Details

analyze338.0ms (6.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	25%	57.9%	7
18%	20.3%	61.8%	8
18.3%	16.4%	65.3%	9
18.5%	13.7%	67.8%	10
18.6%	11.5%	69.9%	11
18.7%	10%	71.3%	12
18.7%	8.9%	72.4%	13
18.7%	8.2%	73.1%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.2s (60.6%)

Results

1.4s	8256×	body	128	valid
1.1s	1412×	body	1024	invalid
394.0ms	746×	body	512	invalid
183.0ms	1192×	body	128	invalid
105.0ms	339×	body	256	invalid

Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess37.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

421×	`div-sub_binary64`
418×	`associate-/l*_binary64`
293×	`associate-l_binary64`
268×	`associate-/r*_binary64`
224×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	52	44
2	119	44
3	256	44
4	668	44
5	1836	40
6	4163	40
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 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 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 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (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 2 (*.f64 (PI.f64) k)) (-.f64 1/2 (/.f64 n 2))))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 n))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 k 2)) (fma.f64 -1/2 n 1/2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 k 2)) (fma.f64 n -1/2 1/2)) (sqrt.f64 n))

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify19.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-/l*_binary64`
544×	`associate-/r*_binary64`
257×	`associate-*l/_binary64`
214×	`unswap-sqr_binary64`
214×	`div-sub_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	140	22
4	354	22
5	958	20
6	2187	20

Stop Event

1×	node limit

Counts

1 → 2

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

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series80.0ms (1.5%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
33.0ms	n	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
23.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
8.0ms	n	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
5.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

rewrite57.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`log-prod_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
212×	`log-pow_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	274	40
2	3306	40

Stop Event

1×	node limit

Counts

3 → 82

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))
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Outputs

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(#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) 2) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
430×	`associate-r_binary64`
373×	`associate-l_binary64`
176×	`distribute-rgt-in_binary64`
172×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1144
1	183	984
2	587	828
3	3439	826

Stop Event

1×	node limit

Counts

130 → 99

Calls

Call 1

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

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

prune119.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	93	8	101

Error

0.0b

Counts

101 → 8

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) (fma.f64 k -1/2 1/2)))
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) 2) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	20.7b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 k -1/2) (.f64 (sqrt.f64 2) (log.f64 (.f64 (*.f64 n (PI.f64)) 2)))))) (sqrt.f64 k))
	1.0b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	0.6b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	0.5b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))

Compiler

Compiled 2459 to 1686 computations (31.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series94.0ms (1.8%)

Counts

3 → 48

Calls

18 calls:

Time	Variable		Point	Expression
47.0ms	n	@	0	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
16.0ms	n	@	-inf	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
10.0ms	k	@	0	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
9.0ms	n	@	inf	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
2.0ms	k	@	0	(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))

rewrite61.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

695×	`log-prod_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
238×	`log-pow_binary64`
146×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	297	51
2	3474	51

Stop Event

1×	node limit

Counts

3 → 59

Calls

Call 1

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

Inputs

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

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

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 3) (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) (pow.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 3) (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) (pow.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))))

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

484×	`fma-neg_binary64`
324×	`distribute-rgt-neg-in_binary64`
312×	`associate-r_binary64`
284×	`associate-l_binary64`
229×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	1312
1	216	997
2	594	975
3	3107	975

Stop Event

1×	node limit

Counts

107 → 80

Calls

Call 1

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

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

prune136.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	99	8	107

Error

Counts

107 → 8

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) n))) (pow.f64 k -1/2)))
	0.6b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) 2) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	19.9b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 (pow.f64 (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3)))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) (fma.f64 k -1/2 1/2)))
	1.0b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	0.5b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))

Compiler

Compiled 2814 to 1983 computations (29.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 (PI.f64) n))
✓	0.2b	(.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 k -1/2))
✓	0.3b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) n))) (pow.f64 k -1/2)))
	0.3b	(*.f64 (PI.f64) n)

series38.0ms (0.7%)

Counts

3 → 0

Calls

15 calls:

Time	Variable		Point	Expression
11.0ms	k	@	0	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) n))) (pow.f64 k -1/2)))
5.0ms	n	@	0	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) n))) (pow.f64 k -1/2)))
3.0ms	n	@	-inf	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) n))) (pow.f64 k -1/2)))
3.0ms	k	@	-inf	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) n))) (pow.f64 k -1/2)))
2.0ms	k	@	inf	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) n))) (pow.f64 k -1/2)))

rewrite55.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

302×	`expm1-udef_binary64`
302×	`log1p-udef_binary64`
176×	`add-sqr-sqrt_binary64`
172×	`pow1_binary64`
169×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	361	53
2	4317	53

