Details

analyze133.0ms (1.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
0%	0%	50%	0.1%	0%	50%	0%	3
0%	0%	50%	0.1%	0%	50%	0%	4
25%	12.5%	37.5%	0.1%	0%	50%	0%	5
26.7%	12.5%	34.3%	0.1%	0%	53.1%	0%	6
37%	15.6%	26.5%	0.1%	1.6%	54.6%	1.6%	7
40.8%	15.6%	22.6%	0.1%	2.3%	57%	2.3%	8
49.4%	17.2%	17.6%	0.1%	3.5%	58.1%	3.5%	9
53.3%	17.2%	15%	0.1%	4.1%	59.5%	4.1%	10
59.5%	18%	12.2%	0.1%	4.8%	60.2%	4.8%	11
62.5%	18%	10.8%	0.1%	5.1%	60.9%	5.1%	12

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample2.9s (23.9%)

Results

1.5s	8256×	body	256	valid
801.0ms	1319×	body	1024	invalid
263.0ms	718×	body	512	invalid
208.0ms	1580×	body	256	invalid
100.0ms	483×	body	256	infinite
63.0ms	232×	body	256	unsamplable

Bogosity

preprocess64.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

454×	`neg-mul-1_binary64`
436×	`fma-def_binary64`
428×	`unswap-sqr_binary64`
424×	`div-sub_binary64`
419×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	52	44
2	119	44
3	257	44
4	670	44
5	1879	40
6	4230	40
7	7364	40
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 20 to 17 computations (15% saved)

simplify45.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l*_binary64`
561×	`associate-/r*_binary64`
453×	`div-sub_binary64`
450×	`distribute-frac-neg_binary64`
416×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	141	22
4	360	22
5	983	20
6	2213	20
7	5663	20

Stop Event

1×	node limit

Counts

1 → 7

Calls

Call 1

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

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

eval2.0ms (0%)

Compiler: Compiled 102 to 64 computations (37.3% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	5	2	7
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	5	3	8

Error

0.5b

Counts

8 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 56 to 38 computations (32.1% saved)

series86.0ms (0.7%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
31.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
30.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
9.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
2.0ms	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
2.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite85.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

751×	`log-prod_binary64`
382×	`pow2_binary64`
265×	`pow1/3_binary64`
260×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	307	51
2	3926	47

Stop Event

1×	node limit

Counts

4 → 105

Calls

Call 1

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

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

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
354×	`log-prod_binary64`
272×	`times-frac_binary64`
238×	`exp-prod_binary64`
225×	`exp-sum_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	306	3027
1	696	2800
2	2465	2472
3	6620	2466

Stop Event

1×	node limit

Counts

153 → 185

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 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(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 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (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 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 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 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 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 0 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 1)
(.f64 1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1)
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)))
(.f64 (pow.f64 1 (-.f64 1/2 (.f64 k 1/2))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 k 1/2))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (*.f64 k 1/2))))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (*.f64 k 1/2))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 k 1/2)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1))
(+.f64 0 (.f64 2 (.f64 (PI.f64) n)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) 1)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 3)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)
(pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)
(pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)) 1/3)
(sqrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)))
(log.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))
(cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))
(exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 1))
(+.f64 0 (pow.f64 k -1/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)
(*.f64 1 (pow.f64 k -1/2))
(*.f64 (pow.f64 k -1/2) 1)
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))
(*.f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 k -1/2)))
(*.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))
(*.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 (cbrt.f64 k) -1) (cbrt.f64 (pow.f64 k -1/2)))
(pow.f64 k -1/2)
(pow.f64 (sqrt.f64 k) -1)
(pow.f64 (pow.f64 k -1/2) 1)
(pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)
(pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)
(pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) -1)
(sqrt.f64 (/.f64 1 k))
(log.f64 (exp.f64 (pow.f64 k -1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))
(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))
(log1p.f64 (expm1.f64 (pow.f64 k -1/2)))
(exp.f64 (*.f64 -1/2 (log.f64 k)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) -1))
(exp.f64 (.f64 (.f64 -1/2 (log.f64 k)) 1))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (.f64 -1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1) (neg.f64 (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) -1)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))

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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 (.f64 k (sqrt.f64 2))) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.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))) (+.f64 (.f64 (.f64 -1/2 (.f64 k (sqrt.f64 2))) (log.f64 (.f64 n (.f64 2 (PI.f64))))) (fma.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (sqrt.f64 2) (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 (.f64 k (sqrt.f64 2))) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))) (.f64 -1/48 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)) (.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 1/8 (.f64 k (.f64 k (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))))))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
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(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(pow.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3)))
(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)))
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3)))
(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)))
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) -1)
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3)))
(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)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3)))
(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)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

localize24.0ms (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 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.3b	(*.f64 (PI.f64) n)
✓	0.4b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))

Compiler

Compiled 50 to 30 computations (40% saved)

series10.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

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

rewrite73.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

759×	`log-prod_binary64`
385×	`pow2_binary64`
262×	`pow1/3_binary64`
261×	`expm1-udef_binary64`
261×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	295	44
2	3931	40

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

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

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

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simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
539×	`distribute-rgt-in_binary64`
524×	`distribute-lft-in_binary64`
467×	`unswap-sqr_binary64`
367×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	290	3006
1	668	2738
2	2308	2687

Stop Event

1×	node limit

Counts

140 → 162

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 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 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(+.f64 0 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) 1)
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 1)
(.f64 1 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 1 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k))))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 1 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (neg.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))))
(log.f64 (exp.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) 1))
(+.f64 0 (*.f64 (PI.f64) n))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)
(pow.f64 (*.f64 (PI.f64) n) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) 1))
(+.f64 0 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (neg.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k) 1/2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) -1)
(neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))

Outputs
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
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(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (neg.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k) 1/2)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) -1)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

eval154.0ms (1.3%)

Compiler: Compiled 7490 to 5061 computations (32.4% saved)

prune83.0ms (0.7%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	321	26	347
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	322	27	349

Error

0.0b

Counts

349 → 27

Alt Table

Click to see full alt table

Status	Error	Program
	21.1b	(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
▶	10.8b	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
	11.2b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	3.4b	(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
	0.7b	(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
▶	0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))) (sqrt.f64 k))
	19.7b	(/.f64 (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 k))
	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
	20.0b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	3.4b	(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
	0.6b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (.f64 2 (*.f64 k -1/2)))))
▶	1.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (expm1.f64 (log1p.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k))))
	19.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))
▶	3.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
	3.5b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.5b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	12.8b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	28.5b	(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
	28.9b	(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)))

Compiler

Compiled 1034 to 833 computations (19.4% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 70 to 46 computations (34.3% saved)

series25.0ms (0.2%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
4.0ms	k	@	0	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))) (sqrt.f64 k))
2.0ms	n	@	0	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))) (sqrt.f64 k))
2.0ms	n	@	-inf	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
2.0ms	n	@	-inf	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))) (sqrt.f64 k))
2.0ms	n	@	inf	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))) (sqrt.f64 k))

rewrite84.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

834×	`log-prod_binary64`
386×	`pow2_binary64`
265×	`pow1/3_binary64`
261×	`log-pow_binary64`
261×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	73
1	302	55
2	4000	55

Stop Event

1×	node limit

Counts

4 → 147

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.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 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.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 +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))) (log.f64 (sqrt.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 -.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 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (/.f64 1 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) 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(.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 2) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.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 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 1/2 k -1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 2) 1) (/.f64 (cbrt.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 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 1) (/.f64 (sqrt.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 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 k)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 2) (cbrt.f64 k)) (cbrt.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 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 k)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (pow.f64 k 1/4)))))) (#(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 (sqrt.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 pow.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 1/2 k -1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 1/2 k -1/2)) (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 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simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

366×	`associate-/r/_binary64`
321×	`log-prod_binary64`
283×	`associate-r_binary64`
246×	`associate-l_binary64`
233×	`sqr-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	392	3873
1	917	3618
2	4144	3536

Stop Event

1×	node limit

Counts

171 → 289

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (pow.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1 (.f64 (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/48 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (.f64 -1/16 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (pow.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
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(pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))
(pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) 1)
(pow.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 3)
(pow.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 2)
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 1/2 k -1/2)) -1)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) 3)) 1/3)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 1/2 k -1/2)) 1) -1)
(neg.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k))))
(sqrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) 2))
(log.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)))))
(cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) 3)))
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 1))

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 (PI.f64) (.f64 2 n))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) k) (log.f64 (.f64 (.f64 2 n) (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (*.f64 2 n))))) 1) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (pow.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) k) (log.f64 (.f64 (.f64 2 n) (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 (.f64 2 n) (PI.f64))) 2)) -1/8) (*.f64 k k))))))
(-.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (.f64 k (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) -1/8))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (.f64 2 n))))) 1) (sqrt.f64 2)) (.f64 k (.f64 k (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 2) -1/8))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1 (.f64 (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/48 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (.f64 -1/16 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (pow.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) k) (log.f64 (.f64 (.f64 2 n) (PI.f64))))) (fma.f64 -1 (.f64 (pow.f64 k 3) (.f64 (fma.f64 -1/2 (.f64 (log.f64 (.f64 (.f64 2 n) (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 (.f64 2 n) (PI.f64))) 2)) -1/8)) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 (.f64 2 n) (PI.f64))) 3)) -1/24)) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 (.f64 2 n) (PI.f64))) 2)) -1/8) (*.f64 k k)))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (neg.f64 (.f64 k (.f64 k (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) -1/8))))) (sqrt.f64 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (neg.f64 (.f64 (pow.f64 k 3) (fma.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) -1/8) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (.f64 (sqrt.f64 2) -1/24))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (+.f64 (sqrt.f64 2) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2) (.f64 (sqrt.f64 2) 1/8)) (.f64 k k))) (-.f64 (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 (sqrt.f64 2) k))) (.f64 (pow.f64 k 3) (fma.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 3)) -1/8) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 3) (.f64 (sqrt.f64 2) -1/24)))))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 (*.f64 2 n) (PI.f64))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k)))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 (*.f64 2 n) (PI.f64))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k)))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 (*.f64 2 n) (PI.f64))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k)))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 (*.f64 2 n) (PI.f64))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k)))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 (*.f64 2 n) (PI.f64))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k)))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 (*.f64 2 n) (PI.f64))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k)))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 (*.f64 2 n) (PI.f64))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k)))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 (*.f64 2 n) (PI.f64))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k)))
(+.f64 0 (.f64 2 (.f64 (PI.f64) n)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(-.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) 1)
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 2) 1/2)
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3) 1/3)
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 3)
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)) 1/3)
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 2))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(log.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 1))
(.f64 (.f64 2 n) (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(+.f64 0 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
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(pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1 k))
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 1/2 k -1/2)) -1)
(/.f64 1 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (fma.f64 1/2 k -1/2)))
(/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2)))
(/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k 1/2 -1/2)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) 3)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) k) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k) 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 1/2 k -1/2)) 1) -1)
(/.f64 1 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (fma.f64 1/2 k -1/2)))
(/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2)))
(/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k 1/2 -1/2)))
(neg.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k))))
(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))) (/.f64 1 (neg.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 n) (PI.f64))) k))))
(.f64 1 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k))
(sqrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) 2))
(pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1 k))
(log.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))))
(pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1 k))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)))))
(pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1 k))
(cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) 3))
(pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1 k))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) k) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) k) 3)))
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))))
(pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1 k))
(log1p.f64 (expm1.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))))
(pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
(pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1 k))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 1))
(pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1 k))

