f64 n)))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.9b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (/.f64 (.f64 (.f64 n (PI.f64)) 6) 1/3) (/.f64 (.f64 (*.f64 n (PI.f64)) -5) 1/3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (.f64 (.f64 n (PI.f64)) 6) 3) (.f64 3 (.f64 (*.f64 n (PI.f64)) -5))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.6b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (PI.f64) (.f64 3 (.f64 n -4))) (.f64 (.f64 n (PI.f64)) 15)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (/.f64 n (/.f64 1 (PI.f64))) 3))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.3b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (neg.f64 n) (/.f64 -1 (/.f64 1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 n 3) (.f64 (+.f64 n n) 2)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.7b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))))
	22.1b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
✓	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
	0.8b	(/.f64 1 (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k)))
	1.2b	(-.f64 (.f64 (/.f64 4 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))))
	3.6b	(-.f64 (.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))) (.f64 (sqrt.f64 (/.f64 1 k)) 4)) (.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))) (.f64 3 (sqrt.f64 (/.f64 1 k)))))
	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (-.f64 (.f64 n 3) (*.f64 n 4)) (neg.f64 (/.f64 1/2 (PI.f64)))) (/.f64 (-.f64 k 1) -2)))
✓	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))
✓	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 2 (/.f64 (/.f64 1 (PI.f64)) n)) (/.f64 (-.f64 k 1) -2)))
▶	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (.f64 n -2))) (/.f64 (-.f64 k 1) -2)))
✓	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (neg.f64 n) (.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2)))
	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (+.f64 (-.f64 n (+.f64 (.f64 2 (*.f64 n (PI.f64))) (+.f64 n n))) (+.f64 n n))) (/.f64 (-.f64 k 1) -2)))
	21.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 -1/2 (.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))))))) (.f64 1/8 (.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) 2))))))
	21.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (+.f64 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1/8)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
	21.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))))
▶	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))
	3.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
	0.9b	(.f64 (-.f64 (.f64 1/2 (/.f64 3 (sqrt.f64 k))) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))
	25.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 (log.f64 n) 2)) (log.f64 n)) 1/2)))
✓	3.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
✓	25.0b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))

Compiler

Compiled 1993 to 1549 computations (22.3% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
	0.2b	(*.f64 (PI.f64) (+.f64 n n))
✓	0.3b	(-.f64 (*.f64 (PI.f64) (+.f64 n n)) n)
✓	0.5b	(pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k)))

Compiler

Compiled 73 to 26 computations (64.4% saved)

series3.0ms (0%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(/.f64 (pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
0.0ms	k	@	-inf	(/.f64 (pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
0.0ms	k	@	inf	(/.f64 (pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
0.0ms	k	@	0	(pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k)))
0.0ms	n	@	0	(pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k)))

rewrite75.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

794×	`rational.json-1`
794×	`rational.json-2`
794×	`rational.json-4`
794×	`rational.json-3`
676×	`rational.json-simplify-23`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	121
1	106	121
2	364	97
3	1897	97

Stop Event

1×	node limit

Counts

3 → 205

Calls

Call 1

Inputs

(pow.f64 (+.f64 n (-.f64 (*.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (*.f64 1/2 k)))

(-.f64 (*.f64 (PI.f64) (+.f64 n n)) n)

(/.f64 (pow.f64 (+.f64 n (-.f64 (*.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 0) (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))) (*.f64 1/2 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))) (neg.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))) (*.f64 -1 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 2) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 3) 1/2) (*.f64 1/2 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 2) (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 2)) (+.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 2) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 0) (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 3) (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (neg.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (+.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (-.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (-.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (*.f64 1 (neg.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (/.f64 1/2 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 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simplify133.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1036×	`rational.json-simplify-24`
640×	`rational.json-simplify-50`
616×	`rational.json-simplify-42`
488×	`rational.json-simplify-63`
486×	`rational.json-simplify-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	462	10447
1	1481	10113
2	7951	10093

Stop Event

1×	node limit

Counts

253 → 279

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(.f64 -1 (.f64 (+.f64 1 (*.f64 -2 (PI.f64))) n))
(.f64 -1 (.f64 (+.f64 1 (*.f64 -2 (PI.f64))) n))
(.f64 -1 (.f64 (+.f64 1 (*.f64 -2 (PI.f64))) n))
(.f64 -1 (.f64 (+.f64 1 (*.f64 -2 (PI.f64))) n))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
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(-.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 3))
(-.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 3) 1/2) (.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))
(-.f64 (+.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2)) (+.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 3)))
(.f64 1/2 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 1)
(.f64 1 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)))
(.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 1/2)
(.f64 -1 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))))
(.f64 -1 (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 0) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))))
(.f64 -1 (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 3) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2)))
(.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) -1)
(.f64 -1/2 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)))
(.f64 -1/2 (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))
(.f64 -1/2 (-.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 3)))
(.f64 -1/2 (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2)))
(.f64 -1/2 (.f64 1 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2))))
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)) -1/2)
(.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) 1/4)
(.f64 (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))) -1/2)
(/.f64 1/2 (/.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 1)
(/.f64 1 (/.f64 1 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))
(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2)
(/.f64 -1 (/.f64 1 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))
(/.f64 -1 (/.f64 -1 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))))
(/.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2))) -1)
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(.f64 1 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2))
(.f64 -1 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k))))
(.f64 -1 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (sqrt.f64 k)) 0) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (sqrt.f64 k))))
(.f64 -1 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (sqrt.f64 k)) 3) (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (/.f64 (sqrt.f64 k) 2)) 2)))
(.f64 -1 (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 0) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (sqrt.f64 k))))
(.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (-.f64 0 (/.f64 1 (sqrt.f64 k))))
(.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (/.f64 -1 (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)))
(.f64 -1/2 (+.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k)))))
(.f64 -1/2 (/.f64 (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))) (sqrt.f64 k)))
(.f64 -1/2 (-.f64 0 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (/.f64 (sqrt.f64 k) 2))))
(.f64 -1/2 (-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (/.f64 (sqrt.f64 k) 2))))
(.f64 -1/2 (-.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (sqrt.f64 k)) (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (sqrt.f64 k)) 3)))
(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (/.f64 (sqrt.f64 k) 2)) 1/2)
(.f64 2 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (/.f64 1/2 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k))) -1)
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (/.f64 -1 (/.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)))))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (-.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 3)))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2)))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (.f64 1 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2))))
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)) (/.f64 -1/2 (sqrt.f64 k)))
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2)) (.f64 1 (/.f64 -1/2 (sqrt.f64 k))))
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)) (-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(.f64 (.f64 1/2 (/.f64 1/2 (sqrt.f64 k))) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 2))
(.f64 (.f64 1/2 (/.f64 1/2 (sqrt.f64 k))) (/.f64 2 (/.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))
(.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)
(.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (*.f64 1/2 (/.f64 1/2 (sqrt.f64 k))))
(.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (.f64 1 (.f64 1/2 (/.f64 1/2 (sqrt.f64 k)))))
(.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (*.f64 (/.f64 1/2 (sqrt.f64 k)) 1/2))
(.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (-.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 1/2 (/.f64 1/2 (sqrt.f64 k)))))
(.f64 (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))) (/.f64 -1/2 (sqrt.f64 k)))
(.f64 (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)))) (.f64 1 (/.f64 -1/2 (sqrt.f64 k))))
(.f64 (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)))) (.f64 (/.f64 1 (sqrt.f64 k)) -1/2))
(.f64 (+.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k)))) -1/2)
(.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))))
(.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 0) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))))
(.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 3) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2)))
(neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k))))

Outputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (sqrt.f64 2) k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (.f64 -1/2 (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 1/8 (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (sqrt.f64 2) k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) -1/2)) (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 1/8))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (.f64 -1/2 (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 1/8 (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3))) (.f64 -1/48 (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (sqrt.f64 2) k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) -1/2)) (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) -1/48)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(-.f64 (.f64 n (.f64 2 (PI.f64))) n)
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(-.f64 (.f64 n (.f64 2 (PI.f64))) n)
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(-.f64 (.f64 n (.f64 2 (PI.f64))) n)
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(-.f64 (.f64 n (.f64 2 (PI.f64))) n)
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(-.f64 (.f64 n (.f64 2 (PI.f64))) n)
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(-.f64 (.f64 n (.f64 2 (PI.f64))) n)
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(-.f64 (.f64 n (.f64 2 (PI.f64))) n)
(.f64 n (-.f64 (.f64 2 (PI.f64)) 1))
(-.f64 (.f64 n (.f64 2 (PI.f64))) n)
(.f64 -1 (.f64 (+.f64 1 (*.f64 -2 (PI.f64))) n))
(.f64 (+.f64 1 (.f64 (PI.f64) -2)) (*.f64 -1 n))
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(.f64 -1/2 (-.f64 0 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (/.f64 (sqrt.f64 k) 2))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 -1/2 (-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (/.f64 (sqrt.f64 k) 2))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 -1/2 (-.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (sqrt.f64 k)) (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (sqrt.f64 k)) 3)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (/.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 2 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (/.f64 -1 (/.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (-.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 3)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (/.f64 -1/2 (sqrt.f64 k)) (.f64 1 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)) (/.f64 -1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2)) (.f64 1 (/.f64 -1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (neg.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2)) (-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (.f64 1/2 (/.f64 1/2 (sqrt.f64 k))) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) 2) 2))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (.f64 1/2 (/.f64 1/2 (sqrt.f64 k))) (/.f64 2 (/.f64 1/2 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (/.f64 1/2 (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (*.f64 1/2 (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (.f64 1 (.f64 1/2 (/.f64 1/2 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (*.f64 (/.f64 1/2 (sqrt.f64 k)) 1/2))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2) (-.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 1/2 (/.f64 1/2 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)))) (/.f64 -1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)))) (.f64 1 (/.f64 -1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (+.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)))) (.f64 (/.f64 1 (sqrt.f64 k)) -1/2))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (+.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k)))) -1/2)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 0) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (-.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 3) (.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (.f64 k -1/2) -1/2)) 2) 2)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 (*.f64 k -1/2) -1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 (*.f64 k -1/2) -1/2)) (sqrt.f64 k))

