Details

analyze339.0ms (4.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
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)

sample3.0s (41.4%)

Results

1.3s	8256×	body	128	valid
1.1s	1402×	body	1024	invalid
361.0ms	677×	body	512	invalid
176.0ms	1181×	body	128	invalid
121.0ms	376×	body	256	invalid

Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess31.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

454×	`rules-20_binary64`
407×	`rules-11_binary64`
364×	`rules-24-rev_binary64`
232×	`rules-4_binary64`
160×	`rules-9-rev_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	34	50
2	82	44
3	155	44
4	361	44
5	892	44
6	2407	44
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 n (PI.f64))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 k (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (PI.f64) (*.f64 k 2)) (/.f64 (-.f64 1 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 (-.f64 1 n) 1/2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 2 (.f64 k (PI.f64))) (*.f64 (-.f64 1 n) 1/2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 2 (.f64 k (PI.f64))) (-.f64 1/2 (*.f64 1/2 n))) (sqrt.f64 n))

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

397×	`rules-22-rev_binary64`
391×	`rules-6_binary64`
325×	`rules-20_binary64`
227×	`rules-11_binary64`
220×	`rules-5-rev_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	22	25
2	47	22
3	86	22
4	199	22
5	483	22
6	1530	22

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

0.4b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 100 to 80 computations (20% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series391.0ms (5.4%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
62.0ms	n	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
61.0ms	n	@	0	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))
61.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
61.0ms	n	@	inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))
59.0ms	n	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))

rewrite62.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

304×	`rules-34-rev_binary64`
143×	`add-sqr-sqrt_binary64`
138×	`pow1_binary64`
138×	`rules-40_binary64`
138×	`rules-41_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	44
1	332	42
2	4188	42

Stop Event

1×	node limit

Counts

3 → 103

Calls

Call 1

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

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

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

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

309×	`rules-15-rev_binary64`
292×	`rules-1_binary64`
256×	`rules-20_binary64`
254×	`rules-1-rev_binary64`
236×	`rules-4_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	1168
1	208	994
2	757	951
3	3962	946

Stop Event

1×	node limit

Counts

151 → 122

Calls

Call 1

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

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

prune160.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	12	122
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Error

0.1b

Counts

124 → 12

Alt Table

Status	Error	Program
	0.8b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/4)) (pow.f64 k 1/4)) 2)
	0.9b	(/.f64 (pow.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 3)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
	0.7b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/4)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/4)) (sqrt.f64 k)))
	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
	3.6b	(exp.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))
	20.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (-.f64 (fma.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (.f64 (sqrt.f64 2) 1)) (.f64 1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 k (sqrt.f64 2))))) (.f64 1/48 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (sqrt.f64 k))
	0.9b	(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k))) (sqrt.f64 k)))
	20.3b	(/.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))))))) (sqrt.f64 k))
	14.9b	(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) 3)) (sqrt.f64 k))
▶	0.5b	(/.f64 (pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
	17.8b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)) 3) 1/3)
	3.3b	(/.f64 (exp.f64 (log.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)))) (sqrt.f64 k))

Compiler

Compiled 3075 to 2033 computations (33.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) n)
✓	0.3b	(pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (*.f64 (-.f64 1 k) 1/2))
✓	0.4b	(sqrt.f64 (*.f64 (PI.f64) n))
✓	0.5b	(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)

series155.0ms (2.1%)

Counts

3 → 20

Calls

12 calls:

Time	Variable		Point	Expression
63.0ms	n	@	0	(pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (*.f64 (-.f64 1 k) 1/2))
57.0ms	n	@	inf	(pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (*.f64 (-.f64 1 k) 1/2))
14.0ms	n	@	-inf	(pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (*.f64 (-.f64 1 k) 1/2))
3.0ms	n	@	0	(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)
3.0ms	n	@	-inf	(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)

rewrite58.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

277×	`rules-34-rev_binary64`
144×	`rules-24_binary64`
132×	`add-sqr-sqrt_binary64`
128×	`pow1_binary64`
128×	`rules-40_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	29
1	335	28
2	3862	28

Stop Event

1×	node limit

Counts

3 → 146

Calls

Call 1

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

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

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egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))))))

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

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

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

301×	`rules-15-rev_binary64`
283×	`rules-1_binary64`
246×	`rules-1-rev_binary64`
237×	`rules-20_binary64`
231×	`rules-4_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	620
1	176	494
2	690	467
3	3694	462