Stop Event

1×	node limit

Counts

3 → 55

Calls

Call 1

Inputs

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

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

(sqrt.f64 (*.f64 (PI.f64) n))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 (pow.f64 k -1) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 2)) (pow.f64 4 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 3) (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) (pow.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 k -1) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (cbrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) 1/4) (pow.f64 (*.f64 (PI.f64) n) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2)) 1/2) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) n) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))))

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

55 → 55

Calls

Call 1

Inputs

Outputs

prune110.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Error

Counts

101 → 8

Alt Table

Status	Error	Program
	19.9b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 (pow.f64 (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3)))
	12.5b	(sqrt.f64 (.f64 (.f64 (pow.f64 k -1) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 2)) (pow.f64 4 (fma.f64 k -1/2 1/2))))
✓	0.3b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) n))) (pow.f64 k -1/2)))
	0.6b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
▶	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) (fma.f64 k -1/2 1/2)))
	1.0b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	0.5b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))

Compiler

Compiled 2701 to 1775 computations (34.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 k))
✓	0.2b	(pow.f64 (.f64 (.f64 n (PI.f64)) 2) (fma.f64 k -1/2 1/2))
✓	0.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) (fma.f64 k -1/2 1/2)))
✓	0.3b	(*.f64 n (PI.f64))

series9.0ms (0.2%)

Counts

4 → 36

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	k	@	0	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) (fma.f64 k -1/2 1/2)))
1.0ms	k	@	-inf	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) (fma.f64 k -1/2 1/2)))
1.0ms	n	@	inf	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) (fma.f64 k -1/2 1/2)))
1.0ms	k	@	inf	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) (fma.f64 k -1/2 1/2)))
0.0ms	k	@	-inf	(sqrt.f64 (/.f64 1 k))

rewrite58.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

678×	`log-prod_binary64`
249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
228×	`log-pow_binary64`
148×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	49
1	308	44
2	3508	44

Stop Event

1×	node limit

Counts

4 → 93

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 n (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 n (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 n (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 n (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 n (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 n (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 n (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 n (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 3) (/.f64 (pow.f64 k -1/2) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) (cbrt.f64 (exp.f64 (pow.f64 k -1/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 k -2))) (sqrt.f64 (cbrt.f64 (/.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 k -2)) 1/2) (pow.f64 (cbrt.f64 (/.f64 1 k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k -1/2) k) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 k) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 k -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 k -1/2) k))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -1/2 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 -1/2 (log.f64 k)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -1/2)))))))

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
430×	`associate-r_binary64`
373×	`associate-l_binary64`
176×	`distribute-rgt-in_binary64`
172×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1084
1	183	924
2	587	768
3	3439	766

Stop Event

1×	node limit

Counts

129 → 109

Calls

Call 1

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

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

prune128.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	109	8	117

Error

Counts

117 → 8

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) n))) (pow.f64 k -1/2)))
	0.6b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	12.5b	(sqrt.f64 (.f64 (.f64 (pow.f64 k -1) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 2)) (pow.f64 4 (fma.f64 k -1/2 1/2))))
✓	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) (fma.f64 k -1/2 1/2)))
	1.0b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2))))
	0.5b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))

Compiler

Compiled 2462 to 1754 computations (28.8% saved)

regimes364.0ms (7%)

Accuracy

Total 0.4b remaining (85%)

Threshold costs 0.4b (85%)

Counts

152 → 1

Compiler

Compiled 2989 to 2078 computations (30.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	36
1	22	36

Stop Event

1×

saturated

Calls

Call 1

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

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

end154.0ms (3%)

Stop Event

1×

fuel

Compiler

Compiled 233 to 182 computations (21.9% saved)

Details

analyze338.0ms (6.5%)

sample3.2s (60.6%)

preprocess37.0ms (0.7%)

simplify19.0ms (0.4%)

prune6.0ms (0.1%)

localize9.0ms (0.2%)

series80.0ms (1.5%)

rewrite57.0ms (1.1%)

simplify43.0ms (0.8%)

prune119.0ms (2.3%)

localize13.0ms (0.2%)

series94.0ms (1.8%)

rewrite61.0ms (1.2%)

simplify43.0ms (0.8%)

prune136.0ms (2.6%)

localize15.0ms (0.3%)

series38.0ms (0.7%)

rewrite55.0ms (1.1%)

simplify6.0ms (0.1%)

prune110.0ms (2.1%)

localize10.0ms (0.2%)

series9.0ms (0.2%)

rewrite58.0ms (1.1%)

simplify43.0ms (0.8%)

prune128.0ms (2.5%)

regimes364.0ms (7%)

simplify2.0ms (0%)

end154.0ms (3%)

Profiling