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (sqrt.f64 k))
	0.2b	(*.f64 (PI.f64) n)
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))
✓	0.4b	(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))

Compiler

Compiled 38 to 20 computations (47.4% saved)

series5.0ms (0%)

Counts

2 → 0

Calls

9 calls:

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

rewrite58.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

938×	`rational.json-simplify-6`
848×	`rational.json-simplify-3`
844×	`rational.json-simplify-4`
834×	`rational.json-simplify-5`
754×	`rational.json-simplify-24`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	85	48
2	249	48
3	1253	48

Stop Event

1×	node limit

Counts

2 → 135

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))

Outputs

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simplify99.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1116×	`rational.json-simplify-67`
1110×	`rational.json-simplify-1`
1082×	`rational.json-simplify-35`
720×	`rational.json-simplify-50`
680×	`rational.json-simplify-63`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	251	3585
1	830	3585
2	4076	3585
3	7876	3585

Stop Event

1×	node limit

Counts

135 → 136

Calls

Call 1

Inputs
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Outputs
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(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))
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(-.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))) (/.f64 (.f64 2 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 0) (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (/.f64 0 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (+.f64 (/.f64 0 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 0)) (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 0) (/.f64 0 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (+.f64 (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)))) (+.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)))) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)))) (-.f64 (+.f64 (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)))) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (-.f64 (+.f64 (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)))) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (/.f64 0 (sqrt.f64 k)))) (+.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 0) (+.f64 (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))))) (+.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (+.f64 (/.f64 0 (sqrt.f64 k)) (+.f64 (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))))) (+.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (/.f64 (+.f64 (.f64 2 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (.f64 2 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) (sqrt.f64 k)) (/.f64 (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 2 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (/.f64 (+.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) (/.f64 (+.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(-.f64 (/.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 2 (.f64 (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 2 (/.f64 (.f64 (sqrt.f64 k) 2) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 1 (sqrt.f64 k)) (.f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) 1)
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (/.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (/.f64 1 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (sqrt.f64 k) (.f64 2 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 1/2 (.f64 (.f64 1/2 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 1/2 (/.f64 (.f64 1/2 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 -1 (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 -1 (/.f64 (-.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 2 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 -1 (sqrt.f64 k)) (/.f64 -1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))) -1)
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (/.f64 1/2 (sqrt.f64 k))) 1/2)
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 -1/2 (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 2 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (.f64 2 (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))) 2)
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (.f64 2 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (.f64 (sqrt.f64 k) 2))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1/2) (.f64 1/2 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1/2) (.f64 (sqrt.f64 k) 1/2))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2) (.f64 (neg.f64 (sqrt.f64 k)) 1/2))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 0) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (/.f64 1/2 (sqrt.f64 k)))) -1/2)
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) 1/2) 1/2) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) -1/2) 1/2) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (-.f64 0 (.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (/.f64 1/2 (sqrt.f64 k)))) -1/2)
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 k))) -1/2)
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 2 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n)))) 1/2) (/.f64 (sqrt.f64 k) 1/4))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (-.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k)))) -1)
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(neg.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))

localize41.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2))
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (.f64 n -2))) (/.f64 (-.f64 k 1) -2)))
✓	0.3b	(-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (*.f64 n -2))
✓	0.5b	(pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (*.f64 n -2))) (/.f64 (-.f64 k 1) -2))

Compiler

Compiled 102 to 72 computations (29.4% saved)

series42.0ms (0.3%)

Counts

4 → 60

Calls

18 calls:

Time	Variable		Point	Expression
15.0ms	n	@	-inf	(pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (*.f64 n -2))) (/.f64 (-.f64 k 1) -2))
13.0ms	n	@	0	(pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (*.f64 n -2))) (/.f64 (-.f64 k 1) -2))
6.0ms	n	@	inf	(pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (*.f64 n -2))) (/.f64 (-.f64 k 1) -2))
2.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (.f64 n -2))) (/.f64 (-.f64 k 1) -2)))
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (.f64 n -2))) (/.f64 (-.f64 k 1) -2)))

rewrite81.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1346×	`rational.json-1`
1346×	`rational.json-2`
1344×	`rational.json-4`
1344×	`rational.json-3`
1300×	`rational.json-simplify-29`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	184
1	141	160
2	504	142
3	2799	126

Stop Event

1×	node limit

Counts

4 → 246

Calls

Call 1

Inputs
(pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (*.f64 n -2))) (/.f64 (-.f64 k 1) -2))
(-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (*.f64 n -2))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (.f64 n -2))) (/.f64 (-.f64 k 1) -2)))
(.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2))

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

simplify147.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1682×	`rational.json-simplify-21`
658×	`rational.json-simplify-50`
602×	`rational.json-simplify-24`
444×	`rational.json-simplify-2`
430×	`rational.json-simplify-67`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	535	12280
1	1613	11040
2	6998	10926

