Details

analyze247.0ms (1.6%)

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)

sample4.1s (26.8%)

Results

2.0s	8256×	body	256	valid
1.2s	1342×	body	1024	invalid
324.0ms	668×	body	512	invalid
296.0ms	1604×	body	256	invalid
137.0ms	502×	body	256	infinite
90.0ms	245×	body	256	unsamplable

Bogosity

preprocess116.0ms (0.8%)

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)

simplify49.0ms (0.3%)

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 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 31 to 23 computations (25.8% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.6b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.6b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
▶	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 33 to 27 computations (18.2% saved)

localize28.0ms (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)))
✓	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

Compiler

Compiled 56 to 38 computations (32.1% saved)

series70.0ms (0.5%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
27.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
23.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
8.0ms	n	@	inf	(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)))
2.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite78.0ms (0.5%)

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

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-+r+_binary64`
528×	`associate-+l+_binary64`
424×	`associate-r_binary64`
408×	`associate-l_binary64`
325×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1206
1	227	1124
2	750	969
3	4129	958

Stop Event

1×	node limit

Counts

153 → 126

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))))))))

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

localize22.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 45 to 26 computations (42.2% saved)

series9.0ms (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)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
1.0ms	n	@	0	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
1.0ms	k	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
1.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
1.0ms	n	@	-inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))

rewrite74.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`log-prod_binary64`
377×	`pow-unpow_binary64`
376×	`pow-prod-down_binary64`
340×	`pow2_binary64`
258×	`pow-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	274	40
2	3305	40

Stop Event

1×	node limit

Counts

3 → 87

Calls

Call 1

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

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 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))) (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))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.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))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.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)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x 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Outputs

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

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

683×	`exp-sum_binary64`
401×	`associate-+r+_binary64`
395×	`associate-+l+_binary64`
391×	`associate-r_binary64`
367×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	1106
1	204	1024
2	643	901
3	3618	842
4	6908	842

Stop Event

1×	node limit

Counts

135 → 106

Calls

Call 1

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

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

eval92.0ms (0.6%)

Compiler: Compiled 4795 to 3263 computations (31.9% saved)

prune55.0ms (0.4%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	211	21	232
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	211	23	234

Error

Counts

234 → 23

Alt Table

Click to see full alt table

Status	Error	Program
	16.1b	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
	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))
	3.3b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	23.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	23.8b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 (.f64 -1/2 (.f64 k (sqrt.f64 2))) (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 k))
▶	9.0b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	1.0b	(/.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)))))
	23.4b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
✓	0.6b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (.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))))
	9.6b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
	1.1b	(.f64 (/.f64 1 (sqrt.f64 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)))))
	17.7b	(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
▶	1.2b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
▶	11.0b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	1.0b	(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
✓	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.6b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.5b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))
	3.1b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (sqrt.f64 k))

Compiler

Compiled 831 to 677 computations (18.5% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 70 to 46 computations (34.3% saved)

series23.0ms (0.2%)

Counts

4 → 36

Calls

18 calls:

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

rewrite149.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`log-prod_binary64`
698×	`pow-unpow_binary64`
378×	`pow2_binary64`
260×	`pow1/3_binary64`
256×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	63
1	298	54
2	3810	52

Stop Event

1×	node limit

Counts

4 → 122

Calls

Call 1

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

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

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-+l+_binary64`
528×	`associate-+r+_binary64`
451×	`*-commutative_binary64`
445×	`unsub-neg_binary64`
313×	`exp-prod_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	55	634
1	159	596
2	475	530
3	2325	522
4	6231	502

Stop Event

1×	node limit

Counts

158 → 137

Calls

Call 1

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

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

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)
✓	0.2b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
	0.2b	(*.f64 (PI.f64) n)
✓	8.3b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Compiler

Compiled 50 to 28 computations (44% 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 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
2.0ms	k	@	-inf	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
1.0ms	k	@	inf	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
1.0ms	n	@	0	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
1.0ms	n	@	-inf	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

rewrite101.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

656×	`log-prod_binary64`
453×	`pow-unpow_binary64`
332×	`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	3385	50

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

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

Outputs

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

simplify109.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-+l+_binary64`
473×	`associate-l_binary64`
439×	`fma-def_binary64`
401×	`associate-r_binary64`
351×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	1569
1	241	1477
2	780	1289
3	4232	1184