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
	0.3b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
✓	9.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 50 to 33 computations (34% saved)

series14.0ms (0.1%)

Counts

3 → 60

Calls

18 calls:

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

rewrite78.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`log-prod_binary64`
468×	`pow-unpow_binary64`
333×	`pow2_binary64`
226×	`pow1/3_binary64`
222×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	259	50
2	3391	50

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

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

Outputs

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

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

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-*l/_binary64`
607×	`associate-/r*_binary64`
266×	`log-prod_binary64`
242×	`associate-r_binary64`
225×	`exp-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	337	4442
1	787	3848
2	3186	3803

Stop Event

1×	node limit

Counts

176 → 209

Calls

Call 1

Inputs
(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 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(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))))))
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(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (-.f64 1 k)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 n (pow.f64 n k)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (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))))
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) 2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) 3)
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3) (pow.f64 k 3)) 1/3)
(pow.f64 (/.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 1) -1)
(neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) (neg.f64 k)))
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 2))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3) (pow.f64 k 3)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1))

Outputs
(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)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (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)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (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)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (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)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 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 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 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 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 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 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (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)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (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)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (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)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (.f64 n (*.f64 2 (PI.f64))))
(fma.f64 n (.f64 2 (PI.f64)) (.f64 (.f64 (.f64 k -2) (.f64 n (PI.f64))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (PI.f64) (+.f64 (.f64 (.f64 k -2) (.f64 n (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (*.f64 n 2)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))))
(fma.f64 (.f64 k -2) (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 2 (.f64 n (PI.f64)))))
(+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) -2) (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) k)))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.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 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (fma.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2))))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 -1/3 (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (pow.f64 k 3))) (fma.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 2 (*.f64 n (PI.f64))))))
(+.f64 (.f64 n (+.f64 (.f64 (.f64 -1/3 (pow.f64 k 3)) (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (.f64 2 (PI.f64)))) (.f64 k (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) -2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) k)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
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(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (.f64 (/.f64 1 k) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) 2)))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) 2))) k) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) k))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(.f64 (/.f64 (/.f64 n (pow.f64 n k)) 1) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) k))
(.f64 (/.f64 n (pow.f64 n k)) (.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k))))
(.f64 (/.f64 1 k) (.f64 (/.f64 n (pow.f64 n k)) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k))))
(/.f64 (.f64 n (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k))) (*.f64 k (pow.f64 n k)))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) (cbrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) (cbrt.f64 k)) (cbrt.f64 (*.f64 k k)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) (.f64 (cbrt.f64 (.f64 k k)) (cbrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (-.f64 1 k)))) (cbrt.f64 (.f64 k k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 (-.f64 1 k) 2))) (cbrt.f64 (*.f64 k k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) 2))) (cbrt.f64 (*.f64 k k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 (.f64 k k))) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) (cbrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) (cbrt.f64 k)) (cbrt.f64 (*.f64 k k)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) (.f64 (cbrt.f64 (.f64 k k)) (cbrt.f64 k)))
(.f64 (/.f64 (/.f64 n (pow.f64 n k)) (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (cbrt.f64 k)))
(/.f64 (.f64 (/.f64 n (pow.f64 n k)) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (cbrt.f64 k))) (cbrt.f64 (*.f64 k k)))
(.f64 (/.f64 n (.f64 (pow.f64 n k) (cbrt.f64 (.f64 k k)))) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (cbrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (-.f64 1 k)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 (-.f64 1 k) 2))) (.f64 (/.f64 1 k) (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (.f64 (/.f64 1 k) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) 2)))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) 2))) k) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (/.f64 (/.f64 n (pow.f64 n k)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (sqrt.f64 k)))
(.f64 (/.f64 n (pow.f64 n k)) (.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k))))
(.f64 (/.f64 1 k) (.f64 (/.f64 n (pow.f64 n k)) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k))))
(/.f64 (.f64 n (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k))) (*.f64 k (pow.f64 n k)))
(.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (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))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (.f64 (sqrt.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)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))) 4))
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) 2)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 2) 1/2)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3) 1/3)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) 3)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3) (pow.f64 k 3)) 1/3)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (/.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 1) -1)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) (neg.f64 k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 2))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3) (pow.f64 k 3)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
✓	0.3b	(*.f64 n (PI.f64))
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	3.3b	(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))

Compiler

Compiled 84 to 52 computations (38.1% saved)

series9.0ms (0.1%)

Counts

3 → 32

Calls

15 calls:

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

rewrite77.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

829×	`log-prod_binary64`
296×	`pow1/3_binary64`
291×	`expm1-udef_binary64`
290×	`log1p-udef_binary64`
271×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	348	44
2	4188	44

Stop Event

1×	node limit

Counts

3 → 82

Calls

Call 1

Inputs

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

(*.f64 n (PI.f64))

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

Outputs

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

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

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

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-def_binary64`
368×	`associate-/r*_binary64`
289×	`associate-*l/_binary64`
256×	`associate-*r/_binary64`
195×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	2713
1	599	2402
2	2358	2281
3	7880	2281

Stop Event

1×	node limit

Counts

114 → 154

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 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 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 0 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2))) (cbrt.f64 (exp.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2))) 1)
(.f64 1 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2))
(.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 1)
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) 2))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) 2) (cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2)))
(.f64 (sqrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) (sqrt.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2)))
(pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 1)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)
(pow.f64 (E.f64) (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (-.f64 1 k)))
(pow.f64 (exp.f64 1/2) (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(pow.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3) 1/3)
(pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) 3)
(pow.f64 (sqrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) 2)
(pow.f64 (exp.f64 (sqrt.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (-.f64 1 k)))) (sqrt.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (-.f64 1 k))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (-.f64 1 k))) 2)) (cbrt.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (-.f64 1 k))))
(pow.f64 (exp.f64 (.f64 1/2 (-.f64 1 k))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (pow.f64 (exp.f64 1/2) (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(pow.f64 (pow.f64 (exp.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (-.f64 1 k))
(pow.f64 (pow.f64 (exp.f64 1/2) (cbrt.f64 (pow.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 2))) (cbrt.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(pow.f64 (pow.f64 (exp.f64 1/2) (sqrt.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) (sqrt.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(sqrt.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 2))
(log.f64 (exp.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2))))
(cbrt.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)))
(log1p.f64 (expm1.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)))
(+.f64 0 (*.f64 n (PI.f64)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)
(pow.f64 (*.f64 n (PI.f64)) 1)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 2)
(pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)
(sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 n (PI.f64)))))
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3))
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))
(expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))
(log1p.f64 (expm1.f64 (*.f64 n (PI.f64))))
(exp.f64 (log.f64 (*.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (.f64 n (PI.f64))) 1))
(+.f64 0 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k)))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k)))) 1)
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)))
(/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) 2) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2))))
(/.f64 (sqrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2))))
(/.f64 (neg.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 1) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (.f64 -1 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) -1) (neg.f64 (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k)) 1)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))) 3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))) 2)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) -1)
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 2) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3) (pow.f64 k 3/2)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (-.f64 1 k) (*.f64 -1/2 (log.f64 k))))
(exp.f64 (.f64 (fma.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (-.f64 1 k) (.f64 -1/2 (log.f64 k))) 1))

Outputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) k)) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))) (sqrt.f64 2))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) k))) (fma.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 (sqrt.f64 2) (.f64 k k))) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (sqrt.f64 2) (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))) (.f64 -1/48 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 -1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) k)) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 -1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.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 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.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 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.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 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.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)))
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(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 (pow.f64 k -1/2) 3)))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2)) -1)
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 2) k))
(sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 2) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k)))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k)) 3))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 (pow.f64 k -1/2) 3)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 1/2) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (-.f64 1 k) (*.f64 -1/2 (log.f64 k))))
(exp.f64 (fma.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (*.f64 -1/2 (log.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))
(exp.f64 (.f64 (fma.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (-.f64 1 k) (.f64 -1/2 (log.f64 k))) 1))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (-.f64 1 k) (*.f64 -1/2 (log.f64 k))))
(exp.f64 (fma.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (*.f64 -1/2 (log.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (PI.f64) n)
✓	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
✓	0.4b	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
✓	9.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Compiler

Compiled 78 to 46 computations (41% saved)

series136.0ms (1.1%)

Counts

3 → 60

Calls

18 calls:

Time	Variable		Point	Expression
46.0ms	n	@	0	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
22.0ms	k	@	-inf	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
20.0ms	k	@	inf	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
19.0ms	n	@	inf	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
18.0ms	n	@	-inf	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)

rewrite85.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

694×	`log-prod_binary64`
475×	`pow-unpow_binary64`
348×	`pow2_binary64`
238×	`pow1/3_binary64`
234×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	52
1	302	52
2	3617	52

Stop Event

1×	node limit

Counts

3 → 105

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
345×	`associate-+l+_binary64`
309×	`associate-+r+_binary64`
219×	`associate-/l*_binary64`
205×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	5196
1	817	4191
2	2974	3988