Stop Event

1×	node limit

Counts

306 → 346

Calls

Call 1

Inputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (neg.f64 (+.f64 (*.f64 -2 (+.f64 1/2 (PI.f64))) 1))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (neg.f64 (+.f64 (*.f64 -2 (+.f64 1/2 (PI.f64))) 1))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (neg.f64 (+.f64 (*.f64 -2 (+.f64 1/2 (PI.f64))) 1))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (neg.f64 (+.f64 (*.f64 -2 (+.f64 1/2 (PI.f64))) 1))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (+.f64 (.f64 -2 (+.f64 1/2 (PI.f64))) 1)))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (+.f64 (.f64 -2 (+.f64 1/2 (PI.f64))) 1)))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (+.f64 (.f64 -2 (+.f64 1/2 (PI.f64))) 1)))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (+.f64 (.f64 -2 (+.f64 1/2 (PI.f64))) 1)))) (-.f64 k 1))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (.f64 2 (+.f64 1/2 (PI.f64)))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (.f64 2 (+.f64 1/2 (PI.f64)))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (.f64 2 (+.f64 1/2 (PI.f64)))))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (.f64 2 (+.f64 1/2 (PI.f64)))))))))
(sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (*.f64 n (+.f64 1/2 (PI.f64))))))
(+.f64 (sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64)))))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))))) (sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64)))))))))
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(+.f64 0 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (.f64 (.f64 n -2) (PI.f64)) (neg.f64 n))
(+.f64 (.f64 (.f64 n -2) (PI.f64)) (+.f64 (neg.f64 n) (*.f64 (PI.f64) 0)))
(+.f64 (.f64 (.f64 n -2) (PI.f64)) (-.f64 (neg.f64 n) (*.f64 (PI.f64) 0)))
(+.f64 (.f64 (.f64 n -2) (PI.f64)) (-.f64 (+.f64 (.f64 n -2) (.f64 (.f64 n -2) (PI.f64))) (.f64 n (*.f64 -2 (+.f64 (PI.f64) 1/2)))))
(+.f64 (.f64 (.f64 n -2) (PI.f64)) (.f64 1 (+.f64 (neg.f64 n) (.f64 (PI.f64) 0))))
(+.f64 (.f64 (.f64 n -2) (PI.f64)) (.f64 1 (-.f64 (neg.f64 n) (.f64 (PI.f64) 0))))
(+.f64 (.f64 (+.f64 (PI.f64) 1/2) (.f64 n -4)) (+.f64 n (*.f64 (+.f64 n n) (PI.f64))))
(+.f64 (neg.f64 n) (.f64 (.f64 n -2) (PI.f64)))
(+.f64 (+.f64 n (.f64 (+.f64 n n) (PI.f64))) (.f64 (+.f64 (PI.f64) 1/2) (*.f64 n -4)))
(+.f64 (-.f64 n n) (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (.f64 (PI.f64) 0) (.f64 n (*.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (+.f64 (neg.f64 n) (.f64 (PI.f64) 0)) (.f64 (*.f64 n -2) (PI.f64)))
(+.f64 (neg.f64 (-.f64 n n)) (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (neg.f64 (.f64 (PI.f64) 0)) (.f64 n (*.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (-.f64 (neg.f64 n) (.f64 (PI.f64) 0)) (.f64 (*.f64 n -2) (PI.f64)))
(+.f64 (.f64 (+.f64 (PI.f64) 1/2) (-.f64 n n)) (.f64 n (*.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (-.f64 (.f64 (PI.f64) 0) (-.f64 n n)) (.f64 n (*.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (-.f64 (-.f64 n n) (.f64 (PI.f64) 0)) (.f64 n (*.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (-.f64 (+.f64 (.f64 n -2) (.f64 (.f64 n -2) (PI.f64))) (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2)))) (.f64 (*.f64 n -2) (PI.f64)))
(+.f64 (.f64 (.f64 (PI.f64) 2) (.f64 n -2)) (.f64 -2 (*.f64 n (-.f64 1/2 (PI.f64)))))
(+.f64 (.f64 (neg.f64 n) 1/2) (.f64 1/2 (+.f64 n (.f64 (+.f64 (PI.f64) 1/2) (.f64 n -4)))))
(+.f64 (.f64 (.f64 (PI.f64) 0) -2) (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) 1/2) (.f64 1/2 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2)))))
(+.f64 (.f64 (.f64 (.f64 n -2) (PI.f64)) 1/2) (.f64 1/2 (+.f64 (.f64 n -2) (.f64 (*.f64 n -2) (PI.f64)))))
(+.f64 (.f64 (+.f64 (.f64 n -2) (.f64 (.f64 n -2) (PI.f64))) 1/2) (.f64 1/2 (.f64 (*.f64 n -2) (PI.f64))))
(+.f64 (.f64 0 (.f64 -2 (+.f64 (PI.f64) 1/2))) (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (.f64 (+.f64 n n) (.f64 -2 (+.f64 (PI.f64) 1/2))) (.f64 (.f64 -2 (+.f64 (PI.f64) 1/2)) (neg.f64 n)))
(+.f64 (.f64 0 (.f64 (+.f64 (PI.f64) 1/2) 2)) (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))))
(+.f64 (.f64 (neg.f64 n) (.f64 (+.f64 (PI.f64) 1/2) 2)) (*.f64 (PI.f64) 0))
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) 0)
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (-.f64 n n))
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (*.f64 (PI.f64) 0))
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (neg.f64 (-.f64 n n)))
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (neg.f64 (*.f64 (PI.f64) 0)))
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (*.f64 (+.f64 (PI.f64) 1/2) (-.f64 n n)))
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (-.f64 (*.f64 (PI.f64) 0) (-.f64 n n)))
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (-.f64 (-.f64 n n) (*.f64 (PI.f64) 0)))
(-.f64 0 (+.f64 n (*.f64 (+.f64 n n) (PI.f64))))
(-.f64 (.f64 (+.f64 (PI.f64) 1/2) (.f64 n -4)) (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))))
(-.f64 (-.f64 n n) (+.f64 n (*.f64 (+.f64 n n) (PI.f64))))
(-.f64 (.f64 (PI.f64) 0) (+.f64 n (.f64 (+.f64 n n) (PI.f64))))
(-.f64 (+.f64 (.f64 (+.f64 (PI.f64) 1/2) (.f64 n -4)) (.f64 (+.f64 (PI.f64) 1/2) (.f64 n -4))) (+.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (.f64 (+.f64 (PI.f64) 1/2) (.f64 n -4))))
(-.f64 (.f64 0 (neg.f64 (+.f64 (PI.f64) 1/2))) (+.f64 n (.f64 (+.f64 n n) (PI.f64))))
(/.f64 n (/.f64 -1/2 (+.f64 (PI.f64) 1/2)))
(/.f64 n (/.f64 1 (*.f64 -2 (+.f64 (PI.f64) 1/2))))
(/.f64 n (*.f64 -1/2 (/.f64 1 (+.f64 (PI.f64) 1/2))))
(/.f64 -2 (*.f64 (/.f64 1 n) (/.f64 1 (+.f64 (PI.f64) 1/2))))
(/.f64 -2 (/.f64 (/.f64 1 n) (+.f64 (PI.f64) 1/2)))
(/.f64 -2 (*.f64 (/.f64 1 (+.f64 (PI.f64) 1/2)) (/.f64 1 n)))
(/.f64 (*.f64 n -2) (/.f64 1 (+.f64 (PI.f64) 1/2)))
(/.f64 (.f64 n -2) (.f64 -1 (neg.f64 (/.f64 1 (+.f64 (PI.f64) 1/2)))))
(/.f64 1/2 (/.f64 (/.f64 1/2 (+.f64 (PI.f64) 1/2)) (*.f64 n -2)))
(/.f64 1/2 (/.f64 (/.f64 -1/4 n) (+.f64 (PI.f64) 1/2)))
(/.f64 1/2 (/.f64 (/.f64 1/2 n) (*.f64 -2 (+.f64 (PI.f64) 1/2))))
(/.f64 (+.f64 (PI.f64) 1/2) (/.f64 -1/2 n))
(/.f64 (+.f64 (PI.f64) 1/2) (*.f64 -1 (neg.f64 (/.f64 -1/2 n))))
(/.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) 1)
(/.f64 1 (/.f64 -1/2 (*.f64 n (+.f64 (PI.f64) 1/2))))
(/.f64 (neg.f64 n) (/.f64 1/2 (+.f64 (PI.f64) 1/2)))
(/.f64 (+.f64 n n) (neg.f64 (/.f64 1 (+.f64 (PI.f64) 1/2))))
(/.f64 (+.f64 n n) (/.f64 -1 (+.f64 (PI.f64) 1/2)))
(/.f64 (+.f64 n n) (*.f64 1 (neg.f64 (/.f64 1 (+.f64 (PI.f64) 1/2)))))
(/.f64 (neg.f64 (+.f64 (PI.f64) 1/2)) (neg.f64 (/.f64 -1/2 n)))
(/.f64 (neg.f64 (+.f64 (PI.f64) 1/2)) (/.f64 1/2 n))
(/.f64 (neg.f64 (+.f64 (PI.f64) 1/2)) (*.f64 1 (neg.f64 (/.f64 -1/2 n))))
(/.f64 (+.f64 n (*.f64 (+.f64 n n) (PI.f64))) -1)
(/.f64 (*.f64 -2 (+.f64 (PI.f64) 1/2)) (/.f64 1 n))
(/.f64 (*.f64 n (+.f64 (PI.f64) 1/2)) -1/2)
(/.f64 (*.f64 1/2 (+.f64 (PI.f64) 1/2)) (/.f64 -1/4 n))
(/.f64 (/.f64 (*.f64 -2 (+.f64 (PI.f64) 1/2)) 2) (/.f64 1/2 n))
(neg.f64 (+.f64 n (*.f64 (+.f64 n n) (PI.f64))))

Outputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (neg.f64 (+.f64 (*.f64 -2 (+.f64 1/2 (PI.f64))) 1))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (neg.f64 (+.f64 1 (+.f64 -1 (*.f64 -2 (PI.f64)))))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 (.f64 -2 (PI.f64)) 0))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (.f64 -2 (PI.f64)))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (neg.f64 (+.f64 (*.f64 -2 (+.f64 1/2 (PI.f64))) 1))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (neg.f64 (+.f64 1 (+.f64 -1 (*.f64 -2 (PI.f64)))))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 (.f64 -2 (PI.f64)) 0))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (.f64 -2 (PI.f64)))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (neg.f64 (+.f64 (*.f64 -2 (+.f64 1/2 (PI.f64))) 1))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (neg.f64 (+.f64 1 (+.f64 -1 (*.f64 -2 (PI.f64)))))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 (.f64 -2 (PI.f64)) 0))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (.f64 -2 (PI.f64)))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (log.f64 (neg.f64 (+.f64 (*.f64 -2 (+.f64 1/2 (PI.f64))) 1))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (log.f64 (neg.f64 (+.f64 1 (+.f64 -1 (*.f64 -2 (PI.f64)))))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 (.f64 -2 (PI.f64)) 0))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (.f64 -2 (PI.f64)))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (+.f64 (.f64 -2 (+.f64 1/2 (PI.f64))) 1)))) (-.f64 k 1))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 1 (+.f64 -1 (.f64 -2 (PI.f64)))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 (.f64 -2 (PI.f64)) 0))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (+.f64 (.f64 -2 (+.f64 1/2 (PI.f64))) 1)))) (-.f64 k 1))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 1 (+.f64 -1 (.f64 -2 (PI.f64)))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 (.f64 -2 (PI.f64)) 0))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (+.f64 (.f64 -2 (+.f64 1/2 (PI.f64))) 1)))) (-.f64 k 1))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 1 (+.f64 -1 (.f64 -2 (PI.f64)))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 (.f64 -2 (PI.f64)) 0))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (+.f64 (.f64 -2 (+.f64 1/2 (PI.f64))) 1)))) (-.f64 k 1))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 1 (+.f64 -1 (.f64 -2 (PI.f64)))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (.f64 -1/2 (+.f64 k -1))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (+.f64 (.f64 -2 (PI.f64)) 0))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (neg.f64 (.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (.f64 2 (+.f64 1/2 (PI.f64)))))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (+.f64 1 (.f64 (PI.f64) 2))))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (+.f64 1 (.f64 (PI.f64) 2))))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (.f64 2 (+.f64 1/2 (PI.f64)))))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (+.f64 1 (.f64 (PI.f64) 2))))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (+.f64 1 (.f64 (PI.f64) 2))))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (.f64 2 (+.f64 1/2 (PI.f64)))))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (+.f64 1 (.f64 (PI.f64) 2))))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (+.f64 1 (.f64 (PI.f64) 2))))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (.f64 2 (+.f64 1/2 (PI.f64)))))))))
(exp.f64 (.f64 -1/2 (.f64 (+.f64 k -1) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (+.f64 1 (.f64 (PI.f64) 2))))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (-.f64 1 (+.f64 1 (.f64 (PI.f64) 2))))) (+.f64 1/2 (*.f64 -1/2 k))))
(sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (*.f64 n (+.f64 1/2 (PI.f64))))))
(sqrt.f64 (+.f64 n (-.f64 (.f64 -2 n) (.f64 n (+.f64 -1 (*.f64 -2 (PI.f64)))))))
(sqrt.f64 (+.f64 n (.f64 n (-.f64 -1 (.f64 -2 (PI.f64))))))
(+.f64 (sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64)))))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))))) (sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64)))))))))
(+.f64 (sqrt.f64 (+.f64 n (-.f64 (.f64 -2 n) (.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))))) (.f64 (.f64 k (log.f64 (+.f64 n (-.f64 (.f64 -2 n) (.f64 n (+.f64 -1 (.f64 -2 (PI.f64)))))))) (.f64 -1/2 (sqrt.f64 (+.f64 n (-.f64 (.f64 -2 n) (.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))))))))
(+.f64 (sqrt.f64 (+.f64 n (.f64 n (-.f64 -1 (.f64 -2 (PI.f64)))))) (.f64 (.f64 k (log.f64 (+.f64 n (.f64 n (-.f64 -1 (.f64 -2 (PI.f64))))))) (.f64 -1/2 (sqrt.f64 (+.f64 n (.f64 n (-.f64 -1 (*.f64 -2 (PI.f64)))))))))
(+.f64 (sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64)))))) (+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64)))))) 2)) (sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64)))))))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))))) (sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (*.f64 n (+.f64 1/2 (PI.f64))))))))))
(+.f64 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (+.f64 n (-.f64 (.f64 -2 n) (.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))))) 2)) (.f64 1/8 (sqrt.f64 (+.f64 n (-.f64 (.f64 -2 n) (.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))))))) (+.f64 (sqrt.f64 (+.f64 n (-.f64 (.f64 -2 n) (.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))))) (.f64 (.f64 k (log.f64 (+.f64 n (-.f64 (.f64 -2 n) (.f64 n (+.f64 -1 (.f64 -2 (PI.f64)))))))) (.f64 -1/2 (sqrt.f64 (+.f64 n (-.f64 (.f64 -2 n) (.f64 n (+.f64 -1 (*.f64 -2 (PI.f64)))))))))))
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(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
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(.f64 1/2 (+.f64 n (+.f64 (neg.f64 n) (.f64 n (*.f64 (+.f64 1/2 (PI.f64)) -4)))))
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(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
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(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
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(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
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(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
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(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
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(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
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(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
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(+.f64 (.f64 (PI.f64) 0) (.f64 2 (*.f64 (neg.f64 n) (+.f64 1/2 (PI.f64)))))
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) 0)
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (-.f64 n n))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (*.f64 (PI.f64) 0))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (neg.f64 (-.f64 n n)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (neg.f64 (*.f64 (PI.f64) 0)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (*.f64 (+.f64 (PI.f64) 1/2) (-.f64 n n)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (-.f64 (*.f64 (PI.f64) 0) (-.f64 n n)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (-.f64 (-.f64 n n) (*.f64 (PI.f64) 0)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 0 (+.f64 n (*.f64 (+.f64 n n) (PI.f64))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 (.f64 (+.f64 (PI.f64) 1/2) (.f64 n -4)) (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 (-.f64 n n) (+.f64 n (*.f64 (+.f64 n n) (PI.f64))))
(-.f64 (-.f64 n n) (+.f64 n (*.f64 (PI.f64) (+.f64 n n))))
(-.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) 1)) (+.f64 n n))
(-.f64 (+.f64 n (.f64 -2 (.f64 (PI.f64) n))) (+.f64 n n))
(-.f64 (.f64 (PI.f64) 0) (+.f64 n (.f64 (+.f64 n n) (PI.f64))))
(-.f64 (.f64 (PI.f64) 0) (+.f64 n (.f64 (PI.f64) (+.f64 n n))))
(-.f64 (+.f64 (.f64 (+.f64 (PI.f64) 1/2) (.f64 n -4)) (.f64 (+.f64 (PI.f64) 1/2) (.f64 n -4))) (+.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) (.f64 (+.f64 (PI.f64) 1/2) (.f64 n -4))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(-.f64 (.f64 0 (neg.f64 (+.f64 (PI.f64) 1/2))) (+.f64 n (.f64 (+.f64 n n) (PI.f64))))
(-.f64 (.f64 (PI.f64) 0) (+.f64 n (.f64 (PI.f64) (+.f64 n n))))
(/.f64 n (/.f64 -1/2 (+.f64 (PI.f64) 1/2)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 n (/.f64 1 (*.f64 -2 (+.f64 (PI.f64) 1/2))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 n (*.f64 -1/2 (/.f64 1 (+.f64 (PI.f64) 1/2))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 -2 (*.f64 (/.f64 1 n) (/.f64 1 (+.f64 (PI.f64) 1/2))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 -2 (/.f64 (/.f64 1 n) (+.f64 (PI.f64) 1/2)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 -2 (*.f64 (/.f64 1 (+.f64 (PI.f64) 1/2)) (/.f64 1 n)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (*.f64 n -2) (/.f64 1 (+.f64 (PI.f64) 1/2)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (.f64 n -2) (.f64 -1 (neg.f64 (/.f64 1 (+.f64 (PI.f64) 1/2)))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 1/2 (/.f64 (/.f64 1/2 (+.f64 (PI.f64) 1/2)) (*.f64 n -2)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 1/2 (/.f64 (/.f64 -1/4 n) (+.f64 (PI.f64) 1/2)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 1/2 (/.f64 (/.f64 1/2 n) (*.f64 -2 (+.f64 (PI.f64) 1/2))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (+.f64 (PI.f64) 1/2) (/.f64 -1/2 n))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (+.f64 (PI.f64) 1/2) (*.f64 -1 (neg.f64 (/.f64 -1/2 n))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (.f64 n (.f64 -2 (+.f64 (PI.f64) 1/2))) 1)
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 1 (/.f64 -1/2 (*.f64 n (+.f64 (PI.f64) 1/2))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (neg.f64 n) (/.f64 1/2 (+.f64 (PI.f64) 1/2)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (+.f64 n n) (neg.f64 (/.f64 1 (+.f64 (PI.f64) 1/2))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (+.f64 n n) (/.f64 -1 (+.f64 (PI.f64) 1/2)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (+.f64 n n) (*.f64 1 (neg.f64 (/.f64 1 (+.f64 (PI.f64) 1/2)))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (neg.f64 (+.f64 (PI.f64) 1/2)) (neg.f64 (/.f64 -1/2 n)))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (neg.f64 (+.f64 (PI.f64) 1/2)) (/.f64 1/2 n))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (neg.f64 (+.f64 (PI.f64) 1/2)) (*.f64 1 (neg.f64 (/.f64 -1/2 n))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (+.f64 n (*.f64 (+.f64 n n) (PI.f64))) -1)
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (*.f64 -2 (+.f64 (PI.f64) 1/2)) (/.f64 1 n))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (*.f64 n (+.f64 (PI.f64) 1/2)) -1/2)
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (*.f64 1/2 (+.f64 (PI.f64) 1/2)) (/.f64 -1/4 n))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(/.f64 (/.f64 (*.f64 -2 (+.f64 (PI.f64) 1/2)) 2) (/.f64 1/2 n))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)
(neg.f64 (+.f64 n (*.f64 (+.f64 n n) (PI.f64))))
(.f64 n (+.f64 -1 (.f64 -2 (PI.f64))))
(.f64 -2 (.f64 n (+.f64 1/2 (PI.f64))))
(-.f64 (.f64 -2 (.f64 (PI.f64) n)) n)

localize47.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 n (.f64 (PI.f64) -2))
✓	0.3b	(/.f64 (/.f64 1/2 n) (PI.f64))
✓	0.5b	(pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))) (-.f64 1/2 (/.f64 k 2)))
✓	1.1b	(+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))

Compiler

Compiled 115 to 82 computations (28.7% saved)

series3.0ms (0%)

Counts

4 → 60

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	n	@	inf	(/.f64 (/.f64 1/2 n) (PI.f64))
0.0ms	n	@	0	(/.f64 (/.f64 1/2 n) (PI.f64))
0.0ms	k	@	0	(pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))) (-.f64 1/2 (/.f64 k 2)))
0.0ms	n	@	-inf	(/.f64 (/.f64 1/2 n) (PI.f64))
0.0ms	n	@	-inf	(pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))) (-.f64 1/2 (/.f64 k 2)))

rewrite98.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1072×	`rational.json-simplify-67`
992×	`rational.json-1`
992×	`rational.json-2`
992×	`rational.json-4`
992×	`rational.json-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	136
1	133	124
2	478	72
3	2824	72
4	7991	72

Stop Event

1×	node limit

Counts

4 → 416

Calls

Call 1

Inputs
(+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))
(pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))) (-.f64 1/2 (/.f64 k 2)))
(/.f64 (/.f64 1/2 n) (PI.f64))
(.f64 n (.f64 (PI.f64) -2))

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

simplify135.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1246×	`rational.json-simplify-24`
688×	`rational.json-simplify-5`
624×	`rational.json-simplify-13`
604×	`rational.json-simplify-1`
514×	`rational.json-simplify-2`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	811	13580
1	2205	12026

