Details

analyze134.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
12.5%	34.3%	53.2%	6
15.6%	26.5%	57.9%	7
15.6%	22.6%	61.8%	8
17.2%	17.6%	65.3%	9
17.2%	15%	67.8%	10
18%	12.2%	69.9%	11
18%	10.8%	71.3%	12

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.7s (38%)

Results

1.9s	8256×	body	256	valid
904.0ms	1300×	body	1024	invalid
597.0ms	2374×	body	256	invalid
258.0ms	670×	body	512	invalid

preprocess49.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	52	44
2	119	44
3	256	44
4	668	44
5	1836	40
6	4163	40
7	7307	40
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 20 to 17 computations (15% saved)

simplify28.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-/l*_binary64`
544×	`associate-/r*_binary64`
456×	`div-sub_binary64`
445×	`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	140	22
4	354	22
5	958	20
6	2187	20
7	5609	20

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

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

0.4b

Counts

3 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 33 to 27 computations (18.2% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

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

series77.0ms (0.8%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
27.0ms	n	@	0	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
22.0ms	n	@	-inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
11.0ms	n	@	inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
3.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
2.0ms	k	@	0	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))

rewrite65.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 87

Calls

Call 1

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

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

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

684×	`exp-sum_binary64`
402×	`associate-+r+_binary64`
395×	`associate-+l+_binary64`
393×	`associate-r_binary64`
367×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	1106
1	203	1024
2	637	901
3	3614	842
4	6894	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 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))

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

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

series19.0ms (0.2%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
7.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
1.0ms	k	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
1.0ms	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite70.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	307	51
2	3925	47

Stop Event

1×	node limit

Counts

4 → 108

Calls

Call 1

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

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

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-+r+_binary64`
528×	`associate-+l+_binary64`
423×	`associate-r_binary64`
405×	`associate-l_binary64`
338×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1206
1	226	1124
2	739	969
3	4114	958

Stop Event

1×	node limit

Counts

156 → 129

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

eval102.0ms (1.1%)

Compiler: Compiled 4845 to 3298 computations (31.9% saved)

prune74.0ms (0.8%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	209	26	235
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	209	28	237

Error

0.0b

Counts

237 → 28

Alt Table

Click to see full alt table

Status	Error	Program
	20.7b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 (.f64 (.f64 -1/2 k) (sqrt.f64 2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 k))
	21.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
✓	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	21.2b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.6b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
▶	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
▶	12.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	3.6b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	14.2b	(.f64 (cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))))
	0.6b	(.f64 (pow.f64 k -1/4) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
	20.7b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (+.f64 (.f64 1/8 (.f64 k k)) (.f64 -1/48 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 3))))))))) (sqrt.f64 k))
	13.3b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
▶	0.6b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	14.7b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	21.4b	(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
	16.5b	(/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (fma.f64 k -1/2 1/2) 3))) (sqrt.f64 k))
	19.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	3.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
▶	12.9b	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)

Compiler

Compiled 1071 to 867 computations (19% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

series25.0ms (0.3%)

Counts

4 → 24

Calls

18 calls:

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

rewrite79.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`log-prod_binary64`
699×	`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	75
1	298	57
2	3808	53

Stop Event

1×	node limit

Counts

4 → 121

Calls

Call 1

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

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

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

660×	`distribute-lft-out_binary64`
550×	`+-commutative_binary64`
377×	`sqr-pow_binary64`
366×	`associate-r_binary64`
354×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	598
1	122	572
2	409	513
3	2665	502
4	4203	495
5	5799	495
6	7247	495

Stop Event

1×	node limit

Counts

145 → 132

Calls

Call 1

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

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

localize17.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	11.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	0.3b	(*.f64 (PI.f64) n)
	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
	0.1b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)
✓	0.1b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)
✓	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
	0.3b	(*.f64 (PI.f64) n)
✓	11.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

series16.0ms (0.2%)

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))
2.0ms	n	@	-inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 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))

rewrite73.0ms (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	3381	50

Stop Event

1×	node limit

Counts

3 → 119

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

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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 0 (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 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.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 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 (neg.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 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simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-+l+_binary64`
475×	`associate-l_binary64`
439×	`fma-def_binary64`
400×	`associate-r_binary64`
330×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	1569
1	241	1477
2	774	1289
3	4236	1184