Stop Event

1×	node limit

Counts

176 → 151

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

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

localize50.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 67 to 38 computations (43.3% saved)

series25.0ms (0.2%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	n	@	inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
4.0ms	k	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
4.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
3.0ms	k	@	0	(sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))
2.0ms	k	@	inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))

rewrite107.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

699×	`log-prod_binary64`
509×	`pow-unpow_binary64`
350×	`pow2_binary64`
241×	`pow1/3_binary64`
236×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	279	35
2	3600	35

Stop Event

1×	node limit

Counts

2 → 77

Calls

Call 1

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

Outputs

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

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

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

391×	`associate-/r/_binary64`
286×	`cancel-sign-sub-inv_binary64`
285×	`associate-r_binary64`
274×	`associate-l_binary64`
269×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1186
1	263	1101
2	844	984
3	4288	933

Stop Event

1×	node limit

Counts

113 → 97

Calls

Call 1

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

localize59.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) n)
✓	0.2b	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
✓	3.1b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	8.3b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Compiler

Compiled 77 to 45 computations (41.6% saved)

series123.0ms (0.8%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
61.0ms	n	@	0	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
31.0ms	n	@	inf	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
19.0ms	n	@	-inf	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
3.0ms	k	@	0	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
2.0ms	k	@	-inf	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))

rewrite79.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

694×	`log-prod_binary64`
467×	`pow-unpow_binary64`
352×	`pow2_binary64`
240×	`pow1/3_binary64`
236×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	283	40
2	3571	40

Stop Event

1×	node limit

Counts

2 → 87

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.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 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 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simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

542×	`exp-sum_binary64`
412×	`unsub-neg_binary64`
325×	`associate--r+_binary64`
308×	`associate--l+_binary64`
308×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	624
1	94	624
2	248	624
3	829	480
4	3363	480

Stop Event

1×	node limit

Counts

111 → 95

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

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

localize73.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.6b	(cbrt.f64 (pow.f64 k -1/2))
✓	0.7b	(pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)

Compiler

Compiled 67 to 50 computations (25.4% saved)

series60.0ms (0.4%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
22.0ms	k	@	0	(pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)
21.0ms	k	@	-inf	(pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)
16.0ms	k	@	inf	(pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)
1.0ms	k	@	0	(cbrt.f64 (pow.f64 k -1/2))
0.0ms	k	@	-inf	(cbrt.f64 (pow.f64 k -1/2))

rewrite71.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

524×	`pow1_binary64`
520×	`add-sqr-sqrt_binary64`
500×	`add-log-exp_binary64`
500×	`log1p-expm1-u_binary64`
500×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	153	8
2	1434	8

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)
(cbrt.f64 (pow.f64 k -1/2))

Outputs

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

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
518×	`associate-l_binary64`
429×	`associate-r_binary64`
263×	`unswap-sqr_binary64`
214×	`exp-diff_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	18	192
1	48	156
2	88	156
3	214	156
4	689	156
5	3528	120
6	7765	120

Stop Event

1×	node limit

Counts

66 → 48

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 1 1/6))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 1 1/6))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 1 1/6))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 1 1/6))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))) 3)
(pow.f64 (/.f64 1 k) 1/6)
(pow.f64 (/.f64 1 k) 1/6)
(pow.f64 (/.f64 1 k) 1/6)
(pow.f64 (/.f64 1 k) 1/6)
(pow.f64 (/.f64 1 k) 1/6)
(pow.f64 (/.f64 1 k) 1/6)
(pow.f64 (/.f64 1 k) 1/6)
(pow.f64 (/.f64 1 k) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))

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

eval444.0ms (2.9%)

Compiler: Compiled 16342 to 11078 computations (32.2% saved)

prune203.0ms (1.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	741	13	754
Fresh	13	3	16
Picked	1	0	1
Done	5	1	6
Total	760	17	777

Error

Counts

777 → 17

Alt Table

Click to see full alt table

Status	Error	Program
▶	8.4b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
✓	9.0b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	1.0b	(/.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)))))
	11.0b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1/2))
	16.2b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
	23.4b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	23.6b	(/.f64 (.f64 1 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
	0.7b	(/.f64 1 (.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) -1/2) (sqrt.f64 k)))
	17.7b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2) 1/3)
	9.0b	(sqrt.f64 (pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1))
	0.6b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	32.0b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
▶	11.0b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))
▶	32.0b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
▶	0.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	23.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
▶	8.8b	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))

Compiler

Compiled 512 to 415 computations (18.9% saved)

localize92.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 k))
✓	0.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

Compiler

Compiled 57 to 41 computations (28.1% saved)

series9.0ms (0.1%)

Counts

2 → 12

Calls

9 calls:

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

rewrite89.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

734×	`log-prod_binary64`
518×	`pow-unpow_binary64`
380×	`pow2_binary64`
262×	`pow1/3_binary64`
258×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	306	26
2	3861	25

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

811×	`exp-sum_binary64`
717×	`unsub-neg_binary64`
629×	`exp-prod_binary64`
473×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	388
1	96	384
2	309	372
3	1180	360
4	5300	288

Stop Event

1×	node limit

Counts

66 → 59

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))))))))

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

localize24.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 n k) (.f64 2 (PI.f64)))
✓	8.4b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))

Compiler

Compiled 27 to 14 computations (48.1% saved)

series18.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

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

rewrite84.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

954×	`pow1_binary64`
883×	`add-log-exp_binary64`
883×	`log1p-expm1-u_binary64`
883×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	189	24
2	2392	24

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

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

Outputs

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

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

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
15×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
10×	`associate-r_binary64`
8×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	264
1	14	264
2	29	264
3	56	264
4	86	264
5	97	264

Stop Event

1×

saturated

Counts

75 → 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))

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

localize54.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
✓	0.2b	(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))
✓	0.2b	(.f64 (PI.f64) (.f64 n 2))
✓	7.7b	(sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))

Compiler

Compiled 64 to 43 computations (32.8% saved)

series17.0ms (0.1%)

Counts

4 → 60

Calls

21 calls:

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

rewrite119.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

713×	`log-prod_binary64`
477×	`pow-unpow_binary64`
360×	`pow2_binary64`
245×	`pow1/3_binary64`
241×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	63
1	285	60
2	3753	60

Stop Event

1×	node limit

Counts

4 → 124

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 k (pow.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 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.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 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 k) (/.f64 1 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1/4) (pow.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 2))) (sqrt.f64 (cbrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) n) (.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) 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 (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 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2)))) (#(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 (.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 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.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 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (neg.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1)))) (#(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 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 (PI.f64) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (-.f64 1 k)) (pow.f64 (cbrt.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)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) n) (-.f64 1 k)) (pow.f64 2 (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 n n) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (cbrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (pow.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 2 (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.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 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.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 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 1))))))
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simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

413×	`associate-+r+_binary64`
405×	`associate-+l+_binary64`
350×	`associate-l_binary64`
311×	`fma-neg_binary64`
308×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	1326
1	191	1250
2	609	1117
3	3292	1022
4	7353	1022

Stop Event

1×	node limit

Counts

184 → 149

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

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

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) n)
✓	0.3b	(log.f64 (.f64 2 (.f64 (PI.f64) n)))
✓	3.5b	(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))
✓	8.3b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))

Compiler

Compiled 72 to 43 computations (40.3% saved)

series6.0ms (0%)

Counts

3 → 48

Calls

15 calls:

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

rewrite87.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log-prod_binary64`
351×	`pow2_binary64`
267×	`pow-unpow_binary64`
248×	`pow1/3_binary64`
242×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	51
1	285	43
2	3532	43

Stop Event

1×	node limit

Counts

3 → 163

Calls

Call 1

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

Outputs

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

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

626×	`exp-sum_binary64`
413×	`associate-+r+_binary64`
405×	`associate-+l+_binary64`
348×	`associate-l_binary64`
311×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	978
1	185	934
2	605	897
3	3257	826
4	7188	826

Stop Event

1×	node limit

Counts

211 → 186

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

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

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k)
	0.2b	(*.f64 (PI.f64) n)
✓	0.2b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) k)
✓	8.3b	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))

Compiler

Compiled 74 to 36 computations (51.4% saved)

series174.0ms (1.1%)

Counts

3 → 48

Calls

18 calls:

Time	Variable		Point	Expression
92.0ms	n	@	inf	(/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k)
55.0ms	n	@	inf	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
6.0ms	n	@	-inf	(/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k)
3.0ms	k	@	0	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
3.0ms	n	@	0	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))

rewrite93.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

843×	`log-prod_binary64`
358×	`pow2_binary64`
249×	`pow1/3_binary64`
242×	`log-div_binary64`
242×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	61
1	273	61
2	4027	61

Stop Event

1×	node limit

Counts

3 → 118

Calls

Call 1

Inputs

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

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

(/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k)

Outputs

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

simplify152.0ms (1%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-l_binary64`
626×	`associate-r_binary64`
606×	`fma-neg_binary64`
412×	`fma-def_binary64`
345×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1406
1	330	1265
2	1155	1085
3	7098	1043