Stop Event

1×	node limit

Counts

476 → 541

Calls

Call 1

Inputs
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (*.f64 n (PI.f64))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))))) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))))))
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(pow.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))) (+.f64 1/2 (.f64 -1/2 k)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(/.f64 1/2 (*.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
(.f64 -2 (.f64 n (PI.f64)))
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(-.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 n (PI.f64)))
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(-.f64 (*.f64 n (PI.f64)) 0)
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(-.f64 (.f64 n (PI.f64)) (.f64 (PI.f64) 0))
(-.f64 (*.f64 n (PI.f64)) (/.f64 0 (/.f64 1 (PI.f64))))
(-.f64 (*.f64 n (PI.f64)) (/.f64 1 (/.f64 (/.f64 -1/2 n) 0)))
(-.f64 (*.f64 n (PI.f64)) (+.f64 (-.f64 n n) (-.f64 n n)))
(-.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (PI.f64) 0) (*.f64 (PI.f64) 0)))
(-.f64 (.f64 n (PI.f64)) (+.f64 (-.f64 n n) (.f64 (PI.f64) 0)))
(-.f64 (.f64 n (PI.f64)) (+.f64 (.f64 0 (.f64 n 3)) (.f64 0 (*.f64 n 3))))
(-.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (PI.f64) 0) (-.f64 n n)))
(-.f64 (.f64 n (PI.f64)) (+.f64 (.f64 n (*.f64 (PI.f64) 0)) (-.f64 n n)))
(-.f64 (.f64 n (PI.f64)) (+.f64 (.f64 n (.f64 (PI.f64) 0)) (.f64 (PI.f64) 0)))
(-.f64 (.f64 n (PI.f64)) (+.f64 0 (.f64 n (*.f64 (PI.f64) 0))))
(-.f64 (.f64 n (PI.f64)) (+.f64 (-.f64 n n) (.f64 n (*.f64 (PI.f64) 0))))
(-.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (PI.f64) 0) (.f64 n (.f64 (PI.f64) 0))))
(-.f64 (.f64 n (PI.f64)) (+.f64 (.f64 n (.f64 (PI.f64) 0)) (.f64 n (*.f64 (PI.f64) 0))))
(-.f64 (.f64 n (PI.f64)) (+.f64 (-.f64 n n) (.f64 0 (*.f64 n 3))))
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(/.f64 n (-.f64 (/.f64 1/2 (PI.f64)) (/.f64 1 (PI.f64))))
(/.f64 (PI.f64) (/.f64 1 (*.f64 n -2)))
(/.f64 -2 (/.f64 1 (*.f64 n (PI.f64))))
(/.f64 (*.f64 (PI.f64) -2) (/.f64 1 n))
(/.f64 (.f64 n (.f64 (PI.f64) -2)) 1)
(/.f64 1 (neg.f64 (/.f64 1/2 (*.f64 n (PI.f64)))))
(/.f64 1 (/.f64 (/.f64 1 n) (*.f64 (PI.f64) -2)))
(/.f64 1 (/.f64 (/.f64 -1/2 (PI.f64)) n))
(/.f64 1 (/.f64 1 (.f64 n (.f64 (PI.f64) -2))))
(/.f64 1 (/.f64 -1 (*.f64 (PI.f64) (+.f64 n n))))
(/.f64 (*.f64 n -2) (/.f64 1 (PI.f64)))
(/.f64 (*.f64 (PI.f64) (+.f64 n n)) -1)
(/.f64 (*.f64 (PI.f64) 2) (neg.f64 (/.f64 1 n)))
(/.f64 (.f64 (PI.f64) 2) (-.f64 (/.f64 1 n) (/.f64 1 (.f64 n 1/2))))
(/.f64 (.f64 (PI.f64) 2) (-.f64 (/.f64 1/2 n) (.f64 (/.f64 1/2 n) 3)))
(/.f64 -1 (/.f64 1/2 (*.f64 n (PI.f64))))
(/.f64 (neg.f64 n) (/.f64 1/2 (PI.f64)))
(/.f64 (.f64 n (.f64 (PI.f64) -4)) 2)
(/.f64 (.f64 -2 (.f64 n 1/2)) (/.f64 1/2 (PI.f64)))
(neg.f64 (*.f64 (PI.f64) (+.f64 n n)))

Outputs
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -2)))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -2)))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -2)))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -2)))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -2)))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -2)))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -2)))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 3 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3)))
(.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -2)))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (.f64 -1 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2))))
(neg.f64 (.f64 n (+.f64 (.f64 (PI.f64) -3) (*.f64 (PI.f64) 2))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (.f64 -1 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2))))
(neg.f64 (.f64 n (+.f64 (.f64 (PI.f64) -3) (*.f64 (PI.f64) 2))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (.f64 -1 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2))))
(neg.f64 (.f64 n (+.f64 (.f64 (PI.f64) -3) (*.f64 (PI.f64) 2))))
(.f64 -1 (.f64 n (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))
(.f64 n (.f64 -1 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2))))
(neg.f64 (.f64 n (+.f64 (.f64 (PI.f64) -3) (*.f64 (PI.f64) 2))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (+.f64 (.f64 (.f64 -2 (PI.f64)) 2) (.f64 (PI.f64) 6))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (+.f64 (.f64 (.f64 -2 (PI.f64)) 2) (.f64 (PI.f64) 6))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (+.f64 (.f64 (.f64 -2 (PI.f64)) 2) (.f64 (PI.f64) 6))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (+.f64 (.f64 (.f64 -2 (PI.f64)) 2) (.f64 (PI.f64) 6))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (+.f64 (.f64 (.f64 -2 (PI.f64)) 2) (*.f64 (PI.f64) 6))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (+.f64 (.f64 (.f64 -2 (PI.f64)) 2) (*.f64 (PI.f64) 6))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (+.f64 (.f64 (.f64 -2 (PI.f64)) 2) (*.f64 (PI.f64) 6))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (+.f64 (.f64 -2 (PI.f64)) (.f64 3 (PI.f64))))) (.f64 -1 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)) 2)) (.f64 -1 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (log.f64 (+.f64 (.f64 (.f64 -2 (PI.f64)) 2) (*.f64 (PI.f64) 6))) (neg.f64 (log.f64 (/.f64 1 n))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (+.f64 (.f64 (PI.f64) 4) (.f64 (*.f64 (PI.f64) -3) 2))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (+.f64 (.f64 (PI.f64) 4) (.f64 (*.f64 (PI.f64) -3) 2))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (+.f64 (.f64 (PI.f64) 4) (.f64 (*.f64 (PI.f64) -3) 2))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 -3 (PI.f64)) (.f64 2 (PI.f64)))))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (+.f64 (.f64 (PI.f64) -3) (.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (+.f64 (.f64 (PI.f64) 4) (.f64 (*.f64 (PI.f64) -3) 2))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (*.f64 n (PI.f64))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))))) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3))))) (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3))))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2))))) (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2))))))) (.f64 -1/2 (sqrt.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -2)))))))
(+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))) 2))) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))))) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (*.f64 n (PI.f64)))))))))
(+.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3))))) (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))))))))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3))))) 2))))))
(+.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2))))) (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2))))))) (.f64 -1/2 (sqrt.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2))))))) (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2)))) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2))))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2))))))
(+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))) 2))) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))))) (+.f64 (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))) 3))) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64)))))))) (sqrt.f64 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))))))))
(+.f64 (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3))))) 2))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3))))) (+.f64 (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3))))) 3))))) (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (*.f64 (PI.f64) 3))))))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2))))) (+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2)))) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2))))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2))))) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2))))))) (.f64 -1/2 (sqrt.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2)))))) (.f64 (.f64 (pow.f64 k 3) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2))))) 3))) (.f64 -1/48 (sqrt.f64 (.f64 (PI.f64) (+.f64 (.f64 n 3) (*.f64 n -2)))))))))
(pow.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2)))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2)))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2)))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 (PI.f64) (+.f64 (.f64 n 3) (.f64 n -2)))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (+.f64 (.f64 3 (.f64 n (PI.f64))) (.f64 -2 (.f64 n (PI.f64))))) (+.f64 1/2 (.f64 -1/2 k)))
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(-.f64 (.f64 n (.f64 -2 (PI.f64))) (+.f64 (.f64 n (.f64 (PI.f64) 0)) (*.f64 -2 (-.f64 n n))))
(-.f64 (.f64 n (/.f64 (PI.f64) -1/2)) (+.f64 (.f64 n (.f64 (PI.f64) 0)) (.f64 n 0)))
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(-.f64 (.f64 n (/.f64 (PI.f64) -1/2)) (+.f64 (.f64 n 0) (*.f64 n 0)))
(-.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 0 (.f64 n -2)) (.f64 0 (.f64 n -2))))
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(-.f64 (.f64 n (/.f64 (PI.f64) -1/2)) (+.f64 (.f64 (PI.f64) (.f64 n -4)) (.f64 (PI.f64) (*.f64 n 4))))
(-.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
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(*.f64 n (/.f64 (PI.f64) -1/2))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 n (*.f64 (PI.f64) 4)))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (PI.f64) (*.f64 n 4)))
(.f64 (PI.f64) (-.f64 (+.f64 n n) (.f64 n 4)))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 n (.f64 (PI.f64) 4)) (.f64 (PI.f64) 0)))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 (PI.f64) 0) (.f64 (PI.f64) (.f64 n 4))))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 n (*.f64 (PI.f64) 4)) (/.f64 0 (/.f64 -1/2 (PI.f64)))))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 (PI.f64) 0) (.f64 (PI.f64) (.f64 n 4))))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 n (.f64 (PI.f64) 4)) (.f64 -2 (-.f64 n n))))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 (PI.f64) (.f64 n 4)) (.f64 -2 (-.f64 n n))))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 (PI.f64) (.f64 n 4)) (.f64 n 0)))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 n (.f64 (PI.f64) 4)) (.f64 0 (*.f64 n -2))))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 (PI.f64) (.f64 n 4)) (.f64 -2 (-.f64 n n))))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 (PI.f64) (.f64 n 4)) (.f64 n 0)))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (/.f64 0 (/.f64 1/2 (PI.f64))) (.f64 n (*.f64 (PI.f64) 4))))
(-.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 (PI.f64) 0) (.f64 (PI.f64) (.f64 n 4))))
(-.f64 (-.f64 n n) (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (.f64 n (.f64 -2 (PI.f64))) (-.f64 n n))
(-.f64 (.f64 n (.f64 (PI.f64) -4)) (.f64 n (.f64 (PI.f64) -2)))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(-.f64 (.f64 n (.f64 (PI.f64) 4)) (.f64 (.f64 n (PI.f64)) 6))
(-.f64 (.f64 (PI.f64) (.f64 n 4)) (.f64 (.f64 n (PI.f64)) 6))
(-.f64 (.f64 (PI.f64) (.f64 n 4)) (.f64 (PI.f64) (.f64 6 n)))
(-.f64 (.f64 n (.f64 (PI.f64) 0)) (*.f64 (PI.f64) (+.f64 n n)))
(-.f64 (.f64 (PI.f64) 0) (.f64 (PI.f64) (+.f64 n n)))
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(*.f64 n (/.f64 (PI.f64) -1/2))
(-.f64 (.f64 (.f64 n (.f64 (PI.f64) -2)) 4) (.f64 n (*.f64 (PI.f64) -6)))
(-.f64 (.f64 (.f64 n (.f64 -2 (PI.f64))) 4) (.f64 n (*.f64 (PI.f64) -6)))
(-.f64 (.f64 (.f64 n (PI.f64)) -8) (.f64 (PI.f64) (.f64 n -6)))
(-.f64 (+.f64 (-.f64 n n) (-.f64 n n)) (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (-.f64 n n) (-.f64 (-.f64 n n) (*.f64 (PI.f64) (+.f64 n n))))
(+.f64 n (-.f64 (-.f64 (-.f64 n n) n) (*.f64 (PI.f64) (+.f64 n n))))
(-.f64 (+.f64 (.f64 (PI.f64) 0) (.f64 (PI.f64) 0)) (+.f64 (.f64 (PI.f64) 0) (.f64 (PI.f64) (+.f64 n n))))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(-.f64 (+.f64 (.f64 (.f64 n (.f64 (PI.f64) -2)) 4) (.f64 (.f64 n (.f64 (PI.f64) -2)) 4)) (+.f64 (.f64 (.f64 n (.f64 (PI.f64) -2)) 4) (.f64 n (*.f64 (PI.f64) -6))))
(-.f64 (.f64 (.f64 n (.f64 -2 (PI.f64))) 4) (.f64 n (*.f64 (PI.f64) -6)))
(-.f64 (.f64 (.f64 n (PI.f64)) -8) (.f64 (PI.f64) (.f64 n -6)))
(-.f64 (-.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 n (.f64 (PI.f64) -4))) (.f64 (*.f64 n (PI.f64)) 8))
(-.f64 (.f64 (PI.f64) (-.f64 (+.f64 n n) (.f64 n -4))) (.f64 n (.f64 8 (PI.f64))))
(-.f64 (-.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (.f64 n (PI.f64)) 6)) (.f64 n (*.f64 (PI.f64) -2)))
(-.f64 (-.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (.f64 n (PI.f64)) 6)) (.f64 n (*.f64 -2 (PI.f64))))
(-.f64 (.f64 (PI.f64) (-.f64 (+.f64 n n) (.f64 n -2))) (.f64 (PI.f64) (.f64 6 n)))
(/.f64 n (/.f64 -1/2 (PI.f64)))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 n (-.f64 (/.f64 1/2 (PI.f64)) (/.f64 1 (PI.f64))))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 (PI.f64) (/.f64 1 (*.f64 n -2)))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 -2 (/.f64 1 (*.f64 n (PI.f64))))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 (*.f64 (PI.f64) -2) (/.f64 1 n))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 (.f64 n (.f64 (PI.f64) -2)) 1)
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 1 (neg.f64 (/.f64 1/2 (*.f64 n (PI.f64)))))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 1 (/.f64 (/.f64 1 n) (*.f64 (PI.f64) -2)))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 1 (/.f64 (/.f64 -1/2 (PI.f64)) n))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 1 (/.f64 1 (.f64 n (.f64 (PI.f64) -2))))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 1 (/.f64 -1 (*.f64 (PI.f64) (+.f64 n n))))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 (*.f64 n -2) (/.f64 1 (PI.f64)))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 (*.f64 (PI.f64) (+.f64 n n)) -1)
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 (*.f64 (PI.f64) 2) (neg.f64 (/.f64 1 n)))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 (.f64 (PI.f64) 2) (-.f64 (/.f64 1 n) (/.f64 1 (.f64 n 1/2))))
(*.f64 2 (/.f64 (PI.f64) (-.f64 (/.f64 1 n) (/.f64 (/.f64 1 n) 1/2))))
(*.f64 2 (/.f64 (PI.f64) (+.f64 (/.f64 1 n) (/.f64 -2 n))))
(/.f64 (.f64 (PI.f64) 2) (-.f64 (/.f64 1/2 n) (.f64 (/.f64 1/2 n) 3)))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 -1 (/.f64 1/2 (*.f64 n (PI.f64))))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 (neg.f64 n) (/.f64 1/2 (PI.f64)))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 (.f64 n (.f64 (PI.f64) -4)) 2)
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(/.f64 (.f64 -2 (.f64 n 1/2)) (/.f64 1/2 (PI.f64)))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))
(neg.f64 (*.f64 (PI.f64) (+.f64 n n)))
(.f64 n (.f64 -2 (PI.f64)))
(*.f64 n (/.f64 (PI.f64) -1/2))