Stop Event

1×	node limit

Counts

179 → 154

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

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

series7.0ms (0.1%)

Counts

3 → 36

Calls

15 calls:

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

rewrite68.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

716×	`log-prod_binary64`
512×	`pow-unpow_binary64`
365×	`pow2_binary64`
251×	`pow1/3_binary64`
247×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	299	37
2	3718	37

Stop Event

1×	node limit

Counts

3 → 93

Calls

Call 1

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

Outputs

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

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

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

627×	`exp-sum_binary64`
414×	`associate-+r+_binary64`
407×	`associate-+l+_binary64`
349×	`associate-l_binary64`
311×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	914
1	185	858
2	599	757
3	3263	686
4	7165	686

Stop Event

1×	node limit

Counts

129 → 113

Calls

Call 1

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

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (PI.f64) n)
	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
	0.1b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)
	0.1b	(sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
	0.3b	(*.f64 (PI.f64) n)
✓	0.3b	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
	11.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

series145.0ms (1.5%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
51.0ms	n	@	inf	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
24.0ms	k	@	inf	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
23.0ms	n	@	-inf	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
21.0ms	n	@	0	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
21.0ms	k	@	-inf	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)

rewrite57.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	302	19
2	3612	19

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

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

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

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-def_binary64`
606×	`distribute-rgt-in_binary64`
576×	`distribute-lft-in_binary64`
550×	`associate-l_binary64`
532×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	1423
1	367	1096
2	1340	883

Stop Event

1×	node limit

Counts

56 → 49

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (.f64 k (+.f64 (.f64 -1/4 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1/4 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 2))))))
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (+.f64 (.f64 k (+.f64 (.f64 -1/4 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1/4 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2))))) (.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 2 (.f64 (+.f64 (.f64 1/8 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 1/32 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 2)))) (pow.f64 k 2))))
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (+.f64 (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/4 (.f64 (+.f64 (.f64 1/8 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 1/32 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 -1/4 (.f64 (+.f64 (.f64 1/8 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 1/32 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)))) (.f64 2 (.f64 (+.f64 (.f64 1/24 (+.f64 (.f64 3 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 -1/384 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1/32 (.f64 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)))))) (+.f64 (.f64 k (+.f64 (.f64 -1/4 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1/4 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2))))) (.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 2 (.f64 (+.f64 (.f64 1/8 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 1/32 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)))) (pow.f64 k 2)))))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 2)
(.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))) 2) (sqrt.f64 -1))
(.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))) 2) (sqrt.f64 -1))
(.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))) 2) (sqrt.f64 -1))
(.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))) 2) (sqrt.f64 -1))

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

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)
	0.2b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.1b	(pow.f64 (sqrt.f64 k) -1/2)
✓	0.2b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)
	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.6b	(pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)

series14.0ms (0.1%)

Counts

2 → 12

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	k	@	0	(pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)
3.0ms	k	@	-inf	(pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)
2.0ms	k	@	inf	(pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)
1.0ms	k	@	0	(.f64 (pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	n	@	0	(.f64 (pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite72.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`log-prod_binary64`
289×	`pow1/3_binary64`
286×	`expm1-udef_binary64`
285×	`log1p-udef_binary64`
265×	`pow3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	353	27
2	4253	26

Stop Event

1×	node limit

Counts

2 → 45

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) (cbrt.f64 (exp.f64 (pow.f64 k -1/2))))) (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 (pow.f64 k -1/4) (pow.f64 k -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.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 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1/2)) (*.f64 (cbrt.f64 (pow.f64 k -1/4)) (pow.f64 k -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/8) (*.f64 (pow.f64 k -1/8) (pow.f64 k -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 k -1/8) 3) (pow.f64 k -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 k) -1) (pow.f64 (cbrt.f64 (sqrt.f64 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 k 1/4) -1) (pow.f64 (pow.f64 k 1/4) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/4) (cbrt.f64 (pow.f64 k -1/2))) (cbrt.f64 (pow.f64 k -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 k))))) (#(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 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 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))) (pow.f64 k -1/2))) (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))) (pow.f64 k -1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 4))) 2)))) (#(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 (PI.f64) (*.f64 2 n)) (-.f64 1 k))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 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 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)))) 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 (PI.f64) (*.f64 2 n)) (-.f64 1 k))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k))))) 1))))))