Stop Event

1×	node limit

Counts

166 → 145

Calls

Call 1

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

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

eval713.0ms (4.7%)

Compiler: Compiled 14534 to 9476 computations (34.8% saved)

prune206.0ms (1.4%)

Pruning

26 alts after pruning (20 fresh and 6 done)

	Pruned	Kept	Total
New	691	14	705
Fresh	5	6	11
Picked	0	1	1
Done	0	5	5
Total	696	26	722

Error

Counts

722 → 26

Alt Table

Click to see full alt table

Status	Error	Program
	11.0b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
▶	32.1b	(.f64 (sqrt.f64 (.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
	0.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
✓	8.4b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
✓	9.0b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	1.0b	(/.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)))))
	16.2b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
	23.4b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	33.4b	(sqrt.f64 (expm1.f64 (log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))))
	32.2b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
	32.1b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))) 1/4) 2)
	0.7b	(/.f64 1 (.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) -1/2) (sqrt.f64 k)))
	32.0b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
	32.0b	(sqrt.f64 (/.f64 1 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
	23.6b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
▶	0.6b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	32.0b	(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
✓	11.0b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))
▶	32.0b	(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
✓	32.0b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
	8.4b	(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2)
✓	0.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	23.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
	37.0b	(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))) 3/2))
	38.5b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))) 3/2) 1/3)
✓	8.8b	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))

Compiler

Compiled 640 to 522 computations (18.4% saved)

localize38.0ms (0.3%)

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)))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
	0.5b	(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
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	n	@	0	(.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)))
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	n	@	-inf	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite62.0ms (0.4%)

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))))))

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

811×	`exp-sum_binary64`
717×	`unsub-neg_binary64`
629×	`exp-prod_binary64`
473×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	388
1	96	384
2	309	372
3	1180	360
4	5300	288

Stop Event

1×	node limit

Counts

33 → 26

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))))))))

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

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 k (*.f64 2 (PI.f64)))
✓	0.3b	(/.f64 n (/.f64 k (*.f64 2 (PI.f64))))
✓	8.4b	(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))

Compiler

Compiled 29 to 18 computations (37.9% saved)

series58.0ms (0.4%)

Counts

3 → 36

Calls

15 calls:

Time	Variable		Point	Expression
51.0ms	k	@	-inf	(/.f64 k (*.f64 2 (PI.f64)))
1.0ms	k	@	-inf	(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
1.0ms	k	@	0	(/.f64 k (*.f64 2 (PI.f64)))
1.0ms	k	@	inf	(/.f64 k (*.f64 2 (PI.f64)))
1.0ms	n	@	0	(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))

rewrite114.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

543×	`log-prod_binary64`
414×	`exp-prod_binary64`
305×	`pow-prod-down_binary64`
250×	`pow2_binary64`
206×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	195	32
2	2699	32

Stop Event

1×	node limit

Counts

3 → 176

Calls

Call 1

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

Outputs

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

simplify32.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
17×	`associate-/l*_binary64`
12×	`associate-/r/_binary64`
10×	`associate-r_binary64`
8×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	360
1	19	360
2	38	360
3	68	360
4	99	360
5	110	360

Stop Event

1×

saturated

Counts

212 → 179

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 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))

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

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
✓	1.0b	(sqrt.f64 (PI.f64))
✓	8.3b	(sqrt.f64 (*.f64 (/.f64 n k) 2))

Compiler

Compiled 31 to 15 computations (51.6% saved)

series8.0ms (0.1%)

Counts

3 → 0

Calls

12 calls:

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

rewrite71.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

517×	`log-prod_binary64`
436×	`prod-exp_binary64`
376×	`exp-prod_binary64`
348×	`pow-prod-down_binary64`
254×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	208	26
2	2555	26

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

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

Outputs

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

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

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

116 → 116

Calls

Call 1

Inputs

Outputs

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 43 to 27 computations (37.2% saved)

series63.0ms (0.4%)

Counts

2 → 0

Calls

12 calls:

Time	Variable		Point	Expression
53.0ms	k	@	-inf	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
1.0ms	k	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
1.0ms	n	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
1.0ms	n	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
1.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))

rewrite95.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

619×	`log-prod_binary64`
375×	`pow-prod-down_binary64`
289×	`pow2_binary64`
244×	`pow-unpow_binary64`
205×	`pow-to-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	249	26
2	3094	26

Stop Event

1×	node limit

Counts

2 → 114

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)))))) (#(struct:change #<rule 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)) 1)))) (#(struct:change #<rule 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 n)) (sqrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 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k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 3/2) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 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simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