Stop Event

1×	node limit

Counts

165 → 164

Calls

Call 1

Inputs
(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 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 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 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)
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(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 1))
(+.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))) 1)
(.f64 (.f64 (PI.f64) (.f64 n 2)) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (neg.f64 k)))
(.f64 (.f64 (PI.f64) (.f64 n 2)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) k)))
(.f64 (.f64 (PI.f64) (.f64 n 2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (neg.f64 k) 1)))
(.f64 1 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1)
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (-.f64 1 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))
(.f64 (.f64 2 (pow.f64 1/2 k)) (pow.f64 (*.f64 (PI.f64) n) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 (PI.f64) n) (-.f64 1 k)) (*.f64 2 (pow.f64 1/2 k)))
(.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (-.f64 1 k)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (-.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (neg.f64 k)) (.f64 (PI.f64) (*.f64 n 2)))
(/.f64 2 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) k) (*.f64 (PI.f64) n)))
(/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) k) 2))
(/.f64 (.f64 (PI.f64) (.f64 n 2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) k))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) k) (.f64 (PI.f64) (.f64 n 2))))
(/.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) k) (cbrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) k) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))
(/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) k) n))
(/.f64 (neg.f64 (.f64 (PI.f64) (.f64 n 2))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) k)))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (-.f64 1 k))))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (*.f64 n 2)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (.f64 n 2)))) 1))

Outputs
(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 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 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))
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(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) 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 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
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(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 k))) 2)
(pow.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k) 1/2)
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(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2) (.f64 k (.f64 -1/4 (+.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2)) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2))))))
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(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (.f64 n 2)))) 1))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (PI.f64) n)
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.4b	(pow.f64 (expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2))
✓	3.6b	(expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))

Compiler

Compiled 73 to 45 computations (38.4% saved)

series3.0ms (0%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(pow.f64 (expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2))
0.0ms	n	@	0	(expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))
0.0ms	n	@	inf	(pow.f64 (expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2))
0.0ms	n	@	inf	(expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))
0.0ms	n	@	-inf	(pow.f64 (expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2))

rewrite61.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

599×	`log-prod_binary64`
429×	`prod-diff_binary64`
336×	`pow-unpow_binary64`
319×	`pow2_binary64`
227×	`pow-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	259	25
2	3181	24

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

Inputs
(expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))
(pow.f64 (expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/6) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (neg.f64 (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/4) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/4))))) (#(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 1 (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2)) (-.f64 1 k)) (pow.f64 (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (-.f64 1 k)) (pow.f64 (sqrt.f64 n) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (/.f64 (-.f64 1 k) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (exp.f64 (log1p.f64 (-.f64 1/2 (*.f64 k 1/2))))) (*.f64 (PI.f64) (*.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 4) 1/4) (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 4) (/.f64 (*.f64 k 1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 1))))))

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
432×	`log-prod_binary64`
356×	`*-commutative_binary64`
288×	`sqr-pow_binary64`
245×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	1915
1	580	1781
2	1912	1559
3	5925	1559

Stop Event

1×	node limit

Counts

104 → 122

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(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 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(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 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(+.f64 (fma.f64 2 (*.f64 (PI.f64) n) 1) -1)
(+.f64 0 (.f64 (PI.f64) (.f64 n 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (.f64 n 2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (.f64 n 2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (.f64 n 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (.f64 n 2)))))
(-.f64 (fma.f64 2 (*.f64 (PI.f64) n) 1) 1)
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 n 2))
(.f64 n (.f64 2 (PI.f64)))
(.f64 (.f64 (PI.f64) n) 2)
(.f64 (.f64 (PI.f64) (*.f64 n 2)) 1)
(.f64 1 (.f64 (PI.f64) (*.f64 n 2)))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 2) (.f64 (cbrt.f64 (.f64 (PI.f64) n)) 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2))
(.f64 (.f64 2 (PI.f64)) n)
(.f64 (.f64 2 n) (PI.f64))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 2)) (cbrt.f64 (.f64 (PI.f64) n)))
(.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (.f64 (*.f64 2 (PI.f64)) 1) n)
(.f64 (.f64 (*.f64 2 (PI.f64)) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
(.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n))
(/.f64 (-.f64 (pow.f64 (fma.f64 2 (.f64 (PI.f64) n) 1) 3) 1) (+.f64 (pow.f64 (fma.f64 2 (.f64 (PI.f64) n) 1) 2) (+.f64 1 (.f64 (fma.f64 2 (.f64 (PI.f64) n) 1) 1))))
(/.f64 (-.f64 (pow.f64 (fma.f64 2 (.f64 (PI.f64) n) 1) 2) 1) (+.f64 (fma.f64 2 (.f64 (PI.f64) n) 1) 1))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1)
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) 2) 4) 1/2)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3)
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2)
(sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) 2) 4))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 n 2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (.f64 n 2)))))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3))
(log1p.f64 (expm1.f64 (.f64 (PI.f64) (.f64 n 2))))
(exp.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 n 2))) 1))
(fma.f64 1 (fma.f64 2 (*.f64 (PI.f64) n) 1) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (.f64 (PI.f64) n) 1)) 2) (cbrt.f64 (fma.f64 2 (.f64 (PI.f64) n) 1)) -1)
(fma.f64 (sqrt.f64 (fma.f64 2 (.f64 (PI.f64) n) 1)) (sqrt.f64 (fma.f64 2 (.f64 (PI.f64) n) 1)) -1)
(+.f64 0 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))) 1)
(.f64 1 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) 1)
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/6) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/6))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (neg.f64 (.f64 k 1/2))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 1/4) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/4))
(.f64 (pow.f64 (sqrt.f64 2) (-.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 (sqrt.f64 2) (-.f64 1 k)))
(.f64 (pow.f64 1 (-.f64 1/2 (.f64 k 1/2))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))
(.f64 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2)) (-.f64 1 k)) (pow.f64 (sqrt.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (-.f64 1 k)) (pow.f64 (sqrt.f64 n) (-.f64 1 k)))
(/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (/.f64 (-.f64 1 k) -2)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 k 1/2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (exp.f64 (log1p.f64 (-.f64 1/2 (.f64 k 1/2))))) (.f64 (PI.f64) (*.f64 n 2)))
(/.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) 2) 4) 1/4) (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) 2) 4) (/.f64 (*.f64 k 1/2) 2)))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 1))

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(*.f64 (PI.f64) (+.f64 n n))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 2))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 (.f64 -1/2 (.f64 k (sqrt.f64 2))) (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 2)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 1/8 (sqrt.f64 2)) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (fma.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (.f64 k (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)))) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 3))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 2)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (.f64 1/8 (sqrt.f64 2)) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2))) (.f64 (.f64 -1/48 (.f64 (sqrt.f64 2) (pow.f64 k 3))) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 (.f64 -1/2 (.f64 k (sqrt.f64 2))) (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/8 (.f64 k (.f64 k (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2)))) (.f64 -1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(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 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
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(pow.f64 (exp.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) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))))
(pow.f64 (exp.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) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) 3/2))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) 3/2))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(pow.f64 (exp.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) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(pow.f64 (exp.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) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(pow.f64 (exp.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) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 1))
(pow.f64 (exp.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) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))

eval1.3s (10.3%)

Compiler: Compiled 26245 to 17447 computations (33.5% saved)

prune263.0ms (2.2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	1086	12	1098
Fresh	19	2	21
Picked	1	0	1
Done	3	2	5
Total	1109	16	1125

Error

Counts

1125 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	21.1b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.5b	(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
	20.0b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	10.6b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
▶	0.5b	(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (-.f64 1 k)) (pow.f64 k -1/2))
	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 -1/2 (/.f64 k -2)))))
✓	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))
	30.1b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
	12.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	30.1b	(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
	10.7b	(sqrt.f64 (.f64 (neg.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
▶	30.1b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	12.8b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))

Compiler

Compiled 454 to 366 computations (19.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 49 to 32 computations (34.7% saved)

series22.0ms (0.2%)

Counts

4 → 24

Calls

18 calls:

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

rewrite78.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

674×	`log-prod_binary64`
420×	`pow-unpow_binary64`
344×	`pow2_binary64`
237×	`pow1/3_binary64`
232×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	277	53
2	3508	53

Stop Event

1×	node limit

Counts

4 → 125

Calls

Call 1

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

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

simplify156.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

522×	`log-prod_binary64`
408×	`associate-/r*_binary64`
358×	`fma-neg_binary64`
224×	`sqr-pow_binary64`
185×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	2954
1	667	2810
2	2675	2754
3	7310	2754

Stop Event

1×	node limit

Counts

149 → 192

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/6 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 3))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(+.f64 0 (.f64 2 (.f64 n (PI.f64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(-.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 n (PI.f64))))) 1)
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2)
(pow.f64 (.f64 4 (pow.f64 (.f64 n (PI.f64)) 2)) 1/2)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 3)
(pow.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)
(sqrt.f64 (.f64 4 (pow.f64 (.f64 n (PI.f64)) 2)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 n (PI.f64))))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3))
(cbrt.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 n (PI.f64)))))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 n (PI.f64)))))
(exp.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 1))
(+.f64 0 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)))) 1)
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (neg.f64 k)))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 1 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (neg.f64 k) 1)))
(.f64 1 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 1)
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))))
(.f64 (pow.f64 2 (.f64 (-.f64 1 k) 1/2)) (pow.f64 (.f64 n (PI.f64)) (.f64 (-.f64 1 k) 1/2)))
(.f64 (pow.f64 (+.f64 n n) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (PI.f64) (*.f64 (-.f64 1 k) 1/2)))
(.f64 (pow.f64 (PI.f64) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (+.f64 n n) (*.f64 (-.f64 1 k) 1/2)))
(.f64 (pow.f64 1 (.f64 (-.f64 1 k) 1/2)) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 (-.f64 1 k) 1/2)) (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 (-.f64 1 k) 1/2)))
(.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (-.f64 1 k)))
(.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (-.f64 1 k)) (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4) (-.f64 1 k)))
(*.f64 (pow.f64 (sqrt.f64 (+.f64 n n)) (-.f64 1 k)) (pow.f64 (sqrt.f64 (PI.f64)) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (neg.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))
(/.f64 (sqrt.f64 (+.f64 n n)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (sqrt.f64 (PI.f64))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(log.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)))))
(cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (-.f64 1 k) 1/2)))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 1))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)))) 1)
(.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)) 1)
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))
(.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))
(.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (pow.f64 k -1/2)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 1) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (pow.f64 k 1/4)))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) 1)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) 2)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) 1) -1)
(neg.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))) 1))
(+.f64 0 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 1)
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) 1)
(.f64 1 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (cbrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) 3)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) 2)
(fabs.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) 1))