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

813×	`exp-sum_binary64`
716×	`unsub-neg_binary64`
629×	`exp-prod_binary64`
494×	`distribute-rgt-in_binary64`
479×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	388
1	96	384
2	297	372
3	1177	360
4	5281	288

Stop Event

1×	node limit

Counts

57 → 50

Calls

Call 1

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

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

eval331.0ms (3.4%)

Compiler: Compiled 16044 to 11279 computations (29.7% saved)

prune119.0ms (1.2%)

Pruning

22 alts after pruning (19 fresh and 3 done)

	Pruned	Kept	Total
New	718	15	733
Fresh	17	4	21
Picked	1	0	1
Done	3	3	6
Total	739	22	761

Error

Counts

761 → 22

Alt Table

Click to see full alt table

Status	Error	Program
	21.2b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.7b	(pow.f64 (.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 4))) 2)
	0.5b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
✓	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
	33.3b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
▶	33.3b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
✓	12.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
▶	14.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))))
	12.9b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) 2)
▶	12.6b	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))
	12.8b	(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
	12.6b	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) 2)) k))
	21.4b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
▶	12.3b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
	21.1b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
	0.6b	(.f64 (.f64 (pow.f64 k -1/4) (pow.f64 k -1/4)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	12.8b	(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
✓	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))

Compiler

Compiled 688 to 557 computations (19% saved)

localize12.0ms (0.1%)

Local error

Found 6 expressions with local error:

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

series5.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

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

rewrite51.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	307	23
2	3793	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 (*.f64 (pow.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 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 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 (*.f64 (pow.f64 k -1/2) (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 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 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 (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 (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 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 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.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 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 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 expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 -1/2 (log.f64 k) (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 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 1))))))

simplify38.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

815×	`exp-sum_binary64`
717×	`unsub-neg_binary64`
629×	`exp-prod_binary64`
496×	`distribute-rgt-in_binary64`
479×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	388
1	96	384
2	303	372
3	1178	360
4	5281	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 (PI.f64) (/.f64 -2 (/.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 (PI.f64) (/.f64 -2 (/.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 (PI.f64) (/.f64 -2 (/.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 (PI.f64) (/.f64 -2 (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))

localize5.0ms (0.1%)

Local error

Found 6 expressions with local error:

New	Error	Program
	11.9b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
	0.3b	(*.f64 n (PI.f64))
	0.2b	(/.f64 (.f64 2 (.f64 n (PI.f64))) k)
✓	0.2b	(/.f64 (.f64 2 (.f64 n (PI.f64))) k)
✓	0.3b	(*.f64 n (PI.f64))
✓	11.9b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))

series10.0ms (0.1%)

Counts

3 → 24

Calls

15 calls:

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

rewrite77.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

524×	`log-prod_binary64`
396×	`exp-prod_binary64`
353×	`prod-exp_binary64`
295×	`pow-prod-down_binary64`
240×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	189	29
2	2487	29

Stop Event

1×	node limit

Counts

3 → 159

Calls

Call 1

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

Outputs

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

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

15×	`associate-/l*_binary64`
14×	`*-commutative_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	55	264
4	85	264
5	96	264

Stop Event

1×

saturated

Counts

183 → 160

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

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(.f64 (PI.f64) (.f64 n 2))
	0.3b	(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))
	0.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
	0.1b	(/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))
✓	0.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
✓	0.3b	(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))
✓	0.3b	(.f64 (PI.f64) (.f64 n 2))
✓	11.3b	(sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))

series15.0ms (0.2%)

Counts

4 → 60

Calls

21 calls:

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

rewrite79.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

713×	`log-prod_binary64`
476×	`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	3750	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
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simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