114 → 114

Calls

Call 1

Inputs

Outputs

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (/.f64 n k) (.f64 2 (PI.f64)))
✓	2.9b	(expm1.f64 (log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64)))))
✓	8.4b	(sqrt.f64 (expm1.f64 (log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))))
✓	8.5b	(log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))

Compiler

Compiled 46 to 25 computations (45.7% saved)

series60.0ms (0.4%)

Counts

3 → 48

Calls

18 calls:

Time	Variable		Point	Expression
51.0ms	n	@	inf	(log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
1.0ms	n	@	0	(log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
1.0ms	n	@	-inf	(log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
1.0ms	k	@	-inf	(log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
1.0ms	k	@	0	(log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))

rewrite83.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`log-prod_binary64`
514×	`prod-diff_binary64`
394×	`exp-prod_binary64`
335×	`pow-prod-down_binary64`
260×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	209	37
2	2590	37

Stop Event

1×	node limit

Counts

3 → 145

Calls

Call 1

Inputs
(log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
(sqrt.f64 (expm1.f64 (log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))))
(expm1.f64 (log1p.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64)))))

Outputs

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

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

756×	`times-frac_binary64`
510×	`unswap-sqr_binary64`
458×	`cancel-sign-sub-inv_binary64`
376×	`associate-/l*_binary64`
304×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	1255
1	242	1227
2	832	1200
3	5411	1125

Stop Event

1×	node limit

Counts

193 → 173

Calls

Call 1

Inputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))) (.f64 8/3 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) (pow.f64 k 3)))))
(+.f64 (.f64 -4 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (PI.f64) 4)) (pow.f64 k 4))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))) (.f64 8/3 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) (pow.f64 k 3))))))
(+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))
(+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))
(+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 k 2) (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(+.f64 (.f64 1/24 (/.f64 (pow.f64 k 3) (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))) (+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 k 2) (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))))
(+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (/.f64 (PI.f64) k))))
(+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (/.f64 (PI.f64) k)))))
(+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 k 2) (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (/.f64 (PI.f64) k))))))
(+.f64 (.f64 1/24 (/.f64 (pow.f64 k 3) (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))) (+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 k 2) (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (/.f64 (PI.f64) k)))))))
(+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 k 2) (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 1/24 (/.f64 (pow.f64 k 3) (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))) (+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 k 2) (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))) (.f64 8/3 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) (pow.f64 k 3)))))
(+.f64 (.f64 -4 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (PI.f64) 4)) (pow.f64 k 4))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))) (.f64 8/3 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) (pow.f64 k 3))))))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))) (.f64 8/3 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) (pow.f64 k 3)))))
(+.f64 (.f64 -4 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (PI.f64) 4)) (pow.f64 k 4))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))) (.f64 8/3 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) (pow.f64 k 3))))))
(.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))

Outputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (.f64 -2 (/.f64 (.f64 n n) (/.f64 (*.f64 k k) (pow.f64 (PI.f64) 2)))))
(fma.f64 2 (.f64 (/.f64 n k) (PI.f64)) (.f64 -2 (.f64 (/.f64 (.f64 n n) k) (/.f64 (pow.f64 (PI.f64) 2) k))))
(fma.f64 (/.f64 -2 k) (/.f64 (pow.f64 (PI.f64) 2) (/.f64 k (.f64 n n))) (.f64 (*.f64 (/.f64 2 k) (PI.f64)) n))
(.f64 (PI.f64) (+.f64 (/.f64 2 (/.f64 k n)) (/.f64 (.f64 n (*.f64 n -2)) (/.f64 k (/.f64 (PI.f64) k)))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))) (.f64 8/3 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) (pow.f64 k 3)))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 -2 (/.f64 (.f64 n n) (/.f64 (.f64 k k) (pow.f64 (PI.f64) 2))) (*.f64 8/3 (/.f64 (pow.f64 n 3) (/.f64 (pow.f64 k 3) (pow.f64 (PI.f64) 3))))))
(fma.f64 2 (.f64 (/.f64 n k) (PI.f64)) (fma.f64 -2 (.f64 (/.f64 (.f64 n n) k) (/.f64 (pow.f64 (PI.f64) 2) k)) (.f64 8/3 (*.f64 (/.f64 (pow.f64 n 3) (pow.f64 k 3)) (pow.f64 (PI.f64) 3)))))
(fma.f64 2 (.f64 (PI.f64) (/.f64 n k)) (fma.f64 -2 (.f64 (pow.f64 (PI.f64) 2) (.f64 (/.f64 n k) (/.f64 n k))) (.f64 (/.f64 8/3 (pow.f64 (/.f64 k (PI.f64)) 3)) (pow.f64 n 3))))
(fma.f64 8/3 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 3) (.f64 (PI.f64) (+.f64 (/.f64 2 (/.f64 k n)) (/.f64 (.f64 n (.f64 n -2)) (/.f64 k (/.f64 (PI.f64) k))))))
(+.f64 (.f64 -4 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (PI.f64) 4)) (pow.f64 k 4))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)) (pow.f64 k 2))) (.f64 8/3 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) (pow.f64 k 3))))))
(fma.f64 -4 (/.f64 (pow.f64 n 4) (/.f64 (pow.f64 k 4) (pow.f64 (PI.f64) 4))) (fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 -2 (/.f64 (.f64 n n) (/.f64 (.f64 k k) (pow.f64 (PI.f64) 2))) (*.f64 8/3 (/.f64 (pow.f64 n 3) (/.f64 (pow.f64 k 3) (pow.f64 (PI.f64) 3)))))))
(fma.f64 -4 (.f64 (/.f64 (pow.f64 n 4) (pow.f64 k 4)) (pow.f64 (PI.f64) 4)) (fma.f64 2 (.f64 (/.f64 n k) (PI.f64)) (fma.f64 -2 (.f64 (/.f64 (.f64 n n) k) (/.f64 (pow.f64 (PI.f64) 2) k)) (.f64 8/3 (.f64 (/.f64 (pow.f64 n 3) (pow.f64 k 3)) (pow.f64 (PI.f64) 3))))))
(fma.f64 2 (.f64 (PI.f64) (/.f64 n k)) (fma.f64 -4 (.f64 (/.f64 (pow.f64 (PI.f64) 4) (pow.f64 k 4)) (pow.f64 n 4)) (fma.f64 -2 (.f64 (pow.f64 (PI.f64) 2) (.f64 (/.f64 n k) (/.f64 n k))) (*.f64 (/.f64 8/3 (pow.f64 (/.f64 k (PI.f64)) 3)) (pow.f64 n 3)))))
(fma.f64 -4 (/.f64 (pow.f64 n 4) (pow.f64 (/.f64 k (PI.f64)) 4)) (fma.f64 8/3 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 3) (.f64 (PI.f64) (+.f64 (/.f64 2 (/.f64 k n)) (/.f64 (.f64 n (.f64 n -2)) (/.f64 k (/.f64 (PI.f64) k)))))))
(+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))
(fma.f64 -1 (neg.f64 (log.f64 n)) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(+.f64 (log.f64 n) (log.f64 (*.f64 (/.f64 2 k) (PI.f64))))
(+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))
(fma.f64 1/2 (/.f64 k (.f64 n (PI.f64))) (fma.f64 -1 (neg.f64 (log.f64 n)) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))
(+.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) k))) (fma.f64 1/2 (/.f64 k (.f64 n (PI.f64))) (log.f64 n)))
(+.f64 (log.f64 (.f64 (/.f64 2 k) (PI.f64))) (fma.f64 1/2 (/.f64 k (.f64 n (PI.f64))) (log.f64 n)))
(+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 k 2) (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(fma.f64 1/2 (/.f64 k (.f64 n (PI.f64))) (fma.f64 -1/8 (/.f64 (.f64 k k) (.f64 (.f64 n n) (pow.f64 (PI.f64) 2))) (fma.f64 -1 (neg.f64 (log.f64 n)) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
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(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(.f64 (.f64 (/.f64 2 k) (PI.f64)) n)

eval585.0ms (3.8%)

Compiler: Compiled 11247 to 7402 computations (34.2% saved)

prune386.0ms (2.5%)

Pruning

40 alts after pruning (33 fresh and 7 done)

	Pruned	Kept	Total
New	715	30	745
Fresh	12	3	15
Picked	1	0	1
Done	3	7	10
Total	731	40	771