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (neg.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (sqrt.f64 2) (.f64 k (.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 2)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)))) (neg.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))))))
(-.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (.f64 k k))) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)))) (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 k (sqrt.f64 (.f64 n (PI.f64)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (neg.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))))))))
(+.f64 (.f64 -1/6 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 3))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/6 (.f64 (sqrt.f64 2) (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 3)) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)))) (neg.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64)))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (neg.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))) (.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (.f64 k k))) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (.f64 -1/6 (.f64 (sqrt.f64 2) (pow.f64 k 3))) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) 3)) (sqrt.f64 2))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (neg.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))))) (.f64 (+.f64 (.f64 -1/6 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 3))) 1) (sqrt.f64 2))))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(+.f64 0 (.f64 2 (.f64 n (PI.f64))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(-.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 n (PI.f64))))) 1)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 (PI.f64) 2))
(pow.f64 (.f64 4 (pow.f64 (.f64 n (PI.f64)) 2)) 1/2)
(sqrt.f64 (.f64 4 (pow.f64 (.f64 n (PI.f64)) 2)))
(fabs.f64 (.f64 n (.f64 (PI.f64) 2)))
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(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (pow.f64 k -1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 1) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 k)))
(/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (-.f64 1 k))) (cbrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k 1/4)))
(.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (pow.f64 k 1/4)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (sqrt.f64 k)))
(/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k))) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) 1)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k) 1/2)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) 3) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) 3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))) 2)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) -1)
(.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) 3) (pow.f64 k 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) 3) (pow.f64 k 3/2)))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) 1) -1)
(.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (neg.f64 (sqrt.f64 k))))
(.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) 3))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))) 1))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1 k)) k))
(+.f64 0 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 1)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) 1)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(.f64 1 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (cbrt.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (cbrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (cbrt.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (fabs.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 (cbrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) 1/3)
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3/2))
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) 3)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) 2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(fabs.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(log.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 1/2))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) 1))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (PI.f64) (/.f64 k n))
✓	9.7b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series8.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

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

rewrite58.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`log-prod_binary64`
411×	`exp-prod_binary64`
284×	`pow-prod-down_binary64`
250×	`pow2_binary64`
223×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	195	21
2	2641	21

Stop Event

1×	node limit

Counts

2 → 99

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 1) 1))))))

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

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

677×	`associate-*l/_binary64`
574×	`associate-*r/_binary64`
425×	`associate-/l*_binary64`
252×	`times-frac_binary64`
231×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	253	1470
1	588	1422
2	1621	1422
3	7836	1422

Stop Event

1×	node limit

Counts

123 → 134

Calls

Call 1

Inputs
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(+.f64 0 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))) 1)
(.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1)
(.f64 1 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))
(.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6))
(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) (cbrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))
(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/2)
(pow.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1)
(pow.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)) 1/4)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3) 1/6)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
(pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))))
(fabs.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1/2) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))) 1) 1))
(+.f64 0 (*.f64 (PI.f64) (/.f64 n k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k)))) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (PI.f64) (/.f64 n k)) 1)
(.f64 1 (.f64 (PI.f64) (/.f64 n k)))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) k) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)) (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (/.f64 k n))))
(*.f64 (pow.f64 (/.f64 k n) -1/2) (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (sqrt.f64 (/.f64 k n))) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n))))
(*.f64 (/.f64 (PI.f64) 1) (/.f64 n k))
(*.f64 (/.f64 (PI.f64) (neg.f64 k)) (neg.f64 n))
(.f64 (.f64 (/.f64 (PI.f64) k) 1) n)
(.f64 (.f64 (/.f64 (PI.f64) k) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
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(pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 3)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2)
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -1)
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(pow.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) 1) -1)
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(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k)))))
(neg.f64 (/.f64 (PI.f64) (/.f64 (neg.f64 k) n)))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(cbrt.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3))
(cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)))
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(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) -3)) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 2))
(exp.f64 (.f64 (log.f64 (/.f64 k (.f64 (PI.f64) n))) -1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) 1) 1))
(exp.f64 (-.f64 (*.f64 (log.f64 (PI.f64)) 1) (log.f64 (/.f64 k n))))
(exp.f64 (-.f64 (log.f64 (PI.f64)) (*.f64 (log.f64 (/.f64 k n)) 1)))
(exp.f64 (-.f64 (.f64 (log.f64 (PI.f64)) 1) (.f64 (log.f64 (/.f64 k n)) 1)))

Outputs
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
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(/.f64 (*.f64 n (PI.f64)) k)
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(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
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(/.f64 (*.f64 n (PI.f64)) k)
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(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
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(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
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(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6)) 3))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
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(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1/2) 1))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
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(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(+.f64 0 (*.f64 (PI.f64) (/.f64 n k)))
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(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(*.f64 (PI.f64) (/.f64 n k))
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(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k)))) 1)
(*.f64 (PI.f64) (/.f64 n k))
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(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(.f64 (.f64 (PI.f64) (/.f64 n k)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 1 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)))
(.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) -2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)))
(.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) -2)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) k) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)) (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)))
(.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (/.f64 k n))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))
(*.f64 (pow.f64 (/.f64 k n) -1/2) (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))))
(/.f64 (pow.f64 (/.f64 k n) -1/2) (/.f64 (sqrt.f64 (/.f64 k n)) (PI.f64)))
(*.f64 (/.f64 (pow.f64 (/.f64 k n) -1/2) (sqrt.f64 (/.f64 k n))) (PI.f64))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (sqrt.f64 (/.f64 k n))) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n))))
(/.f64 (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))) (sqrt.f64 (/.f64 k n)))
(/.f64 (PI.f64) (*.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (/.f64 k n))))
(*.f64 (/.f64 (PI.f64) 1) (/.f64 n k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (PI.f64) (neg.f64 k)) (neg.f64 n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 (PI.f64) k) 1) n)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 (PI.f64) k) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 (PI.f64) k) (sqrt.f64 n)) (sqrt.f64 n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2) 1/2)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3) 1/3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)) 1/3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) 1) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k)))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))) 2)) (cbrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k))))) (sqrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))))
(neg.f64 (/.f64 (PI.f64) (/.f64 (neg.f64 k) n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) -3)) 1/3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 2))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (/.f64 k (.f64 (PI.f64) n))) -1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) 1) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (-.f64 (*.f64 (log.f64 (PI.f64)) 1) (log.f64 (/.f64 k n))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (-.f64 (log.f64 (PI.f64)) (*.f64 (log.f64 (/.f64 k n)) 1)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (-.f64 (.f64 (log.f64 (PI.f64)) 1) (.f64 (log.f64 (/.f64 k n)) 1)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
	0.3b	(.f64 n (.f64 2 (PI.f64)))
	0.3b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
✓	9.6b	(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))

Compiler

Compiled 64 to 43 computations (32.8% saved)

series15.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	n	@	-inf	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
2.0ms	k	@	0	(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
2.0ms	k	@	-inf	(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
1.0ms	k	@	inf	(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
1.0ms	n	@	-inf	(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))

rewrite68.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

713×	`log-prod_binary64`
484×	`pow-unpow_binary64`
359×	`pow2_binary64`
244×	`pow1/3_binary64`
241×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	285	38
2	3747	38

Stop Event

1×	node limit

Counts

2 → 67

Calls

Call 1

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

Outputs

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

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

589×	`log-prod_binary64`
518×	`associate-l_binary64`
473×	`associate-r_binary64`
465×	`exp-prod_binary64`
241×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	2487
1	362	2392
2	1156	2055
3	6765	2045

Stop Event

1×	node limit

Counts

91 → 110

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(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 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(+.f64 0 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
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(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))) 1)
(.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) 1)
(.f64 (cbrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))
(.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 (-.f64 1 k)))))
(.f64 (sqrt.f64 k) (/.f64 1 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))
(.f64 (pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 1/4) (pow.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 1/4))
(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 2))) (sqrt.f64 (cbrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(/.f64 1 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))) 1)
(/.f64 (cbrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 (pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 1/4) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))) -1)
(/.f64 (sqrt.f64 (neg.f64 k)) (sqrt.f64 (neg.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 1/2)
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))) 1)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) -1)
(pow.f64 (pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))) 3)
(pow.f64 (pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 1/4) 2)
(pow.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) -1)
(fabs.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))))
(cbrt.f64 (pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))))
(exp.f64 (.f64 (log.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) 1))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))) 1)
(.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1)
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(.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))))
(.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))))
(.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))) -1)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))) 2)
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/2)
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))) -1)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) -1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) 1))

Outputs
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
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(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
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(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (+.f64 k -1)))))
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(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (+.f64 k -1)))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
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(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
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(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
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(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) -2) (-.f64 1 k)) (pow.f64 (/.f64 -1 n) (+.f64 k -1))) k))
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(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))
(.f64 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))) 3)
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(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(/.f64 -1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))) -1)
(/.f64 -1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1)
(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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) 3) 1/3)
(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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))) 3)
(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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))) 2)
(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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/2)
(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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))) -1)
(/.f64 -1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) 3))
(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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) -1))
(/.f64 -1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) 1))
(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 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 72 to 39 computations (45.8% saved)

series17.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
3.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 -1/2 (/.f64 k -2)))))
3.0ms	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 -1/2 (/.f64 k -2)))))
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 -1/2 (/.f64 k -2)))))
1.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 -1/2 (/.f64 k -2)))))
1.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 -1/2 (/.f64 k -2)))))

rewrite76.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

551×	`prod-diff_binary64`
300×	`expm1-udef_binary64`
300×	`log1p-udef_binary64`
278×	`log-pow_binary64`
227×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	370	48
2	5148	44

Stop Event

1×	node limit

Counts

3 → 117

Calls

Call 1

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

Outputs

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

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

200×	`associate-r_binary64`
186×	`associate-l_binary64`
112×	`*-commutative_binary64`
95×	`sqr-pow_binary64`
88×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	343	4226
1	832	4226
2	4403	4226