Stop Event

1×	node limit

Counts

166 → 157

Calls

Call 1

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

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

prune244.0ms (3.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	191	12	203

Error

0.1b

Counts

203 → 12

Alt Table

Status	Error	Program
	0.7b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/4)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/4)) (sqrt.f64 k)))
▶	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
	3.6b	(exp.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))
	20.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (-.f64 (fma.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (.f64 (sqrt.f64 2) 1)) (.f64 1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 k (sqrt.f64 2))))) (.f64 1/48 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (sqrt.f64 k))
	0.9b	(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k))) (sqrt.f64 k)))
	20.3b	(/.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))))))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 3)) 2)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
	0.8b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/4)) (pow.f64 k 1/4)) 2)
	0.6b	(/.f64 (pow.f64 (.f64 2 (.f64 (sqrt.f64 n) (.f64 (PI.f64) (sqrt.f64 n)))) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))
	17.8b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)) 3) 1/3)
	3.3b	(/.f64 (exp.f64 (log.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)))) (sqrt.f64 k))

Compiler

Compiled 4651 to 2997 computations (35.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series397.0ms (5.4%)

Counts

4 → 28

Calls

18 calls:

Time	Variable		Point	Expression
64.0ms	n	@	0	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
64.0ms	n	@	inf	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
62.0ms	n	@	-inf	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
58.0ms	n	@	0	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
58.0ms	n	@	inf	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))

rewrite68.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

307×	`rules-34-rev_binary64`
144×	`add-sqr-sqrt_binary64`
139×	`pow1_binary64`
139×	`rules-40_binary64`
139×	`rules-41_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	335	42
2	4334	42

Stop Event

1×	node limit

Counts

4 → 158

Calls

Call 1

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

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

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

440×	`rules-4_binary64`
269×	`rules-1_binary64`
258×	`rules-11_binary64`
236×	`rules-6_binary64`
216×	`rules-1-rev_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	752
1	191	715
2	702	636
3	4535	636

Stop Event

1×	node limit

Counts

186 → 176

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 (/.f64 1 n)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 (/.f64 1 n)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 (/.f64 1 n)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 (/.f64 1 n)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 -2 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(/.f64 (pow.f64 (*.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (-.f64 1 k)))
(exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 -2 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(/.f64 (pow.f64 (*.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (-.f64 1 k)))
(exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 -2 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(/.f64 (pow.f64 (*.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (-.f64 1 k)))
(exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 -2 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(/.f64 (pow.f64 (*.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (-.f64 1 k)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(-.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))))
(-.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))
(.f64 2 (-.f64 (.f64 n (PI.f64)) (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 2 (.f64 (PI.f64) (-.f64 n (.f64 k (.f64 n (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))
(-.f64 (+.f64 (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64)))) (.f64 2 (.f64 n (PI.f64)))) (.f64 2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(-.f64 (fma.f64 (.f64 k k) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 n (PI.f64))) (.f64 n (.f64 2 (PI.f64)))) (.f64 2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))
(+.f64 (.f64 k (.f64 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) k)) (.f64 2 (-.f64 (.f64 n (PI.f64)) (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))))
(fma.f64 k (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 k (.f64 n (PI.f64)))) (.f64 2 (.f64 (PI.f64) (-.f64 n (.f64 k (.f64 n (log.f64 (.f64 n (*.f64 2 (PI.f64))))))))))
(-.f64 (+.f64 (.f64 (pow.f64 k 2) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 2 (.f64 n (PI.f64)))) (+.f64 (.f64 2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 3)))))))
(-.f64 (fma.f64 (.f64 k k) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 n (PI.f64))) (.f64 n (.f64 2 (PI.f64)))) (fma.f64 2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (.f64 1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))))))
(-.f64 (.f64 n (+.f64 (.f64 2 (PI.f64)) (.f64 k (.f64 k (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))) (.f64 1/3 (fma.f64 n (.f64 (pow.f64 k 3) (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (.f64 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 6))))
(+.f64 (.f64 n (-.f64 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 (PI.f64) (.f64 k k))) (.f64 1/3 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 (PI.f64) (pow.f64 k 3)))))) (.f64 2 (.f64 (PI.f64) (-.f64 n (.f64 k (.f64 n (log.f64 (.f64 n (*.f64 2 (PI.f64))))))))))
(+.f64 (.f64 2 (.f64 (PI.f64) (-.f64 n (.f64 k (.f64 n (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) (.f64 n (-.f64 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 (PI.f64) (.f64 k k))) (.f64 1/3 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (*.f64 (PI.f64) (pow.f64 k 3)))))))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 (/.f64 1 n))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 (/.f64 1 n))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 (/.f64 1 n))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 (/.f64 1 n))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 -2 (PI.f64))) (log.f64 (/.f64 -1 n))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 -2 (PI.f64))) (log.f64 (/.f64 -1 n))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 -2 (PI.f64))) (log.f64 (/.f64 -1 n))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 -2 (PI.f64))) (log.f64 (/.f64 -1 n))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (-.f64 1 k))) k))

prune227.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	169	7	176
Fresh	8	2	10
Picked	1	0	1
Done	1	0	1
Total	179	9	188