Error

Counts

771 → 40

Alt Table

Click to see full alt table

Status	Error	Program
	33.7b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/6) -3)
	32.0b	(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
	32.0b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
	34.4b	(pow.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
	31.4b	(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))))
	33.7b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/6) 3)
	32.3b	(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
	23.6b	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
	11.0b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
✓	32.1b	(.f64 (sqrt.f64 (.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
	38.3b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)
	32.0b	(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
	33.5b	(sqrt.f64 (-.f64 (fma.f64 (/.f64 n k) (*.f64 2 (PI.f64)) 1) 1))
	32.0b	(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
	23.6b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
✓	8.4b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
✓	9.0b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	38.5b	(pow.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 3/2) 1/3)
	23.5b	(.f64 (/.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 k)) (sqrt.f64 (PI.f64)))
	31.3b	(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
	16.2b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
	36.9b	(cbrt.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 3/2))
	36.9b	(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2))
	31.4b	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)))
	32.0b	(sqrt.f64 (.f64 (.f64 2 (/.f64 (PI.f64) k)) n))
	32.2b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
	23.6b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
	23.4b	(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
	23.8b	(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/4) (pow.f64 k 1/4)) 2)
✓	0.6b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	31.4b	(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
	32.3b	(.f64 (sqrt.f64 (.f64 (/.f64 n k) 2)) (cbrt.f64 (pow.f64 (PI.f64) 3/2)))
✓	11.0b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))
	34.0b	(.f64 (exp.f64 (.f64 (log.f64 (*.f64 (/.f64 n k) 2)) 1/2)) (sqrt.f64 (PI.f64)))
✓	32.0b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
	8.4b	(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2)
	32.0b	(sqrt.f64 (.f64 (neg.f64 n) (/.f64 1 (.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
	32.3b	(pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64)))) 3/2)
✓	8.8b	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
	33.4b	(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 k (.f64 2 (PI.f64))) n)) -1/2))

Compiler

Compiled 511 to 419 computations (18% saved)

regimes716.0ms (4.7%)

Counts

80 → 1

Calls

Call 1

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

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

Calls

5 calls:

167.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
134.0ms	k
114.0ms	n
113.0ms	(.f64 (.f64 2 (PI.f64)) n)
89.0ms	(.f64 (.f64 2 (PI.f64)) n)

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 1047 to 694 computations (33.7% saved)

regimes533.0ms (3.5%)

Counts

76 → 1

Calls

Call 1

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

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

Calls

4 calls:

164.0ms	k
100.0ms	n
66.0ms	(.f64 (.f64 2 (PI.f64)) n)
43.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.6b	1	`k`
0.6b	1	`n`
0.6b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.6b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 953 to 635 computations (33.4% saved)

regimes88.0ms (0.6%)

Counts

44 → 1

Calls

Call 1

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

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

Calls

3 calls:

27.0ms	(.f64 (.f64 2 (PI.f64)) n)
25.0ms	n
22.0ms	k

Results

Error	Segments	Branch
0.6b	1	`k`
0.6b	1	`n`
0.6b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 455 to 297 computations (34.7% saved)

regimes177.0ms (1.2%)

Counts

43 → 2

Calls

Call 1

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

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

Calls

2 calls:

101.0ms	k
61.0ms	n

Results

Error	Segments	Branch
0.4b	2	`k`
7.3b	3	`n`

Compiler

Compiled 433 to 280 computations (35.3% saved)

bsearch106.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
106.0ms	2.6057697274586915e-83	1.1887820368128312e-81

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes247.0ms (1.6%)

Counts

41 → 2

Calls

Call 1

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

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

Calls

2 calls:

173.0ms	n
53.0ms	k

Results

Error	Segments	Branch
0.4b	2	`k`
6.9b	5	`n`

Compiler

Compiled 406 to 262 computations (35.5% saved)

bsearch35.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
34.0ms	2.6057697274586915e-83	1.1887820368128312e-81

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes117.0ms (0.8%)

Counts

40 → 2

Calls

Call 1

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

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

Calls

2 calls:

59.0ms	n
44.0ms	k

Results

Error	Segments	Branch
15.0b	2	`k`
17.8b	3	`n`

Compiler

Compiled 394 to 254 computations (35.5% saved)

bsearch89.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
88.0ms	3543.6982364082564	49398841.613592155

Compiler

Compiled 231 to 195 computations (15.6% saved)

regimes136.0ms (0.9%)

Counts

33 → 2

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (.f64 (.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))))
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)))
(sqrt.f64 (/.f64 1 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 (neg.f64 n) (/.f64 1 (.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(cbrt.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64)))) 3/2)
(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))) 3/2))
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/6) -3)
(pow.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/6) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)

Outputs
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)

Calls

2 calls:

82.0ms	k
36.0ms	n

Results

Error	Segments	Branch
21.3b	2	`k`
23.4b	1	`n`

Compiler

Compiled 317 to 204 computations (35.6% saved)

bsearch189.0ms (1.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
189.0ms	2.2003024346152368e+74	1.8011951696134836e+80

Compiler

Compiled 257 to 217 computations (15.6% saved)

regimes118.0ms (0.8%)