Stop Event

1×

unsound

Counts

165 → 132

Calls

Call 1

Inputs
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2))
(+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
(+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2))))
(+.f64 (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 (*.f64 1/2 k) 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 (*.f64 1/2 k) 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 (*.f64 1/2 k) 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 (*.f64 1/2 k) 1/2))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (/.f64 1 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))) (sqrt.f64 (/.f64 1 k)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))) 1)
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) 1)
(.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) (cbrt.f64 (pow.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) 2)) (fma.f64 k 1/2 -1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2)) (fma.f64 k 1/2 -1/2))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(*.f64 (pow.f64 (PI.f64) (fma.f64 k 1/2 -1/2)) (pow.f64 (+.f64 n n) (fma.f64 k 1/2 -1/2)))
(*.f64 (pow.f64 (+.f64 n n) (fma.f64 k 1/2 -1/2)) (pow.f64 (PI.f64) (fma.f64 k 1/2 -1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) -1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) -1/2) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(.f64 (pow.f64 1 (fma.f64 k 1/2 -1/2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))
(.f64 (pow.f64 (pow.f64 (.f64 (+.f64 n n) (cbrt.f64 (PI.f64))) 2) (fma.f64 k 1/2 -1/2)) (pow.f64 (*.f64 (+.f64 n n) (cbrt.f64 (PI.f64))) (fma.f64 k 1/2 -1/2)))
(.f64 (pow.f64 (.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (fma.f64 k 1/2 -1/2)) (pow.f64 (*.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (fma.f64 k 1/2 -1/2)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) 1)
(/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) -1/2)))
(/.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2)) (fma.f64 k 1/2 -1/2))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2)))))
(/.f64 (pow.f64 (PI.f64) (fma.f64 k 1/2 -1/2)) (/.f64 1 (pow.f64 (+.f64 n n) (fma.f64 k 1/2 -1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) -1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 -1/2 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) -1)
(/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) -1/2))
(/.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) -1/2)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 -1/2 k))))
(sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) 2)) (fma.f64 k 1/2 -1/2)))
(log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(exp.f64 (.f64 (fma.f64 k 1/2 -1/2) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(exp.f64 (.f64 (.f64 (fma.f64 k 1/2 -1/2) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(+.f64 (.f64 (.f64 (PI.f64) n) 1) (.f64 (.f64 (PI.f64) n) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)
(/.f64 (+.f64 (pow.f64 (.f64 (PI.f64) n) 3) (pow.f64 (.f64 (PI.f64) n) 3)) (fma.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n) (-.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)))))
(/.f64 (-.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)))
(/.f64 (.f64 (.f64 2 (pow.f64 n 3)) (PI.f64)) (fma.f64 n n 0))
(/.f64 (*.f64 0 (PI.f64)) 0)
(/.f64 (.f64 (PI.f64) (.f64 2 (pow.f64 n 3))) (fma.f64 n n 0))
(/.f64 (*.f64 (PI.f64) 0) 0)
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) 1/3)
(pow.f64 (*.f64 (+.f64 n n) (cbrt.f64 (PI.f64))) 3)
(pow.f64 (*.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) 2)
(sqrt.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) 2)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (+.f64 n n)))
(cbrt.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(fma.f64 1 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(fma.f64 (pow.f64 (cbrt.f64 n) 2) (.f64 (cbrt.f64 n) (PI.f64)) (.f64 (PI.f64) n))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) n) (.f64 (PI.f64) n))
(fma.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (PI.f64)) (.f64 (PI.f64) n))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n) (.f64 (PI.f64) n))
(fma.f64 (.f64 (PI.f64) n) 1 (.f64 (*.f64 (PI.f64) n) 1))
(fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) n)) (cbrt.f64 (.f64 (PI.f64) n))) (cbrt.f64 (.f64 (PI.f64) n)) (*.f64 (PI.f64) n))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (PI.f64) n))
(fma.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) n))
(fma.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (*.f64 (PI.f64) n))
(fma.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)) (.f64 (PI.f64) n))
(fma.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (.f64 (PI.f64) n))
(fma.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n) (.f64 (PI.f64) n))
(fma.f64 (.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n) (.f64 (PI.f64) n))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))) 1)
(/.f64 1 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)))
(/.f64 1 (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(/.f64 1 (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) 1))
(/.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (pow.f64 k -1/2)))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2)))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) (sqrt.f64 k))
(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) -2)) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))))))
(/.f64 (cbrt.f64 (/.f64 1 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (cbrt.f64 (pow.f64 k -1/2))))
(/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) -1/2) (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) -1/2)))
(/.f64 (sqrt.f64 (pow.f64 k -1/2)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 (pow.f64 k -1/2))))
(/.f64 -1 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k))))
(/.f64 -1 (.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(/.f64 -1 (.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(/.f64 -1 (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) (sqrt.f64 k)))
(/.f64 -1 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (pow.f64 k -1/2)) (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (/.f64 (pow.f64 k -1/2) 1) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))
(/.f64 (/.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2)) (fma.f64 k 1/2 -1/2)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(/.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (PI.f64) (fma.f64 k 1/2 -1/2))) (pow.f64 (+.f64 n n) (fma.f64 k 1/2 -1/2)))
(/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) 1) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (.f64 -1 (pow.f64 k -1/2)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(/.f64 (.f64 -1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 k -1/2) -1) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) -1) (neg.f64 (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) 1)
(pow.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))) 3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))) 2)
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -1)
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) -2) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) 3)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(exp.f64 (log.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))) 1))

Outputs
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(+.f64 (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))))
(fma.f64 1/48 (.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (.f64 (.f64 (pow.f64 k 3) (sqrt.f64 1/2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (fma.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (.f64 (.f64 (.f64 k k) (sqrt.f64 1/2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (.f64 (.f64 k (sqrt.f64 1/2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 (*.f64 1/2 k) 1/2))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 (*.f64 1/2 k) 1/2))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 (*.f64 1/2 k) 1/2))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 (*.f64 1/2 k) 1/2))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
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(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) n) (.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (PI.f64)) (.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n) (.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (.f64 (PI.f64) n) 1 (.f64 (*.f64 (PI.f64) n) 1))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) n)) (cbrt.f64 (.f64 (PI.f64) n))) (cbrt.f64 (.f64 (PI.f64) n)) (*.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (*.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)) (.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n) (.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(fma.f64 (.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n) (.f64 (PI.f64) n))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))) 1)
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 1 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 1 (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 1 (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) (neg.f64 (sqrt.f64 k))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) 1))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (pow.f64 k -1/2)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2)))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) (sqrt.f64 k))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) -2)) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (cbrt.f64 (/.f64 1 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (cbrt.f64 (pow.f64 k -1/2))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) -1/2) (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) -1/2)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (sqrt.f64 (pow.f64 k -1/2)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 (pow.f64 k -1/2))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 -1 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 -1 (.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 -1 (.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 -1 (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) (sqrt.f64 k)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 -1 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (neg.f64 (sqrt.f64 k))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (neg.f64 (pow.f64 k -1/2)) (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2)))) (neg.f64 (sqrt.f64 k)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (/.f64 (pow.f64 k -1/2) 1) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (/.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2)) (fma.f64 k 1/2 -1/2)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (PI.f64) (fma.f64 k 1/2 -1/2))) (pow.f64 (+.f64 n n) (fma.f64 k 1/2 -1/2)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) 1) (sqrt.f64 k))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (.f64 -1 (pow.f64 k -1/2)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (.f64 -1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2)))) (neg.f64 (sqrt.f64 k)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (.f64 (pow.f64 k -1/2) -1) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) -1) (neg.f64 (sqrt.f64 k)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) 1)
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) 3) 1/3)
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))) 3)
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))) 2)
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -1)
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) -2) k))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(log.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2))) 3))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)) 3)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) 3) (pow.f64 k 3/2)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) 3)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (fma.f64 k 1/2 -1/2))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (log.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 k 1/2 -1/2)))) 1))
(exp.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 52 to 36 computations (30.8% saved)

series10.0ms (0.1%)

Counts

4 → 24

Calls

18 calls:

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

rewrite78.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

685×	`log-prod_binary64`
407×	`pow-unpow_binary64`
364×	`pow2_binary64`
249×	`pow1/3_binary64`
246×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	298	56
2	3575	56

Stop Event

1×	node limit

Counts

4 → 109

Calls

Call 1

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

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

simplify111.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

567×	`times-frac_binary64`
534×	`log-prod_binary64`
312×	`fma-neg_binary64`
301×	`associate-/l*_binary64`
216×	`sqr-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	280	2539
1	600	2422
2	2351	2324
3	7101	2324

Stop Event

1×	node limit

Counts

133 → 176

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/6 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 3))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 1 (*.f64 -1 k)))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 2))
(log.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))
(cbrt.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1))
(+.f64 0 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 1)
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (neg.f64 k) 1)))
(.f64 1 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 1)
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(*.f64 (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (+.f64 n n) (-.f64 1/2 (/.f64 k 2))))
(*.f64 (pow.f64 (+.f64 n n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (/.f64 k 2))))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))
(.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (-.f64 1 k)))
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) (-.f64 1 k)) (pow.f64 (sqrt.f64 (+.f64 n n)) (-.f64 1 k)))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (-.f64 1 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))
(/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(/.f64 (sqrt.f64 (PI.f64)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k) (sqrt.f64 (+.f64 n n))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(log.f64 (exp.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))
(cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (/.f64 k 2))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1))
(+.f64 0 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1))))) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 k -1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))
(/.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))
(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1))) 1)
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1))) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1)))) 3)
(pow.f64 (.f64 (pow.f64 k -1/4) (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 2)
(pow.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3)) 1/3)
(sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1))) 3))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1)))) 1))
(+.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1)
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1)
(.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 n))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 3)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2)
(fabs.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 1))

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

eval416.0ms (3.4%)

Compiler: Compiled 17437 to 10648 computations (38.9% saved)

prune262.0ms (2.1%)

Pruning

28 alts after pruning (23 fresh and 5 done)

	Pruned	Kept	Total
New	854	15	869
Fresh	1	8	9
Picked	0	1	1
Done	2	4	6
Total	857	28	885

Error

Counts

885 → 28

Alt Table

Click to see full alt table

Status	Error	Program
	21.1b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
▶	38.8b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
	30.2b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
	32.6b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
	10.5b	(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
	47.6b	(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
▶	30.4b	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
	30.4b	(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	20.0b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	30.2b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
✓	10.6b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
	30.0b	(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
✓	0.5b	(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (-.f64 1 k)) (pow.f64 k -1/2))
▶	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	30.1b	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
✓	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))
	30.1b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
	12.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	30.1b	(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
▶	30.0b	(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
✓	30.1b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
▶	30.1b	(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
	30.1b	(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
	12.8b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
	32.2b	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
	37.2b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))

Compiler

Compiled 682 to 560 computations (17.9% saved)

localize30.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 53 to 38 computations (28.3% saved)

series5.0ms (0%)

