Details

analyze350.0ms (6.7%)

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
12.5%	34.3%	53.2%	6
15.6%	26.5%	57.9%	7
15.6%	22.6%	61.8%	8
17.2%	17.6%	65.3%	9
17.2%	15%	67.8%	10
18%	12.2%	69.9%	11
18%	10.8%	71.3%	12
18.3%	9.3%	72.4%	13
18.3%	8.5%	73.1%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.3s (61.9%)

Results

1.4s	8256×	body	128	valid
1.2s	1425×	body	1024	invalid
415.0ms	698×	body	512	invalid
174.0ms	1129×	body	128	invalid
104.0ms	322×	body	256	invalid

preprocess41.0ms (0.8%)

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)

simplify23.0ms (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))

prune4.0ms (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
▶	0.3b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize10.0ms (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)

series78.0ms (1.5%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
31.0ms	n	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
30.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
7.0ms	n	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
3.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
2.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

rewrite58.0ms (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 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 log1p.f64 (expm1.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 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 log1p.f64 (expm1.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 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)) 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((#(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 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))))))) (#(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))))))))

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

392×	`associate-r_binary64`
367×	`associate-l_binary64`
239×	`fma-def_binary64`
225×	`distribute-rgt-in_binary64`
224×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	1106
1	203	1024
2	637	901
3	3626	845

Stop Event

1×	node limit

Counts

130 → 101

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

prune200.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	96	7	103

Error

0.0b

Counts

103 → 7

Alt Table

Status	Error	Program
	9.2b	(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k))
	23.0b	(/.f64 (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) (sqrt.f64 k))
	0.5b	(.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)))
	0.5b	(.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))))
	9.5b	(.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)))
	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
▶	0.4b	(/.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))

Compiler

Compiled 2568 to 1746 computations (32% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series25.0ms (0.5%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
5.0ms	k	@	0	(/.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))
3.0ms	n	@	0	(/.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))
2.0ms	k	@	-inf	(/.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))
2.0ms	k	@	inf	(/.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))
2.0ms	n	@	-inf	(/.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))

rewrite62.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`
251×	`log-pow_binary64`
146×	`add-sqr-sqrt_binary64`
142×	`pow1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	298	57
2	3814	53

Stop Event

1×	node limit

Counts

4 → 103

Calls

Call 1

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

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

simplify45.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

540×	`distribute-lft-out_binary64`
366×	`associate-r_binary64`
354×	`associate-l_binary64`
198×	`distribute-rgt-out_binary64`
184×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	598
1	122	572
2	409	513
3	2665	502
4	4203	495

Stop Event

1×	node limit

Counts

127 → 114

Calls

Call 1

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

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

prune242.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	131	8	139

Error

Counts

139 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))
	0.5b	(.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))))
▶	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))
	8.1b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 2 (.f64 (PI.f64) n))))))
	9.2b	(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k))
	0.4b	(/.f64 (.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
	0.5b	(.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 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))

Compiler

Compiled 3215 to 2048 computations (36.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))
✓	0.1b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))
	0.3b	(*.f64 (PI.f64) n)
✓	0.4b	(.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k -1/2))

series13.0ms (0.3%)

Counts

3 → 0

Calls

15 calls:

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

rewrite55.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`log-prod_binary64`
255×	`expm1-udef_binary64`
255×	`log1p-udef_binary64`
249×	`log-pow_binary64`
146×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	298	49
2	3610	47

Stop Event

1×	node limit

Counts

3 → 66

Calls

Call 1

Inputs

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

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

(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))

Outputs

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

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

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

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

66 → 66

Calls

Call 1

Inputs

Outputs

prune157.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	106	6	112

Error

Counts

112 → 6

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))
	9.0b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 n (*.f64 2 (PI.f64))) (pow.f64 k -1))))
▶	0.4b	(/.f64 (.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
	0.5b	(.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 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))
✓	0.4b	(/.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))

Compiler

Compiled 2695 to 1831 computations (32.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
✓	0.3b	(*.f64 n (PI.f64))
✓	0.3b	(.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
✓	0.4b	(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))

series57.0ms (1.1%)

Counts

4 → 16

Calls

21 calls:

Time	Variable		Point	Expression
43.0ms	k	@	0	(.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
1.0ms	n	@	-inf	(/.f64 (.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
1.0ms	n	@	-inf	(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
1.0ms	k	@	inf	(/.f64 (.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
1.0ms	n	@	0	(/.f64 (.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))

rewrite68.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

310×	`log1p-udef_binary64`
177×	`add-sqr-sqrt_binary64`
175×	`associate-r_binary64`
172×	`*-un-lft-identity_binary64`
172×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	87
1	367	75
2	4554	75

Stop Event

1×	node limit

Counts

4 → 95

Calls

Call 1

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

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

simplify46.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

372×	`associate-r_binary64`
347×	`associate-l_binary64`
221×	`associate-+l+_binary64`
213×	`associate-+r+_binary64`
212×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	442
1	169	396
2	489	369
3	3018	358
4	4989	358

Stop Event

1×	node limit

Counts

111 → 107

Calls

Call 1

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

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

prune150.0ms (2.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	123	6	129

Error

Counts

129 → 6

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))
	9.0b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 n (*.f64 2 (PI.f64))) (pow.f64 k -1))))
✓	0.4b	(/.f64 (.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
	0.5b	(.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 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))
✓	0.4b	(/.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))

Compiler

Compiled 3334 to 2104 computations (36.9% saved)

regimes143.0ms (2.7%)

Accuracy

Total -11.4b remaining (-2459.8%)

Threshold costs -11.4b (-2459.8%)

Counts

62 → 1

Compiler

Compiled 1342 to 872 computations (35% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	18	22

Stop Event

1×

saturated

Calls

Call 1

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

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

end84.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 151 to 100 computations (33.8% saved)

Details

analyze350.0ms (6.7%)

sample3.3s (61.9%)

preprocess41.0ms (0.8%)

simplify23.0ms (0.4%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series78.0ms (1.5%)

rewrite58.0ms (1.1%)

simplify44.0ms (0.8%)

prune200.0ms (3.8%)

localize11.0ms (0.2%)

series25.0ms (0.5%)

rewrite62.0ms (1.2%)

simplify45.0ms (0.8%)

prune242.0ms (4.6%)

localize11.0ms (0.2%)

series13.0ms (0.3%)

rewrite55.0ms (1.1%)

simplify6.0ms (0.1%)

prune157.0ms (3%)

localize14.0ms (0.3%)

series57.0ms (1.1%)

rewrite68.0ms (1.3%)

simplify46.0ms (0.9%)

prune150.0ms (2.9%)

regimes143.0ms (2.7%)

simplify2.0ms (0%)

end84.0ms (1.6%)

Profiling