localize62.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2)))
✓	1.0b	(/.f64 1/3 (PI.f64))
✓	1.1b	(-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64))))
✓	1.1b	(+.f64 (.f64 n (.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))

Compiler

Compiled 215 to 98 computations (54.4% saved)

series44.0ms (0.3%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
16.0ms	n	@	0	(pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2)))
14.0ms	n	@	-inf	(pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2)))
6.0ms	n	@	inf	(pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2)))
2.0ms	k	@	0	(pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2)))
1.0ms	n	@	0	(+.f64 (.f64 n (.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))

rewrite76.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1834×	`rational.json-1`
1834×	`rational.json-2`
1834×	`rational.json-4`
1834×	`rational.json-3`
1148×	`rational.json-simplify-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	226
1	169	118
2	677	106
3	4428	106

Stop Event

1×	node limit

Counts

4 → 201

Calls

Call 1

Inputs
(+.f64 (.f64 n (.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))
(-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64))))
(/.f64 1/3 (PI.f64))
(pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2)))

Outputs
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simplify149.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1314×	`rational.json-simplify-63`
1312×	`rational.json-simplify-1`
580×	`rational.json-simplify-24`
562×	`rational.json-simplify-50`
472×	`rational.json-simplify-28`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	477	12665
1	1419	7611
2	6516	7611

Stop Event

1×	node limit

Counts

249 → 287

Calls

Call 1

Inputs
(.f64 n (-.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 12 (PI.f64))) (.f64 9 (PI.f64))))
(.f64 n (-.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 12 (PI.f64))) (.f64 9 (PI.f64))))
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(.f64 n (-.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 12 (PI.f64))) (.f64 9 (PI.f64))))
(.f64 n (-.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 12 (PI.f64))) (.f64 9 (PI.f64))))
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(.f64 -1 (.f64 n (-.f64 (+.f64 (.f64 2 (PI.f64)) (.f64 -12 (PI.f64))) (*.f64 -9 (PI.f64)))))
(.f64 -1 (.f64 n (-.f64 (+.f64 (.f64 2 (PI.f64)) (.f64 -12 (PI.f64))) (*.f64 -9 (PI.f64)))))
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(.f64 -1 (.f64 (-.f64 (.f64 -12 (PI.f64)) (.f64 -9 (PI.f64))) n))
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Outputs
(.f64 n (-.f64 (+.f64 (.f64 -2 (PI.f64)) (.f64 12 (PI.f64))) (.f64 9 (PI.f64))))
(.f64 n (+.f64 (.f64 -2 (PI.f64)) (-.f64 (.f64 (PI.f64) 12) (.f64 (PI.f64) 9))))
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(pow.f64 (.f64 2 (.f64 n (+.f64 (.f64 -2 (PI.f64)) (.f64 (PI.f64) 3)))) (-.f64 1/2 (*.f64 1/2 k)))
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eval1.1s (8.2%)

Compiler: Compiled 53664 to 35059 computations (34.7% saved)

prune893.0ms (6.9%)

Pruning

54 alts after pruning (47 fresh and 7 done)

	Pruned	Kept	Total
New	1886	33	1919
Fresh	13	14	27
Picked	1	0	1
Done	6	7	13
Total	1906	54	1960