Counts

1 → 12

Calls

6 calls:

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

rewrite58.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`log-prod_binary64`
505×	`pow-unpow_binary64`
387×	`pow2_binary64`
265×	`pow1/3_binary64`
261×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	307	23
2	3794	22

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify49.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

833×	`log-prod_binary64`
692×	`associate-l_binary64`
636×	`associate-r_binary64`
415×	`unswap-sqr_binary64`
241×	`exp-sum_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	96	934
1	232	900
2	812	813
3	5741	813

Stop Event

1×	node limit

Counts

33 → 41

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 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 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 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 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 0 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 1)
(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 1)
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 3)
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)) 1/3)
(pow.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 1))

Outputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (pow.f64 k -1/2))
(+.f64 0 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))))))
(.f64 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 1)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 1)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3) 1/3)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 3)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k -1/4)) 2)
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(pow.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 1))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
✓	9.7b	(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))

Compiler

Compiled 29 to 14 computations (51.7% saved)

series6.0ms (0%)

Counts

2 → 24

Calls

12 calls:

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

rewrite62.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

946×	`pow1_binary64`
875×	`add-log-exp_binary64`
875×	`log1p-expm1-u_binary64`
875×	`expm1-log1p-u_binary64`
856×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	189	24
2	2375	24

Stop Event

1×	node limit

Counts

2 → 44

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))

Outputs

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

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

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-def_binary64`
494×	`log-prod_binary64`
352×	`unswap-sqr_binary64`
309×	`log-div_binary64`
271×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	924
1	231	864
2	887	804
3	4392	804

Stop Event

1×	node limit

Counts

68 → 52

Calls

Call 1

Inputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1)
(.f64 1 (sqrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))))
(.f64 (cbrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n)))) (cbrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 2 (/.f64 n k))))
(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n)) 1/4) (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/4))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 n k)))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) 2) 1/2) (sqrt.f64 (/.f64 n k)))
(pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/2)
(pow.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 3)
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/4) 2)
(fabs.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)
(/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))
(/.f64 (.f64 (.f64 2 n) (PI.f64)) k)
(/.f64 (.f64 (PI.f64) (.f64 2 n)) k)
(/.f64 (.f64 (.f64 (PI.f64) 2) n) k)
(/.f64 (.f64 (.f64 (PI.f64) 2) 1) (/.f64 k n))
(/.f64 (.f64 (.f64 (PI.f64) 2) (neg.f64 n)) (neg.f64 k))
(pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1)
(pow.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 2)
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 3)
(sqrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 2))
(log.f64 (pow.f64 (pow.f64 (exp.f64 2) (/.f64 n k)) (PI.f64)))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3))
(cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (.f64 2 (/.f64 n k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (/.f64 n k)) 3) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))
(log1p.f64 (expm1.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))
(exp.f64 (log.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))

Outputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 1 (sqrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (cbrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n)))) (cbrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 2 (/.f64 n k))))
(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n)) 1/4) (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 2 (/.f64 n k))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 (pow.f64 (.f64 (PI.f64) 2) 1/2) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3/2) 1/3)
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(fabs.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3/2))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(+.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(/.f64 (.f64 (.f64 2 n) (PI.f64)) k)
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(/.f64 (.f64 (PI.f64) (.f64 2 n)) k)
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(/.f64 (.f64 (.f64 (PI.f64) 2) n) k)
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(/.f64 (.f64 (.f64 (PI.f64) 2) 1) (/.f64 k n))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(/.f64 (.f64 (.f64 (PI.f64) 2) (neg.f64 n)) (neg.f64 k))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1)
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 2)
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 2) 1/2)
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3) 1/3)
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(pow.f64 (cbrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 3)
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(sqrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 2))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 2) (/.f64 n k)) (PI.f64)))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (.f64 2 (/.f64 n k)) 3)))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (/.f64 n k)) 3) (pow.f64 (PI.f64) 3)))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(log1p.f64 (expm1.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
(exp.f64 (log.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))
(/.f64 (.f64 n (.f64 2 (PI.f64))) k)
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 (PI.f64) (.f64 2 (/.f64 n k)))

localize24.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))
✓	0.3b	(/.f64 (PI.f64) (/.f64 1 n))
✓	9.7b	(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))

Compiler

Compiled 50 to 35 computations (30% saved)

series5.0ms (0%)

Counts

3 → 36

Calls

15 calls:

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

rewrite75.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

639×	`log-prod_binary64`
426×	`pow-prod-down_binary64`
305×	`pow2_binary64`
290×	`pow-unpow_binary64`
216×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	257	26
2	3374	26

Stop Event

1×	node limit

Counts

3 → 133

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) (pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 1/6) (cbrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 1/4) (pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 2 k)))) 1))))))

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

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

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
375×	`distribute-rgt-in_binary64`
361×	`log-prod_binary64`
234×	`cube-prod_binary64`
192×	`div-sub_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	1593
1	747	1517
2	2717	1481

Stop Event

1×	node limit

Counts

169 → 164

Calls

Call 1

Inputs
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(+.f64 0 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k))))) 1)
(.f64 1 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k))))
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(pow.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k))) 1)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 2) 1/4)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 3) 1/6)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k))) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/4) 2)
(fabs.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k))))))
(cbrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k)))) 1))
(+.f64 0 (*.f64 (PI.f64) n))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)
(.f64 1 (.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(.f64 (.f64 (PI.f64) n) 1)
(.f64 (cbrt.f64 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 2) (cbrt.f64 (*.f64 (PI.f64) n)))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) n))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 (sqrt.f64 n) (/.f64 (PI.f64) (pow.f64 n -1/2)))
(*.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 -1 n)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 n -2))) (/.f64 (PI.f64) (/.f64 1 (cbrt.f64 n))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (pow.f64 n -2))) (cbrt.f64 (.f64 (PI.f64) n)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 n -2))) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 (cbrt.f64 n))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 n -1/2)) (/.f64 (cbrt.f64 (PI.f64)) (pow.f64 n -1/2)))
(*.f64 (/.f64 (PI.f64) -1) (neg.f64 n))
(.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
(.f64 (.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
(pow.f64 (*.f64 (PI.f64) n) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)
(pow.f64 (/.f64 1 (*.f64 (PI.f64) n)) -1)
(pow.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 n -3)) 1/3)
(pow.f64 (/.f64 (/.f64 1 (*.f64 (PI.f64) n)) 1) -1)
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)
(pow.f64 (*.f64 (cbrt.f64 n) (cbrt.f64 (PI.f64))) 3)
(pow.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) 2)
(neg.f64 (/.f64 (PI.f64) (/.f64 -1 n)))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))
(cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 n -3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) 1))
(+.f64 0 (*.f64 (PI.f64) (/.f64 n k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k)))) 1)
(/.f64 1 (.f64 k (/.f64 1 (.f64 (PI.f64) n))))
(/.f64 1 (.f64 (/.f64 1 (.f64 (PI.f64) n)) k))
(/.f64 1 (/.f64 (/.f64 k n) (PI.f64)))
(/.f64 1 (/.f64 k (*.f64 (PI.f64) n)))
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(/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (/.f64 (/.f64 k n) (cbrt.f64 (PI.f64))))
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(/.f64 (sqrt.f64 (PI.f64)) (/.f64 (/.f64 k n) (sqrt.f64 (PI.f64))))
(/.f64 -1 (.f64 (neg.f64 k) (/.f64 1 (.f64 (PI.f64) n))))
(/.f64 -1 (.f64 (/.f64 1 (.f64 (PI.f64) n)) (neg.f64 k)))
(/.f64 (neg.f64 (PI.f64)) (neg.f64 (/.f64 k n)))
(/.f64 (neg.f64 (PI.f64)) (*.f64 (neg.f64 k) (/.f64 1 n)))
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(/.f64 (.f64 (PI.f64) -1) (.f64 (/.f64 1 n) (neg.f64 k)))
(/.f64 (.f64 (neg.f64 (PI.f64)) -1) (.f64 (/.f64 -1 n) (neg.f64 k)))
(/.f64 (/.f64 (*.f64 (PI.f64) n) (sqrt.f64 k)) (sqrt.f64 k))
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(/.f64 (/.f64 (*.f64 (PI.f64) n) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k))
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(/.f64 (.f64 (.f64 (PI.f64) n) -1) (neg.f64 k))
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(pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 3)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2)
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) 3) (pow.f64 k 3)) 1/3)
(pow.f64 (.f64 k (/.f64 1 (.f64 (PI.f64) n))) -1)
(pow.f64 (.f64 (/.f64 1 (.f64 (PI.f64) n)) k) -1)
(pow.f64 (/.f64 (/.f64 k n) (PI.f64)) -1)
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(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) 3) (pow.f64 k 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))) 1))

Outputs
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
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(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
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(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
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(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
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(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
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(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
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(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
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(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 2 (PI.f64)) (/.f64 n k))
✓	0.4b	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
✓	10.3b	(cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))

Compiler

Compiled 38 to 21 computations (44.7% saved)

series85.0ms (0.7%)

Counts

3 → 24

Calls

18 calls:

Time	Variable		Point	Expression
67.0ms	n	@	0	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
7.0ms	k	@	inf	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
1.0ms	n	@	-inf	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
1.0ms	k	@	-inf	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
1.0ms	n	@	inf	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)

rewrite82.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`log-prod_binary64`
412×	`exp-prod_binary64`
335×	`pow-prod-down_binary64`
282×	`pow2_binary64`
233×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	233	37
2	2866	37

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

Inputs
(cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(.f64 (.f64 2 (PI.f64)) (/.f64 n k))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule 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k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/3) (log.f64 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(cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 2))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6) (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/4) (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2/3 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1/3) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 3/4) 2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x 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1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 2) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 4) 3/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 2)) (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))) (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2/3 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1) 2))))))

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary64`
523×	`distribute-rgt-in_binary64`
490×	`distribute-lft-in_binary64`
293×	`times-frac_binary64`
277×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	264	1987
1	558	1926
2	1677	1926

