Details

analyze346.0ms (5.9%)

Algorithm

1×

Search

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.1s (52.8%)

Results

1.3s	8256×	body	128	valid
1.1s	1390×	body	1024	invalid
376.0ms	668×	body	512	invalid
182.0ms	1139×	body	128	invalid
129.0ms	378×	body	256	invalid

Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess35.0ms (0.6%)

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))

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series425.0ms (7.2%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
71.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
69.0ms	n	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
68.0ms	n	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
62.0ms	n	@	inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
61.0ms	n	@	0	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))

rewrite62.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 82

Calls

Call 1

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

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

simplify43.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

130 → 99

Calls

Call 1

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

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

prune123.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

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

Error

0.0b

Counts

101 → 8

Alt Table

Status	Error	Program
	3.4b	(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	10.1b	(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k))
	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.4b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
▶	0.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) 2) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	19.4b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 k -1/2) (.f64 (sqrt.f64 2) (log.f64 (.f64 (*.f64 n (PI.f64)) 2)))))) (sqrt.f64 k))

Compiler

Compiled 2405 to 1644 computations (31.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))
✓	0.1b	(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
✓	0.3b	(.f64 (PI.f64) (.f64 n 2))

series94.0ms (1.6%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
15.0ms	k	@	0	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
13.0ms	k	@	-inf	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
7.0ms	n	@	0	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))
7.0ms	n	@	0	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
7.0ms	n	@	inf	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))

rewrite59.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 103

Calls

Call 1

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

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

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
451×	`distribute-rgt-neg-in_binary64`
449×	`distribute-lft-neg-in_binary64`
438×	`associate-r_binary64`
371×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	604
1	127	572
2	460	512
3	2920	510

Stop Event

1×	node limit

Counts

127 → 114

Calls

Call 1

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

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

prune142.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	132	8	140

Error

Counts

140 → 8

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))
	3.4b	(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	10.1b	(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k))
	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.4b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	9.5b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 2 (.f64 (PI.f64) n))))))
▶	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))

Compiler

Compiled 3175 to 2027 computations (36.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series70.0ms (1.2%)

Counts

2 → 0

Calls

9 calls:

Time	Variable		Point	Expression
18.0ms	k	@	-inf	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))
13.0ms	k	@	0	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))
9.0ms	n	@	0	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))
7.0ms	n	@	-inf	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))
7.0ms	n	@	inf	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))

rewrite66.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

298×	`log1p-udef_binary64`
172×	`add-sqr-sqrt_binary64`
168×	`pow1_binary64`
167×	`*-un-lft-identity_binary64`
166×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	41
1	360	39
2	4530	39

Stop Event

1×	node limit

Counts

2 → 64

Calls

Call 1

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

Outputs

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

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

64 → 64

Calls

Call 1

Inputs

Outputs

prune101.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	4	2	6
Picked	0	1	1
Done	1	0	1
Total	105	4	109

Error

Counts

109 → 4

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))
	9.9b	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 (PI.f64) 2)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) -1)) k))
▶	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))

Compiler

Compiled 2566 to 1694 computations (34% 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))
✓	0.2b	(.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))

series395.0ms (6.7%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
67.0ms	n	@	-inf	(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
64.0ms	n	@	0	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
63.0ms	n	@	inf	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
61.0ms	n	@	-inf	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
60.0ms	n	@	inf	(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))

rewrite49.0ms (0.8%)

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	36
1	274	36
2	3187	36

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

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

simplify43.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

78 → 58

Calls

Call 1

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

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

prune72.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	76	4	80

Error

Counts

80 → 4

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))
	9.9b	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 (PI.f64) 2)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) -1)) k))
✓	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))

Compiler

Compiled 1716 to 1094 computations (36.2% saved)

regimes461.0ms (7.8%)

Accuracy

Total 0.3b remaining (79%)

Threshold costs 0.3b (79%)

Counts

105 → 1

Compiler

Compiled 8750 to 6970 computations (20.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	18	31

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.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))

Outputs
(/.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))

end84.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 122 to 94 computations (23% saved)

Details

analyze346.0ms (5.9%)

sample3.1s (52.8%)

preprocess35.0ms (0.6%)

simplify18.0ms (0.3%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series425.0ms (7.2%)

rewrite62.0ms (1.1%)

simplify43.0ms (0.7%)

prune123.0ms (2.1%)

localize12.0ms (0.2%)

series94.0ms (1.6%)

rewrite59.0ms (1%)

simplify34.0ms (0.6%)

prune142.0ms (2.4%)

localize13.0ms (0.2%)

series70.0ms (1.2%)

rewrite66.0ms (1.1%)

simplify6.0ms (0.1%)

prune101.0ms (1.7%)

localize11.0ms (0.2%)

series395.0ms (6.7%)

rewrite49.0ms (0.8%)

simplify43.0ms (0.7%)

prune72.0ms (1.2%)

regimes461.0ms (7.8%)

simplify2.0ms (0%)

end84.0ms (1.4%)

Profiling