Error

0.1b

Counts

1960 → 54

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.7b	(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
	1.5b	(/.f64 (pow.f64 (-.f64 (.f64 2 (.f64 (.f64 n (PI.f64)) 10)) (.f64 3 (.f64 (PI.f64) (.f64 n 6)))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (+.f64 n (/.f64 1 (/.f64 (/.f64 1/2 n) (-.f64 (PI.f64) 1/2)))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
	0.9b	(/.f64 (pow.f64 (+.f64 n (-.f64 (/.f64 (-.f64 (+.f64 (.f64 2 (+.f64 n n)) (.f64 2 (+.f64 n n))) (+.f64 n (+.f64 n (.f64 2 (+.f64 n n))))) (/.f64 1 (PI.f64))) n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
✓	0.7b	(/.f64 (pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (.f64 2 (/.f64 (neg.f64 (PI.f64)) (-.f64 (/.f64 1/2 n) (.f64 (/.f64 1/2 n) 3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	2.7b	(/.f64 (pow.f64 (.f64 2 (-.f64 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (PI.f64) 2)) (/.f64 1/3 (.f64 (+.f64 n n) 2)))) (/.f64 (+.f64 (.f64 (.f64 (+.f64 n n) 2) 2) (+.f64 n (.f64 (/.f64 (.f64 n -2) -2/3) 2))) (/.f64 1/3 (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.5b	(/.f64 (pow.f64 (.f64 2 (-.f64 (+.f64 (.f64 -2 (.f64 n (PI.f64))) (.f64 12 (.f64 n (PI.f64)))) (.f64 3 (.f64 (+.f64 n (.f64 2 n)) (PI.f64))))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
	1.7b	(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (PI.f64) (.f64 (/.f64 (.f64 n -2) -2/3) 3)) (-.f64 (.f64 (PI.f64) (+.f64 (.f64 (.f64 (+.f64 n n) 2) 3) (.f64 n -2))) (.f64 (.f64 n (+.f64 (.f64 (PI.f64) -2) (.f64 (PI.f64) 3))) 2)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.6b	(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) 6)) (.f64 (-.f64 (.f64 (.f64 n -4) -9/4) (*.f64 n -2)) (PI.f64)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.4b	(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (PI.f64) (-.f64 (+.f64 (.f64 n -2) (.f64 (+.f64 n n) 6)) (.f64 (.f64 n -4) -9/4))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (.f64 2 (-.f64 n (-.f64 n (.f64 n (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (*.f64 2 (+.f64 (/.f64 n (/.f64 -1/2 (PI.f64))) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	2.7b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 (.f64 (PI.f64) 4) (.f64 (+.f64 n n) 6)) (-.f64 (.f64 n (/.f64 (PI.f64) -1/2)) (.f64 (+.f64 n (+.f64 (/.f64 (+.f64 n n) 1/3) (*.f64 (+.f64 n n) 4))) (/.f64 (PI.f64) 1/3))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.0b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (-.f64 (neg.f64 (.f64 2 (+.f64 n n))) (neg.f64 (*.f64 -2 (/.f64 n -2/3)))) (/.f64 -1/3 (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.9b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (/.f64 (PI.f64) (/.f64 1/3 n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.6b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 3/2 (-.f64 (+.f64 (.f64 (/.f64 1/2 (.f64 n (PI.f64))) 4) (.f64 (/.f64 1/2 (.f64 n (PI.f64))) 4)) (+.f64 (.f64 (/.f64 1/2 (.f64 n (PI.f64))) 4) (.f64 (/.f64 1/2 (*.f64 n (PI.f64))) 3)))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.9b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (/.f64 (.f64 (.f64 n (PI.f64)) 6) 1/3) (/.f64 (.f64 (*.f64 n (PI.f64)) -5) 1/3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	2.0b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (/.f64 (.f64 (PI.f64) (.f64 4 n)) 1/6) (.f64 (+.f64 n (/.f64 (+.f64 n n) 1/3)) (*.f64 (PI.f64) -3))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (.f64 (.f64 n (PI.f64)) 6) 3) (.f64 3 (.f64 (*.f64 n (PI.f64)) -5))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	3.1b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (.f64 (PI.f64) 4) (.f64 (+.f64 n n) 6)) (/.f64 (+.f64 n (+.f64 (/.f64 (+.f64 n n) 1/3) (*.f64 (+.f64 n n) 4))) (/.f64 -1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.5b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) 6)) (.f64 (PI.f64) (/.f64 (*.f64 n -3) 1/3))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.6b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (PI.f64) (.f64 3 (.f64 n -4))) (.f64 (.f64 n (PI.f64)) 15)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (/.f64 n (/.f64 1 (PI.f64))) 3))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.9b	(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (PI.f64) (/.f64 1 (/.f64 1/3 n))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (+.f64 (*.f64 n 2) (/.f64 n -1/3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (-.f64 (+.f64 (.f64 n -2) (.f64 (+.f64 n n) 6)) (.f64 (.f64 n -4) -9/4)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	22.1b	(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
	22.1b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
	22.2b	(/.f64 2 (.f64 (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (.f64 (sqrt.f64 k) 2)))
✓	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
	22.1b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
	22.2b	(/.f64 1/2 (/.f64 (/.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (/.f64 1 (sqrt.f64 k))))
	1.2b	(-.f64 (.f64 (/.f64 4 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))))
	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (-.f64 (.f64 n 3) (*.f64 n 4)) (neg.f64 (/.f64 1/2 (PI.f64)))) (/.f64 (-.f64 k 1) -2)))
✓	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
	0.7b	(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 2 (/.f64 (/.f64 1 (PI.f64)) n)) (/.f64 (-.f64 k 1) -2)))
	21.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (+.f64 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1/8)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
	21.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64)))))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (+.f64 n (.f64 n (-.f64 -1 (*.f64 -2 (PI.f64)))))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 1 n)))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 n (/.f64 1 (PI.f64))))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 1 (/.f64 (/.f64 1 n) (PI.f64))))))
	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (-.f64 (.f64 (.f64 (PI.f64) n) 4) (*.f64 (PI.f64) (+.f64 n (+.f64 n n)))))))
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (-.f64 n (-.f64 n (*.f64 n (PI.f64)))))))
✓	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))
	3.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
	22.3b	(.f64 (-.f64 (.f64 1/2 (/.f64 3 (sqrt.f64 k))) (/.f64 1/2 (sqrt.f64 k))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))
	25.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 (log.f64 n) 2)) (log.f64 n)) 1/2)))
✓	3.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
✓	25.0b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))

Compiler

Compiled 1426 to 1112 computations (22% saved)

regimes321.0ms (2.5%)