Stop Event

1×	node limit

Counts

140 → 145

Calls

Call 1

Inputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(+.f64 0 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))))
(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))) 1)
(.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1)
(.f64 1 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))
(.f64 (cbrt.f64 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2)) (cbrt.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))
(.f64 (cbrt.f64 (/.f64 n k)) (cbrt.f64 (.f64 2 (PI.f64))))
(.f64 (cbrt.f64 (.f64 2 (PI.f64))) (cbrt.f64 (/.f64 n k)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/6) (pow.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6))
(/.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (cbrt.f64 k))
(pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3)
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1)
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2/3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 2) 1/6)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3) 1/9)
(pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2) 1/2)
(pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 3)
(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2)) 3/2)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/6) 2)
(pow.f64 (exp.f64 1) (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(pow.f64 (exp.f64 1/3) (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))) 2)) (cbrt.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))) (sqrt.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))))
(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2))
(log.f64 (exp.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))))
(expm1.f64 (log1p.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(log1p.f64 (expm1.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(exp.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6)) 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 2))) 3/2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1) 1/3))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1/3) 1))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 1))
(+.f64 0 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))) 1)
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) (pow.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6))
(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1)
(.f64 1 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/6) (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/4) (pow.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/4))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(fabs.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3/2)) 1/3))
(exp.f64 (.f64 (.f64 2/3 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 3/4))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6)) 3))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1/3) 3/2))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 3/2))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 1))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 3/4) 2))
(+.f64 0 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1)
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(/.f64 1 (/.f64 k (.f64 2 (.f64 (PI.f64) n))))
(/.f64 (.f64 2 (.f64 (PI.f64) n)) k)
(/.f64 (neg.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 k))
(/.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) 1) k)
(/.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k))
(/.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 k))
(/.f64 (.f64 (neg.f64 n) (.f64 2 (PI.f64))) (neg.f64 k))
(/.f64 (.f64 (.f64 2 (PI.f64)) (neg.f64 n)) (neg.f64 k))
(pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1)
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 3)
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3/2) 2/3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 2) 1/2)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3) 1/3)
(pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2) 3/2)
(pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 9)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/6) 6)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/4) 4)
(pow.f64 (exp.f64 1) (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(pow.f64 (/.f64 k (.f64 2 (.f64 (PI.f64) n))) -1)
(pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 4) 3/4)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 2))
(log.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3))
(expm1.f64 (log1p.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(log1p.f64 (expm1.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 2))
(exp.f64 (.f64 (.f64 3 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1/3))
(exp.f64 (.f64 (.f64 2/3 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 3/2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1) 1))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1/3) 3))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 3))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 2))

Outputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
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(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 2))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1) 1/2))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1/3) 3/2))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 3/2))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 1))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 3/4) 2))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(+.f64 0 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k))))))
(.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k))))))
(.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (.f64 n (/.f64 (PI.f64) k))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k))))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(/.f64 1 (/.f64 k (.f64 2 (.f64 (PI.f64) n))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(/.f64 (.f64 2 (.f64 (PI.f64) n)) k)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(/.f64 (neg.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(/.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) 1) k)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(/.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(/.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(/.f64 (.f64 (neg.f64 n) (.f64 2 (PI.f64))) (neg.f64 k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(/.f64 (.f64 (.f64 2 (PI.f64)) (neg.f64 n)) (neg.f64 k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 3)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3/2) 2/3)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 2) 1/2)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3) 1/3)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2) 3/2)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 9)
(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))) 9)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/6) 6)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/4) 4)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (exp.f64 1) (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (/.f64 k (.f64 2 (.f64 (PI.f64) n))) -1)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 4) 3/4)
(pow.f64 (pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 4) 3/4)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))) 2)) (cbrt.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))))) (sqrt.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(log.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(expm1.f64 (log1p.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(log1p.f64 (expm1.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (.f64 3 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1/3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (.f64 2/3 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 3/2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1) 1))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1/3) 3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))

localize26.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(.f64 (.f64 2 (PI.f64)) (/.f64 n k))
✓	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2)
✓	23.8b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)

Compiler

Compiled 41 to 24 computations (41.5% saved)

series102.0ms (0.8%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
24.0ms	k	@	0	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
19.0ms	n	@	-inf	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
19.0ms	k	@	-inf	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
18.0ms	n	@	0	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
10.0ms	k	@	inf	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)

rewrite62.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

603×	`log-prod_binary64`
351×	`pow-prod-down_binary64`
315×	`pow2_binary64`
245×	`pow-unpow_binary64`
229×	`pow-to-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	267	27
2	3194	27

Stop Event

1×	node limit

Counts

2 → 64

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6) (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1/6) 2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) 3/2) (pow.f64 (/.f64 n k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 n k) 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 3/2) (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 5/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 9/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 9/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/4 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 3/4) 2))))))

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

549×	`exp-prod_binary64`
527×	`associate-l_binary64`
457×	`associate-r_binary64`
424×	`log-prod_binary64`
381×	`exp-sum_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	2422
1	486	2371
2	1277	1663
3	5421	1615

Stop Event

1×	node limit

Counts

112 → 107

Calls

Call 1

Inputs
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(+.f64 0 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))) 1)
(.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 1)
(.f64 1 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))
(.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 1/6) (cbrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 1/4) (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/4))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (sqrt.f64 k))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(fabs.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 3/2))
(exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))) 3/4))
(exp.f64 (.f64 (.f64 3 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 1/6))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6)) 3))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 1) 1/2))
(exp.f64 (.f64 (.f64 (.f64 3/2 (log.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1) 1/3))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 1/2) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 1) 1))
(exp.f64 (.f64 (.f64 (.f64 3/2 (log.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1/6) 2))
(+.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))) 1)
(.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))
(.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2) 1)
(.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))
(.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2))
(.f64 (pow.f64 (.f64 2 (PI.f64)) 3/2) (pow.f64 (/.f64 n k) 3/2))
(.f64 (pow.f64 (/.f64 n k) 3/2) (pow.f64 (.f64 2 (PI.f64)) 3/2))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/4) (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/4))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 4) (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6))
(.f64 (pow.f64 2 3/2) (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 3/2))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 5/4) (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/4))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3))
(log.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 9/2))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))
(exp.f64 (.f64 3/2 (log.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 3))
(exp.f64 (.f64 (.f64 2 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 3/4))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 9/2)) 1/3))
(exp.f64 (.f64 (.f64 3/4 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 1) 3/2))
(exp.f64 (.f64 (.f64 (.f64 3/2 (log.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1) 1))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 1/2) 3))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 1) 3))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 3/4) 2))

Outputs
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (/.f64 (PI.f64) k) -2)))))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (/.f64 (*.f64 (PI.f64) -2) k)) (log.f64 (/.f64 -1 n)))))
(cbrt.f64 (.f64 (pow.f64 (/.f64 -1 n) -3/2) (pow.f64 (.f64 (/.f64 -2 k) (PI.f64)) 3/2)))
(cbrt.f64 (pow.f64 (*.f64 -2 (/.f64 (/.f64 (PI.f64) k) (/.f64 -1 n))) 3/2))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (/.f64 (PI.f64) k) -2)))))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (/.f64 (*.f64 (PI.f64) -2) k)) (log.f64 (/.f64 -1 n)))))
(cbrt.f64 (.f64 (pow.f64 (/.f64 -1 n) -3/2) (pow.f64 (.f64 (/.f64 -2 k) (PI.f64)) 3/2)))
(cbrt.f64 (pow.f64 (*.f64 -2 (/.f64 (/.f64 (PI.f64) k) (/.f64 -1 n))) 3/2))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (/.f64 (PI.f64) k) -2)))))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (/.f64 (*.f64 (PI.f64) -2) k)) (log.f64 (/.f64 -1 n)))))
(cbrt.f64 (.f64 (pow.f64 (/.f64 -1 n) -3/2) (pow.f64 (.f64 (/.f64 -2 k) (PI.f64)) 3/2)))
(cbrt.f64 (pow.f64 (*.f64 -2 (/.f64 (/.f64 (PI.f64) k) (/.f64 -1 n))) 3/2))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (/.f64 (PI.f64) k) -2)))))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (/.f64 (*.f64 (PI.f64) -2) k)) (log.f64 (/.f64 -1 n)))))
(cbrt.f64 (.f64 (pow.f64 (/.f64 -1 n) -3/2) (pow.f64 (.f64 (/.f64 -2 k) (PI.f64)) 3/2)))
(cbrt.f64 (pow.f64 (*.f64 -2 (/.f64 (/.f64 (PI.f64) k) (/.f64 -1 n))) 3/2))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (.f64 n (PI.f64)))))))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 n (.f64 (PI.f64) -2))))))
(cbrt.f64 (.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (.f64 n (*.f64 (PI.f64) -2)) 3/2)))
(cbrt.f64 (pow.f64 (.f64 (/.f64 -1 k) (.f64 -2 (*.f64 n (PI.f64)))) 3/2))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (.f64 n (PI.f64)))))))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 n (.f64 (PI.f64) -2))))))
(cbrt.f64 (.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (.f64 n (*.f64 (PI.f64) -2)) 3/2)))
(cbrt.f64 (pow.f64 (.f64 (/.f64 -1 k) (.f64 -2 (*.f64 n (PI.f64)))) 3/2))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (.f64 n (PI.f64)))))))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 n (.f64 (PI.f64) -2))))))
(cbrt.f64 (.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (.f64 n (*.f64 (PI.f64) -2)) 3/2)))
(cbrt.f64 (pow.f64 (.f64 (/.f64 -1 k) (.f64 -2 (*.f64 n (PI.f64)))) 3/2))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (.f64 n (PI.f64)))))))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 n (.f64 (PI.f64) -2))))))
(cbrt.f64 (.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (.f64 n (*.f64 (PI.f64) -2)) 3/2)))
(cbrt.f64 (pow.f64 (.f64 (/.f64 -1 k) (.f64 -2 (*.f64 n (PI.f64)))) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
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(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 1/2) 1))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 1) 1))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(exp.f64 (.f64 (.f64 (.f64 3/2 (log.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1/6) 2))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(+.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2)))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 3/2)))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (*.f64 (/.f64 2 k) (PI.f64))) 3/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))) 1)
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2) 1)
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(.f64 (pow.f64 (.f64 2 (PI.f64)) 3/2) (pow.f64 (/.f64 n k) 3/2))
(.f64 (pow.f64 (/.f64 n k) 3/2) (pow.f64 (.f64 2 (PI.f64)) 3/2))
(.f64 (pow.f64 (.f64 2 (PI.f64)) 3/2) (pow.f64 (/.f64 n k) 3/2))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/4) (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/4))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 4) (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(.f64 (pow.f64 2 3/2) (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 3/2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 5/4) (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/4))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(log.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 9/2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(expm1.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(log1p.f64 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 3/2 (log.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 (.f64 3/2 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 1))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 3))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 (.f64 2 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 3/4))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 9/2)) 1/3))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 (.f64 3/4 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 1) 3/2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 (.f64 (.f64 3/2 (log.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 1) 1))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 1/2) 3))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 1) 3))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)
(exp.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 3/4) 2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2)
(pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2)

eval275.0ms (2.2%)