Error

0.0b

Counts

188 → 9

Alt Table

Status	Error	Program
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
▶	0.3b	(.f64 (sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) (sqrt.f64 (/.f64 1 k)))
	21.4b	(.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (-.f64 n (.f64 k (.f64 n (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))) (sqrt.f64 (/.f64 1 k)))
	0.8b	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
	0.8b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/4)) (pow.f64 k 1/4)) 2)
	0.5b	(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 1 (pow.f64 k -1/2)))
	0.5b	(.f64 (sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) (sqrt.f64 (/.f64 1 k)))
	20.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (-.f64 (fma.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (.f64 (sqrt.f64 2) 1)) (.f64 1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 k (sqrt.f64 2))))) (.f64 1/48 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (sqrt.f64 k))
	9.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 3899 to 2705 computations (30.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series297.0ms (4.1%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
82.0ms	n	@	inf	(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
82.0ms	n	@	-inf	(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
62.0ms	n	@	0	(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
14.0ms	k	@	0	(.f64 (sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) (sqrt.f64 (/.f64 1 k)))
10.0ms	n	@	0	(.f64 (sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) (sqrt.f64 (/.f64 1 k)))

rewrite61.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

340×	`rules-34-rev_binary64`
159×	`add-sqr-sqrt_binary64`
155×	`pow1_binary64`
155×	`rules-40_binary64`
155×	`rules-41_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	50
1	378	33
2	4897	33

Stop Event

1×	node limit

Counts

2 → 75

Calls

Call 1

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

Outputs

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

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

simplify26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

542×	`rules-4_binary64`
292×	`rules-6_binary64`
289×	`rules-11_binary64`
286×	`rules-1_binary64`
259×	`rules-20_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	740
1	222	703
2	818	612

Stop Event

1×	node limit

Counts

99 → 89

Calls

Call 1

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

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

prune207.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	160	9	169

Error

0.0b

Counts

169 → 9

Alt Table

Status	Error	Program
	13.3b	(.f64 (sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) (cbrt.f64 (/.f64 (pow.f64 k -1/2) k)))
	20.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (-.f64 (fma.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (.f64 (sqrt.f64 2) 1)) (.f64 1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 k (sqrt.f64 2))))) (.f64 1/48 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (sqrt.f64 k))
	0.8b	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
	0.8b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/4)) (pow.f64 k 1/4)) 2)
	0.5b	(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 1 (pow.f64 k -1/2)))
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
	0.5b	(.f64 (sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) (sqrt.f64 (/.f64 1 k)))
	0.3b	(.f64 (sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) (pow.f64 (sqrt.f64 k) -1))
	9.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 3581 to 2491 computations (30.4% saved)

regimes1.2s (16.3%)

Accuracy

Total 0.3b remaining (76.4%)

Threshold costs 0.3b (76.4%)

Counts

279 → 1

Compiler

Compiled 23450 to 18890 computations (19.4% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29

Stop Event

1×

saturated

Calls

Call 1

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

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

end158.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 256 to 199 computations (22.3% saved)

Details

analyze339.0ms (4.7%)

sample3.0s (41.4%)

preprocess31.0ms (0.4%)

simplify18.0ms (0.2%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series391.0ms (5.4%)

rewrite62.0ms (0.8%)

simplify51.0ms (0.7%)

prune160.0ms (2.2%)

localize11.0ms (0.2%)

series155.0ms (2.1%)

rewrite58.0ms (0.8%)

simplify43.0ms (0.6%)

prune244.0ms (3.3%)

localize9.0ms (0.1%)

series397.0ms (5.4%)

rewrite68.0ms (0.9%)

simplify47.0ms (0.6%)

prune227.0ms (3.1%)

localize11.0ms (0.2%)

series297.0ms (4.1%)

rewrite61.0ms (0.8%)

simplify26.0ms (0.4%)

prune207.0ms (2.8%)

regimes1.2s (16.3%)

simplify1.0ms (0%)

end158.0ms (2.2%)

Profiling