Details

analyze338.0ms (6.4%)

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)

sample3.2s (61.4%)

Results

1.4s	8256×	body	128	valid
1.1s	1387×	body	1024	invalid
389.0ms	688×	body	512	invalid
177.0ms	1147×	body	128	invalid
107.0ms	327×	body	256	invalid

preprocess36.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	52	44
2	119	44
3	256	44
4	668	44
5	1836	40
6	4163	40
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify18.0ms (0.3%)

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))

prune5.0ms (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

0.4b

Counts

3 → 2

Alt Table

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

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series73.0ms (1.4%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
27.0ms	n	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
25.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
11.0ms	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))

rewrite54.0ms (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 log1p.f64 (expm1.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))
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Outputs

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

simplify46.0ms (0.9%)

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

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	92	9	101
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	9	103

Error

0.0b

Counts

103 → 9

Alt Table

Status	Error	Program
	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)))
	20.0b	(/.f64 (.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)))) (sqrt.f64 k))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) 2) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
▶	0.5b	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.8b	(.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))))
	0.5b	(.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)))
	0.6b	(.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)))
	0.5b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)

Compiler

Compiled 2552 to 1754 computations (31.3% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series6.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

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

rewrite60.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`log-prod_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
211×	`log-pow_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	274	44
2	3187	44

Stop Event

1×	node limit

Counts

3 → 61

Calls

Call 1

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

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

Outputs

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

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

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

simplify50.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

389×	`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	1142
1	203	1060
2	639	937
3	3616	878

Stop Event

1×	node limit

Counts

109 → 81

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

prune138.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	81	9	90

Error

0.0b

Counts

90 → 9

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)))) (pow.f64 k -1/2))
	0.5b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
	20.0b	(/.f64 (.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)))) (sqrt.f64 k))
	12.3b	(sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1)))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
▶	0.4b	(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
	0.6b	(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 k -1/2))
	0.5b	(.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)))
	0.6b	(.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)))

Compiler

Compiled 2178 to 1392 computations (36.1% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New

Error

Program

✓

0.2b

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

✓

0.3b

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

✓

0.3b

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

series9.0ms (0.2%)

Counts

3 → 48

Calls

15 calls:

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

rewrite55.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

264×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`
158×	`add-sqr-sqrt_binary64`
151×	`pow1_binary64`
149×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	53
1	321	44
2	3951	44

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

simplify43.0ms (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	1142
1	202	1060
2	636	937
3	3619	881

Stop Event

1×	node limit

Counts

137 → 108

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

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

prune212.0ms (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	108	9	117

Error

0.0b

Counts

117 → 9

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (fma.f64 -1/2 k 1/2))) (sqrt.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 1/2)) (fma.f64 -1/2 k 1/2)))) (pow.f64 k -1/2))
	20.0b	(/.f64 (.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)))) (sqrt.f64 k))
	12.3b	(sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1)))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
✓	0.4b	(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
	0.6b	(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 k -1/2))
▶	0.5b	(.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)))
	0.6b	(.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)))
	0.5b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)

Compiler

Compiled 2638 to 1965 computations (25.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series93.0ms (1.8%)

Counts

3 → 48

Calls

18 calls:

Time	Variable		Point	Expression
48.0ms	n	@	0	(.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)))
14.0ms	n	@	-inf	(.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)))
9.0ms	k	@	-inf	(/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
8.0ms	n	@	inf	(.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)))
4.0ms	k	@	0	(.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)))

rewrite63.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
148×	`pow1_binary64`
146×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	56
1	342	49
2	3884	49

Stop Event

1×	node limit

Counts

3 → 102

Calls

Call 1

Inputs

(*.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)))

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

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

Outputs

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

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

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

317×	`associate-r_binary64`
306×	`associate-l_binary64`
271×	`unswap-sqr_binary64`
236×	`fma-def_binary64`
168×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	1308
1	190	1132
2	591	1116
3	3084	1029

Stop Event

1×	node limit

Counts

150 → 126

Calls

Call 1

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

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

prune375.0ms (7.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	7	145
Fresh	5	2	7
Picked	1	0	1
Done	1	0	1
Total	145	9	154

Error

Counts

154 → 9

Alt Table

Status	Error	Program
	0.4b	(/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
	0.5b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))))
	0.6b	(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 k -1/2))
	7.8b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (+.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k)))
	0.5b	(/.f64 (.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (neg.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))) (neg.f64 (sqrt.f64 k)))
	0.5b	(/.f64 1 (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	12.3b	(sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1)))
	0.6b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k)))
	0.4b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))

Compiler

Compiled 3722 to 2486 computations (33.2% saved)

regimes59.0ms (1.1%)

Accuracy

Total -31.9b remaining (-7492.1%)

Threshold costs -31.9b (-7492.1%)

Counts

23 → 1

Calls

Call 1

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

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

Results

12.0ms	0.4b	`k`
13.0ms	0.4b	`n`
8.0ms	0.4b	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
13.0ms	0.4b	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 517 to 344 computations (33.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	15	20

Stop Event

1×

saturated

Calls

Call 1

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

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

end18.0ms (0.3%)

Stop Event

1×

fuel

Compiler

Compiled 30 to 24 computations (20% saved)

Details

analyze338.0ms (6.4%)

sample3.2s (61.4%)

preprocess36.0ms (0.7%)

simplify18.0ms (0.3%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

series73.0ms (1.4%)

rewrite54.0ms (1%)

simplify46.0ms (0.9%)

prune200.0ms (3.8%)

localize11.0ms (0.2%)

series6.0ms (0.1%)

rewrite60.0ms (1.1%)

simplify50.0ms (0.9%)

prune138.0ms (2.6%)

localize12.0ms (0.2%)

series9.0ms (0.2%)

rewrite55.0ms (1%)

simplify43.0ms (0.8%)

prune212.0ms (4%)

localize16.0ms (0.3%)

series93.0ms (1.8%)

rewrite63.0ms (1.2%)

simplify43.0ms (0.8%)

prune375.0ms (7.1%)

regimes59.0ms (1.1%)

simplify2.0ms (0%)

end18.0ms (0.3%)

Profiling