Compiler: Compiled 10022 to 6617 computations (34% saved)

prune166.0ms (1.4%)

Pruning

42 alts after pruning (35 fresh and 7 done)

	Pruned	Kept	Total
New	624	26	650
Fresh	9	9	18
Picked	1	0	1
Done	2	7	9
Total	636	42	678

Error

Counts

678 → 42

Alt Table

Click to see full alt table

Status	Error	Program
	21.1b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	38.8b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
	32.6b	(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
	32.6b	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 3/2)
	38.8b	(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2) 1/3)
	32.6b	(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 1/6) 3)
	10.5b	(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
	30.4b	(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
✓	30.4b	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
	30.4b	(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))) 3/2)
	30.6b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 3)
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	19.9b	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
	30.2b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
✓	10.6b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
	30.0b	(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
	31.4b	(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
	31.4b	(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
✓	0.5b	(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (-.f64 1 k)) (pow.f64 k -1/2))
✓	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	30.3b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
	19.9b	(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
	30.1b	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
	30.2b	(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
✓	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))
	30.1b	(sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) 2) n) k))
	12.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	30.1b	(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
	30.4b	(sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1))
	30.1b	(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
	30.1b	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
✓	30.0b	(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
	30.1b	(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
	30.0b	(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
	30.1b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
	30.1b	(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
	30.1b	(sqrt.f64 (.f64 2 (/.f64 1 (.f64 (/.f64 1 (*.f64 (PI.f64) n)) k))))
	32.2b	(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))))
	12.8b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
	32.2b	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1/2))
	37.2b	(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 3/2))

Compiler

Compiled 548 to 452 computations (17.5% saved)

regimes425.0ms (3.5%)

Counts

81 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) 2) n) k))
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
(sqrt.f64 (.f64 2 (/.f64 1 (.f64 (/.f64 1 (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 1/6) 3)
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (.f64 (neg.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.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)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 -1/2 (/.f64 k -2)))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 3)
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (-.f64 1 k)) (pow.f64 k -1/2))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (.f64 2 (*.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (expm1.f64 (log1p.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k))))
(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)))
(/.f64 (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))

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

Calls

5 calls:

86.0ms	k
71.0ms	n
67.0ms	(.f64 (.f64 2 (PI.f64)) n)
52.0ms	(.f64 (.f64 2 (PI.f64)) n)
47.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.3b	1	`k`
0.3b	1	`n`
0.3b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1112 to 741 computations (33.4% saved)

regimes321.0ms (2.6%)

Counts

76 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) 2) n) k))
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
(sqrt.f64 (.f64 2 (/.f64 1 (.f64 (/.f64 1 (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 1/6) 3)
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (.f64 (neg.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.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)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 -1/2 (/.f64 k -2)))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 3)
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (-.f64 1 k)) (pow.f64 k -1/2))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (.f64 2 (*.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (expm1.f64 (log1p.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))

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

Calls

5 calls:

96.0ms	(.f64 (.f64 2 (PI.f64)) n)
82.0ms	(.f64 (.f64 2 (PI.f64)) n)
43.0ms	n
42.0ms	k
27.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.3b	1	`k`
0.3b	1	`n`
0.3b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 994 to 669 computations (32.7% saved)

regimes320.0ms (2.6%)

Counts

75 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) 2) n) k))
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
(sqrt.f64 (.f64 2 (/.f64 1 (.f64 (/.f64 1 (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 1/6) 3)
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (.f64 (neg.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.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)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 -1/2 (/.f64 k -2)))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 3)
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (-.f64 1 k)) (pow.f64 k -1/2))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (.f64 2 (*.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(/.f64 (exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (expm1.f64 (log1p.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))

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

Calls

5 calls:

82.0ms	(.f64 (.f64 2 (PI.f64)) n)
54.0ms	n
53.0ms	(.f64 (.f64 2 (PI.f64)) n)
38.0ms	k
25.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.5b	1	`k`
0.5b	1	`n`
0.5b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 975 to 657 computations (32.6% saved)

regimes197.0ms (1.6%)

Counts

53 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) 2) n) k))
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
(sqrt.f64 (.f64 2 (/.f64 1 (.f64 (/.f64 1 (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 1/6) 3)
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (.f64 (neg.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.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)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 -1/2 (/.f64 k -2)))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 3)
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))))

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

Calls

5 calls:

51.0ms	(.f64 (.f64 2 (PI.f64)) n)
35.0ms	(.f64 (.f64 2 (PI.f64)) n)
30.0ms	n
28.0ms	k
20.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.5b	1	`k`
0.5b	1	`n`
0.5b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 621 to 414 computations (33.3% saved)

regimes120.0ms (1%)

Counts

44 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) 2) n) k))
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
(sqrt.f64 (.f64 2 (/.f64 1 (.f64 (/.f64 1 (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 1/6) 3)
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))

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

Calls

2 calls:

54.0ms	n
51.0ms	k

Results

Error	Segments	Branch
0.5b	2	`k`
8.5b	2	`n`

Compiler

Compiled 461 to 301 computations (34.7% saved)

bsearch9.0ms (0.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
8.0ms	3.427345137862898e-28	4.5382757784272625e-28

Results

7.0ms

48×

body

256

valid

Compiler

Compiled 107 to 88 computations (17.8% saved)

regimes107.0ms (0.9%)

Counts

42 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) 2) n) k))
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
(sqrt.f64 (.f64 2 (/.f64 1 (.f64 (/.f64 1 (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 1/6) 3)
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

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

Calls

2 calls:

47.0ms	n
43.0ms	k

Results

Error	Segments	Branch
0.5b	2	`k`
8.6b	2	`n`

Compiler

Compiled 434 to 282 computations (35% saved)

bsearch23.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
23.0ms	5.424204809425196e-19	2.5539397314918673e-17

Results

21.0ms

112×

body

256

valid

Compiler

Compiled 212 to 173 computations (18.4% saved)

regimes286.0ms (2.3%)

Counts

41 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) 2) n) k))
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
(sqrt.f64 (.f64 2 (/.f64 1 (.f64 (/.f64 1 (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)) 1))
(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) (/.f64 2 k))) 1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 2 k))) 1/6) 3)
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 2 k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)

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

Calls

2 calls:

182.0ms	n
89.0ms	k

Results

Error	Segments	Branch
10.8b	2	`k`
14.8b	5	`n`

Compiler

Compiled 422 to 274 computations (35.1% saved)

bsearch8.0ms (0.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
7.0ms	1.525810727964968e+24	4.2865589843583766e+24

Results

5.0ms	16×	body	256	valid
2.0ms	8×	body	256	infinite

Compiler

Compiled 50 to 42 computations (16% saved)

regimes176.0ms (1.4%)

Counts

23 → 2

Calls

Call 1

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

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

Calls

2 calls:

117.0ms	n
45.0ms	k

Results

Error	Segments	Branch
10.8b	2	`k`
14.8b	5	`n`

Compiler

Compiled 232 to 152 computations (34.5% saved)

bsearch18.0ms (0.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
17.0ms	4.2865589843583766e+24	6.0079578329114576e+26

Results

8.0ms	40×	body	256	infinite
8.0ms	48×	body	256	valid

Compiler

Compiled 104 to 88 computations (15.4% saved)

regimes50.0ms (0.4%)

Counts

20 → 2

Calls

Call 1

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

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

Calls

2 calls:

24.0ms	n
20.0ms	k

Results

Error	Segments	Branch
20.8b	2	`k`
20.9b	2	`n`

Compiler

Compiled 205 to 137 computations (33.2% saved)

bsearch6.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
6.0ms	4.2865589843583766e+24	6.0079578329114576e+26

Results

3.0ms	16×	body	256	valid
1.0ms	7×	body	256	infinite

Compiler

Compiled 51 to 43 computations (15.7% saved)

regimes56.0ms (0.5%)

Counts

14 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	n
8.0ms	k

Results

Error	Segments	Branch
30.0b	1	`k`
30.0b	1	`n`

Compiler

Compiled 138 to 93 computations (32.6% saved)

regimes19.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))

Calls

2 calls:

9.0ms	k
7.0ms	n

Results

Error	Segments	Branch
30.0b	1	`k`
30.0b	1	`n`

Compiler

Compiled 92 to 60 computations (34.8% saved)

regimes11.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	n
3.0ms	k

Results

Error	Segments	Branch
30.1b	1	`k`
30.1b	1	`n`

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	349
1	100	349
2	108	349
3	112	349
4	114	349

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 8251275723456331/22300745198530623141535718272648361505980416) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k)) (pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2))
(if (<=.f64 k 1906546502743257/81129638414606681695789005144064) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 1999999999999999966445568) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k)) (sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))
(if (<=.f64 k 100000000000000004764729344) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))
(if (<=.f64 k 5000000000000000452984832) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))))) (sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Outputs
(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 8251275723456331/22300745198530623141535718272648361505980416) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k)) (pow.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) -1/2))
(if (<=.f64 k 1906546502743257/81129638414606681695789005144064) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 1999999999999999966445568) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k)) (sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))
(if (<=.f64 k 1999999999999999966445568) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k)) (sqrt.f64 (+.f64 (+.f64 1 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))) -1)))
(if (<=.f64 k 100000000000000004764729344) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))
(if (<=.f64 k 100000000000000004764729344) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (+.f64 (+.f64 1 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))) -1)))
(if (<=.f64 k 5000000000000000452984832) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))))) (sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))
(if (<=.f64 k 5000000000000000452984832) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))))) (sqrt.f64 (+.f64 (+.f64 1 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))) -1)))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Compiler

Compiled 242 to 188 computations (22.3% saved)

soundness168.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

732×	`fma-def_binary64`
667×	`associate-/l*_binary64`
561×	`associate-/r*_binary64`
539×	`distribute-rgt-in_binary64`
524×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	141	22
4	360	22
5	983	20
6	2213	20
7	5663	20
0	290	3006
1	668	2738
2	2308	2687

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 306 to 252 computations (17.6% saved)

end126.0ms (1%)

Compiler: Compiled 220 to 145 computations (34.1% saved)