Counts

32 → 2

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (.f64 (.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))))
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)))
(sqrt.f64 (/.f64 1 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 (neg.f64 n) (/.f64 1 (.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(cbrt.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64)))) 3/2)
(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))) 3/2))
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/6) -3)
(pow.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/6) 3)

Outputs
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(cbrt.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 3/2))

Calls

2 calls:

56.0ms	k
43.0ms	n

Results

Error	Segments	Branch
21.5b	2	`k`
23.4b	1	`n`

Compiler

Compiled 306 to 196 computations (35.9% saved)

bsearch287.0ms (1.9%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
286.0ms	2.8463896084154485e+86	1.6823500335249536e+88

Compiler

Compiled 198 to 166 computations (16.2% saved)

regimes83.0ms (0.5%)

Counts

24 → 1

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (.f64 (.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))))
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)))
(sqrt.f64 (/.f64 1 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (.f64 (neg.f64 n) (/.f64 1 (.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)

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

Calls

2 calls:

26.0ms	n
24.0ms	k

Results

Error	Segments	Branch
23.4b	1	`k`
23.4b	1	`n`

Compiler

Compiled 223 to 141 computations (36.8% saved)

regimes70.0ms (0.5%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

2 calls:

40.0ms	n
19.0ms	k

Results

Error	Segments	Branch
23.6b	1	`k`
23.6b	1	`n`

Compiler

Compiled 177 to 116 computations (34.5% saved)

regimes76.0ms (0.5%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

42.0ms	k
18.0ms	n

Results

Error	Segments	Branch
31.3b	1	`k`
31.3b	1	`n`

Compiler

Compiled 150 to 100 computations (33.3% saved)

regimes57.0ms (0.4%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

40.0ms	n
12.0ms	k

Results

Error	Segments	Branch
32.0b	1	`k`
32.0b	1	`n`

Compiler

Compiled 80 to 51 computations (36.3% saved)

regimes141.0ms (0.9%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

124.0ms	k
12.0ms	n

Results

Error	Segments	Branch
32.0b	1	`k`
32.0b	1	`n`

Compiler

Compiled 72 to 46 computations (36.1% saved)

regimes18.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0.0b (-0.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	n
7.0ms	k

Results

Error	Segments	Branch
32.0b	1	`k`
32.0b	1	`n`

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify138.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	4294967626
1	103	4294967626
2	107	4294967626
3	109	4294967626
4	110	4294967626

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(if (<=.f64 k 1781084914063017/68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (pow.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 1781084914063017/68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 48000000) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (sqrt.f64 (-.f64 (fma.f64 (/.f64 n k) (.f64 2 (PI.f64)) 1) 1)))
(if (<=.f64 k 179999999999999997415090464761131430319373630034400648404260174402553784691589120) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (pow.f64 (pow.f64 (/.f64 (/.f64 k (.f64 2 (PI.f64))) n) 3/2) -1/3))
(if (<=.f64 k 16500000000000001538934784502761397048739811407847593538905564756334312380698499636789248) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3/2)))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))

Outputs
(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)) (pow.f64 k -1/2))
(if (<=.f64 k 1781084914063017/68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (pow.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 1781084914063017/68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 1781084914063017/68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 48000000) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (sqrt.f64 (-.f64 (fma.f64 (/.f64 n k) (.f64 2 (PI.f64)) 1) 1)))
(if (<=.f64 k 48000000) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (sqrt.f64 (+.f64 (fma.f64 (/.f64 n k) (.f64 2 (PI.f64)) 1) -1)))
(if (<=.f64 k 179999999999999997415090464761131430319373630034400648404260174402553784691589120) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (pow.f64 (pow.f64 (/.f64 (/.f64 k (.f64 2 (PI.f64))) n) 3/2) -1/3))
(if (<=.f64 k 16500000000000001538934784502761397048739811407847593538905564756334312380698499636789248) (/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 k (/.f64 1/2 (PI.f64))))) (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3/2)))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (/.f64 n (*.f64 k (/.f64 1/2 (PI.f64)))))

Compiler

Compiled 261 to 203 computations (22.2% saved)

soundness98.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-+l+_binary64`
473×	`associate-l_binary64`
439×	`fma-def_binary64`
401×	`associate-r_binary64`
351×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	1569
1	241	1477
2	780	1289
3	4232	1184

Stop Event

1×	node limit

Compiler

Compiled 45 to 35 computations (22.2% saved)

end382.0ms (2.5%)

Compiler: Compiled 233 to 153 computations (34.3% saved)