413×	`associate-+r+_binary64`
406×	`associate-+l+_binary64`
347×	`associate-l_binary64`
311×	`fma-neg_binary64`
309×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	1326
1	191	1250
2	608	1117
3	3292	1022
4	7307	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)))))))
(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)))))))
(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)) (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 (*.f64 (PI.f64) -2) (/.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))))))
(sqrt.f64 (/.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k))))
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(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
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(sqrt.f64 (/.f64 k (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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(.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))))))
(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 (*.f64 (PI.f64) -2) (/.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))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.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 (*.f64 (PI.f64) -2) (/.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 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k))
(pow.f64 (*.f64 (PI.f64) (/.f64 -2 (/.f64 -1 n))) (-.f64 1 k))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
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(.f64 n (+.f64 (.f64 k (.f64 -2 (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (*.f64 2 (PI.f64))))
(.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (.f64 k -2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) 2))
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(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 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))))
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(.f64 n (+.f64 (.f64 2 (PI.f64)) (.f64 (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))) (+.f64 (.f64 (.f64 k k) (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 -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))))))
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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 (*.f64 (PI.f64) -2) (/.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 (*.f64 (PI.f64) -2) (/.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 (*.f64 (PI.f64) -2) (/.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 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 -2 (/.f64 -1 n))) (-.f64 1 k)) k))

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

New	Error	Program
	4.0b	(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
	0.3b	(.f64 n (.f64 2 (PI.f64)))
	0.1b	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k)
	0.1b	(.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))
✓	0.1b	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k)
	0.3b	(.f64 n (.f64 2 (PI.f64)))
✓	4.0b	(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
✓	11.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))

series7.0ms (0.1%)

Counts

3 → 60

Calls

18 calls:

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

rewrite76.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	285	50
2	3526	50

Stop Event

1×	node limit

Counts

3 → 158

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-+l+_binary64`
474×	`associate-l_binary64`
439×	`fma-def_binary64`
401×	`associate-r_binary64`
330×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	1377
1	242	1349
2	776	1289
3	4232	1184

Stop Event

1×	node limit

Counts

218 → 192

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 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)
(/.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)

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

localize8.0ms (0.1%)

Local error

Found 8 expressions with local error:

New	Error	Program
	11.8b	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))
	0.3b	(.f64 n (.f64 2 (PI.f64)))
	0.1b	(/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k)
	0.0b	(.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k)))
✓	0.0b	(.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k)))
✓	0.1b	(/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k)
	0.3b	(.f64 n (.f64 2 (PI.f64)))
✓	11.8b	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))

series100.0ms (1%)

Counts

3 → 48

Calls

18 calls:

Time	Variable		Point	Expression
70.0ms	n	@	0	(/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k)
4.0ms	n	@	inf	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))
3.0ms	n	@	0	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))
3.0ms	n	@	-inf	(/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k)
3.0ms	n	@	-inf	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))

rewrite75.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

712×	`log-prod_binary64`
636×	`pow-unpow_binary64`
313×	`pow2_binary64`
217×	`pow1/3_binary64`
213×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	77
1	262	50
2	3690	50

Stop Event

1×	node limit

Counts

3 → 118

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

546×	`associate-l_binary64`
477×	`associate-r_binary64`
468×	`fma-def_binary64`
467×	`times-frac_binary64`
431×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1613
1	318	1541
2	1028	1333
3	4711	1091

Stop Event

1×	node limit

Counts

166 → 147

Calls

Call 1

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

eval308.0ms (3.2%)

Compiler: Compiled 15499 to 10220 computations (34.1% saved)

prune153.0ms (1.6%)

Pruning

36 alts after pruning (31 fresh and 5 done)

	Pruned	Kept	Total
New	779	25	804
Fresh	8	6	14
Picked	0	1	1
Done	3	4	7
Total	790	36	826

Error

Counts

826 → 36

Alt Table

Click to see full alt table

Status	Error	Program
	39.7b	(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))
	33.3b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
	12.2b	(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2)
	33.3b	(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
	21.2b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
✓	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	21.1b	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
	0.7b	(pow.f64 (.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 4))) 2)
	0.5b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
	33.3b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
▶	32.9b	(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
✓	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
	32.8b	(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
	0.5b	(/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (-.f64 1 k))))))
✓	12.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	21.1b	(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
✓	14.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
✓	12.6b	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))
	32.8b	(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
	12.9b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) 2)
	33.5b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/4) 2)
	12.6b	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)) k))
▶	21.4b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
	35.2b	(exp.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 1/2))
	35.6b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
▶	41.1b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
	33.3b	(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
▶	0.3b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
	0.6b	(.f64 (.f64 (pow.f64 k -1/4) (pow.f64 k -1/4)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.7b	(.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
▶	33.3b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	21.1b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))
	33.6b	(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
	48.0b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)