Counts

108 → 1

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 n (/.f64 1 (PI.f64))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 1 n)))))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (-.f64 n (-.f64 n (*.f64 n (PI.f64)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 1 (/.f64 (/.f64 1 n) (PI.f64))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (+.f64 n (.f64 n (-.f64 -1 (*.f64 -2 (PI.f64)))))))
(/.f64 1/2 (/.f64 (/.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (/.f64 1 (sqrt.f64 k))))
(/.f64 2 (.f64 (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (.f64 (sqrt.f64 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (-.f64 (*.f64 n 3) n)) (/.f64 (-.f64 k 1) -2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 2 (/.f64 (/.f64 1 (PI.f64)) n)) (/.f64 (-.f64 k 1) -2)))
(/.f64 1 (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k)))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (+.f64 (.f64 k -1/2) 1/2))))
(/.f64 (/.f64 1 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))) (sqrt.f64 k))
(/.f64 (/.f64 1 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (-.f64 n (-.f64 n (.f64 n (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (+.f64 n (-.f64 (.f64 (PI.f64) (+.f64 n n)) n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (-.f64 (+.f64 n (.f64 -2 n)) (.f64 -2 (.f64 n (+.f64 1/2 (PI.f64)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 n (.f64 2 (*.f64 n (PI.f64))))) (/.f64 (-.f64 k 1) -2)))
(/.f64 2 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2))) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 2 (/.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (+.f64 n (/.f64 1 (/.f64 (/.f64 1/2 n) (-.f64 (PI.f64) 1/2)))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (+.f64 (*.f64 n 2) (/.f64 n -1/3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (neg.f64 n) (.f64 (+.f64 n n) (+.f64 (PI.f64) -1)))) (/.f64 (-.f64 k 1) -2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (/.f64 (-.f64 (.f64 n 3) (*.f64 n 4)) (neg.f64 (/.f64 1/2 (PI.f64)))) (/.f64 (-.f64 k 1) -2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 n 3) (.f64 (+.f64 n n) 2)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (/.f64 (neg.f64 (PI.f64)) (-.f64 (/.f64 1/2 n) (.f64 (/.f64 1/2 n) 3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (-.f64 (.f64 (.f64 n -2) (+.f64 (PI.f64) 1/2)) (.f64 n -2))) (/.f64 (-.f64 k 1) -2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 n (+.f64 (-.f64 n (+.f64 (.f64 2 (*.f64 n (PI.f64))) (+.f64 n n))) (+.f64 n n))) (/.f64 (-.f64 k 1) -2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (-.f64 (+.f64 (.f64 n -2) (.f64 (+.f64 n n) 6)) (.f64 (.f64 n -4) -9/4)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (+.f64 n (-.f64 (/.f64 (-.f64 (+.f64 (.f64 2 (+.f64 n n)) (.f64 2 (+.f64 n n))) (+.f64 n (+.f64 n (.f64 2 (+.f64 n n))))) (/.f64 1 (PI.f64))) n)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (-.f64 (.f64 1/2 (/.f64 3 (sqrt.f64 k))) (/.f64 1/2 (sqrt.f64 k))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 -1/2 (.f64 (-.f64 k 1) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 k -1) (.f64 -1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 (.f64 (.f64 (PI.f64) 3) n) (.f64 (PI.f64) n)) (/.f64 (-.f64 k 1) -2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (-.f64 (.f64 (.f64 (PI.f64) n) 4) (*.f64 (PI.f64) (+.f64 n (+.f64 n n)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 (/.f64 (.f64 n 3) (/.f64 1 (PI.f64))) (*.f64 (PI.f64) n)) (/.f64 (-.f64 k 1) -2)))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (*.f64 n (PI.f64)) 3))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (/.f64 (PI.f64) (/.f64 1/3 n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (.f64 n (PI.f64)) 1/3))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (.f64 n (PI.f64)) 4) (.f64 n (*.f64 (PI.f64) 3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (-.f64 (.f64 1/2 (/.f64 3 (sqrt.f64 k))) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
(.f64 (-.f64 (.f64 1/2 (/.f64 3 (sqrt.f64 k))) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
(.f64 (-.f64 (.f64 1/2 (/.f64 3 (sqrt.f64 k))) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (/.f64 (-.f64 k 1) -2)))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (PI.f64) (/.f64 1 (/.f64 1/3 n))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (/.f64 n (/.f64 1 (PI.f64))) 3))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (PI.f64) (.f64 (/.f64 1 n) 1/3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (+.f64 (/.f64 n (/.f64 -1/2 (PI.f64))) (/.f64 3/2 (/.f64 (/.f64 1/2 n) (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (.f64 (PI.f64) n) 4) (.f64 (PI.f64) (+.f64 n (+.f64 n n))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (-.f64 (.f64 2 (.f64 (.f64 n (PI.f64)) 10)) (.f64 3 (.f64 (PI.f64) (.f64 n 6)))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (-.f64 (.f64 2 (/.f64 2 (sqrt.f64 k))) (.f64 (/.f64 1/2 (sqrt.f64 k)) 6)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
(.f64 (-.f64 (.f64 2 (/.f64 2 (sqrt.f64 k))) (*.f64 (/.f64 1/2 (sqrt.f64 k)) 6)) (pow.f64 (/.f64 n (/.f64 1/2 (PI.f64))) (/.f64 (-.f64 k 1) -2)))
(.f64 (-.f64 (.f64 (.f64 (/.f64 1/2 (sqrt.f64 k)) 6) 1/2) (/.f64 1/2 (sqrt.f64 k))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 k 1) -2)))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (.f64 (neg.f64 n) (/.f64 -1 (/.f64 1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 (/.f64 (.f64 n 4) (/.f64 1/2 (PI.f64))) (/.f64 (*.f64 n 3) (/.f64 1/2 (PI.f64)))) (/.f64 (-.f64 k 1) -2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) 4) (/.f64 1 n)) (/.f64 (.f64 (PI.f64) 6) (/.f64 1 n))) (/.f64 (-.f64 k 1) -2)))
(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) 6)) (.f64 (-.f64 (.f64 (.f64 n -4) -9/4) (*.f64 n -2)) (PI.f64)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (-.f64 (neg.f64 (.f64 2 (+.f64 n n))) (neg.f64 (*.f64 -2 (/.f64 n -2/3)))) (/.f64 -1/3 (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (PI.f64) (-.f64 (+.f64 (.f64 n -2) (.f64 (+.f64 n n) 6)) (.f64 (.f64 n -4) -9/4))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 1/2)))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (-.f64 (.f64 (.f64 n (PI.f64)) 12) (.f64 (*.f64 n (PI.f64)) 9)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (PI.f64) (.f64 3 (.f64 n -4))) (.f64 (.f64 n (PI.f64)) 15)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (-.f64 (.f64 (PI.f64) (.f64 n -3)) (/.f64 (.f64 (PI.f64) 2) (/.f64 1/3 (neg.f64 n)))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) 6)) (.f64 (PI.f64) (/.f64 (*.f64 n -3) 1/3))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (.f64 (.f64 n (PI.f64)) 6) 3) (.f64 3 (.f64 (*.f64 n (PI.f64)) -5))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (/.f64 (.f64 (.f64 n (PI.f64)) 6) 1/3) (/.f64 (.f64 (*.f64 n (PI.f64)) -5) 1/3)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (-.f64 (+.f64 (.f64 -2 (.f64 n (PI.f64))) (.f64 12 (.f64 n (PI.f64)))) (.f64 3 (.f64 (+.f64 n (.f64 2 n)) (PI.f64))))) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (-.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 3) 1/2) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)) 1/2)))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (/.f64 (.f64 (PI.f64) (.f64 4 n)) 1/6) (.f64 (+.f64 n (/.f64 (+.f64 n n) 1/3)) (*.f64 (PI.f64) -3))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (*.f64 (PI.f64) -2)) (-.f64 (/.f64 (+.f64 (+.f64 n n) (+.f64 n n)) (/.f64 1/3 (PI.f64))) (/.f64 (+.f64 n (+.f64 n n)) (/.f64 1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (+.f64 (.f64 (.f64 (PI.f64) 4) (.f64 (+.f64 n n) 6)) (/.f64 (+.f64 n (+.f64 (/.f64 (+.f64 n n) 1/3) (*.f64 (+.f64 n n) 4))) (/.f64 -1/3 (PI.f64)))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 (.f64 (PI.f64) 4) (.f64 (+.f64 n n) 6)) (-.f64 (.f64 n (/.f64 (PI.f64) -1/2)) (.f64 (+.f64 n (+.f64 (/.f64 (+.f64 n n) 1/3) (*.f64 (+.f64 n n) 4))) (/.f64 (PI.f64) 1/3))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 (log.f64 n) 2)) (log.f64 n)) 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 (+.f64 (log.f64 (/.f64 (PI.f64) 1/2)) (.f64 2 (log.f64 n))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(-.f64 (.f64 (/.f64 4 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 3 (sqrt.f64 k))))
(-.f64 (/.f64 (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2))) 2) (sqrt.f64 k)) (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (*.f64 k -1/2) 1/2)) 3) (sqrt.f64 k)))
(-.f64 (/.f64 (.f64 2 (/.f64 2 (sqrt.f64 k))) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))) (/.f64 (.f64 (/.f64 1/2 (sqrt.f64 k)) 6) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (pow.f64 (.f64 2 (-.f64 (.f64 (PI.f64) (.f64 (/.f64 (.f64 n -2) -2/3) 3)) (-.f64 (.f64 (PI.f64) (+.f64 (.f64 (.f64 (+.f64 n n) 2) 3) (.f64 n -2))) (.f64 (.f64 n (+.f64 (.f64 (PI.f64) -2) (.f64 (PI.f64) 3))) 2)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (-.f64 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 (+.f64 (.f64 (PI.f64) 2) (.f64 (PI.f64) 2)) (/.f64 1/3 (.f64 (+.f64 n n) 2)))) (/.f64 (+.f64 (.f64 (.f64 (+.f64 n n) 2) 2) (+.f64 n (.f64 (/.f64 (.f64 n -2) -2/3) 2))) (/.f64 1/3 (PI.f64))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))))
(/.f64 (pow.f64 (.f64 2 (+.f64 (.f64 n (.f64 (PI.f64) -2)) (/.f64 3/2 (-.f64 (+.f64 (.f64 (/.f64 1/2 (.f64 n (PI.f64))) 4) (.f64 (/.f64 1/2 (.f64 n (PI.f64))) 4)) (+.f64 (.f64 (/.f64 1/2 (.f64 n (PI.f64))) 4) (.f64 (/.f64 1/2 (*.f64 n (PI.f64))) 3)))))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 k (*.f64 (sqrt.f64 2) (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n)))))))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k))))) (sqrt.f64 k))
(-.f64 (.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))) (.f64 (sqrt.f64 (/.f64 1 k)) 4)) (.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (+.f64 (log.f64 n) (log.f64 (/.f64 (PI.f64) 1/2))))) (.f64 3 (sqrt.f64 (/.f64 1 k)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (+.f64 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1/8)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 -1/2 (.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 k (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))))))) (.f64 1/8 (.f64 (sqrt.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (+.f64 (.f64 2 n) (.f64 n (.f64 -2 (-.f64 1 (PI.f64)))))) 2))))))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n))))))) (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n))) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 1/8)))) (sqrt.f64 k))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 1/8)))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 2) k)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 (.f64 (pow.f64 k 3) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n))) 3))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) -1/48)) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n))))))) (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (/.f64 (PI.f64) (/.f64 1/2 n))) 2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8))))) (sqrt.f64 k))

Outputs
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))

Calls

4 calls:

56.0ms	n
51.0ms	k
47.0ms	(.f64 (.f64 2 (PI.f64)) n)
37.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.7b	1	`k`
0.7b	1	`n`
0.7b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.7b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 2807 to 1818 computations (35.2% saved)

regimes12.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 n (/.f64 1 (PI.f64))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 1 n)))))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

Outputs
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

Calls

2 calls:

5.0ms	k
5.0ms	n

Results

Error	Segments	Branch
0.7b	1	`k`
0.7b	1	`n`

Compiler

Compiled 92 to 59 computations (35.9% saved)

regimes13.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 n (/.f64 1 (PI.f64))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 1 n)))))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 1 n)))))

Calls

2 calls:

5.0ms	n
5.0ms	k

Results

Error	Segments	Branch
22.1b	1	`k`
22.1b	1	`n`

Compiler

Compiled 78 to 51 computations (34.6% saved)

regimes11.0ms (0.1%)

Accuracy

Total -0.2b remaining (-0.8%)

Threshold costs -0.2b (-0.8%)

Counts

4 → 1

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 n (/.f64 1 (PI.f64))))))

Outputs
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))

Calls

2 calls:

5.0ms	n
4.0ms	k

Results

Error	Segments	Branch
22.1b	1	`k`
22.1b	1	`n`

Compiler

Compiled 52 to 34 computations (34.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	156

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 1 n)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))

Outputs
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 1 n)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))

Compiler

Compiled 58 to 48 computations (17.2% saved)

soundness214.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

1546×	`rational.json-simplify-67`
1258×	`rational.json-simplify-63`
1228×	`rational.json-simplify-1`
786×	`rational.json-simplify-5`
776×	`rational.json-simplify-4`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	37	49
2	88	43
3	228	43
4	820	43
5	5103	43
0	435	8890
1	1296	8652
2	6087	8652

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 388 to 257 computations (33.8% saved)

end35.0ms (0.3%)

Compiler: Compiled 52 to 35 computations (32.7% saved)