Compiler

Compiled 977 to 794 computations (18.7% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

series29.0ms (0.3%)

Counts

2 → 12

Calls

12 calls:

Time	Variable		Point	Expression
9.0ms	n	@	inf	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
4.0ms	k	@	-inf	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
3.0ms	k	@	0	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
3.0ms	n	@	0	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
3.0ms	n	@	-inf	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))

rewrite64.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

732×	`log-prod_binary64`
443×	`pow-unpow_binary64`
323×	`pow2_binary64`
317×	`pow-pow_binary64`
224×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	256	42
2	3360	35

Stop Event

1×	node limit

Counts

2 → 76

Calls

Call 1

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

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

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-def_binary64`
414×	`unswap-sqr_binary64`
365×	`associate-/l*_binary64`
314×	`exp-sum_binary64`
310×	`div-sub_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	264
1	83	264
2	177	228
3	481	192
4	1232	192
5	3450	192

Stop Event

1×	node limit

Counts

88 → 80

Calls

Call 1

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

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

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	11.9b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	0.2b	(/.f64 (PI.f64) (/.f64 k n))
✓	0.2b	(/.f64 (PI.f64) (/.f64 k n))
✓	11.9b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

series5.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

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

rewrite57.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

538×	`log-prod_binary64`
411×	`exp-prod_binary64`
339×	`prod-exp_binary64`
283×	`pow-prod-down_binary64`
250×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 103

Calls

Call 1

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

Outputs

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

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

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	192
1	9	192
2	13	192
3	16	192
4	17	192

Stop Event

1×

saturated

Counts

127 → 104

Calls

Call 1

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

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

localize7.0ms (0.1%)

Local error

Found 6 expressions with local error:

New	Error	Program
	11.4b	(sqrt.f64 (/.f64 (/.f64 k n) (PI.f64)))
	0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
	0.3b	(/.f64 (/.f64 k n) (PI.f64))
✓	0.3b	(/.f64 (/.f64 k n) (PI.f64))
✓	0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
✓	11.4b	(sqrt.f64 (/.f64 (/.f64 k n) (PI.f64)))

series12.0ms (0.1%)

Counts

3 → 24

Calls

18 calls:

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

rewrite67.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`log-prod_binary64`
351×	`pow-prod-down_binary64`
282×	`pow2_binary64`
198×	`pow1/3_binary64`
195×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	220	31
2	3025	31

Stop Event

1×	node limit

Counts

3 → 149

Calls

Call 1

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

Outputs

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

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`associate-/r*_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	192
1	9	192
2	11	192

Stop Event

1×

saturated

Counts

173 → 151

Calls

Call 1

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

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

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

New	Error	Program
	24.3b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
	0.3b	(/.f64 (/.f64 k n) (PI.f64))
	0.2b	(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2)
	0.2b	(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
✓	0.2b	(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
✓	0.2b	(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2)
	0.3b	(/.f64 (/.f64 k n) (PI.f64))
✓	24.3b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)

series101.0ms (1%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
25.0ms	n	@	-inf	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
20.0ms	n	@	0	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
19.0ms	k	@	0	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
17.0ms	k	@	-inf	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
8.0ms	k	@	inf	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)

rewrite63.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`log-prod_binary64`
340×	`pow-prod-down_binary64`
325×	`pow2_binary64`
223×	`pow1/3_binary64`
222×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	277	38
2	3519	38

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

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

Outputs

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

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

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

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-def_binary64`
543×	`exp-sum_binary64`
312×	`distribute-rgt-in_binary64`
286×	`associate--r+_binary64`
283×	`associate-+l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	1320
1	168	1272
2	394	1128
3	1011	984
4	2969	984

Stop Event

1×	node limit

Counts

164 → 108

Calls

Call 1

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

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(.f64 n (.f64 2 (PI.f64)))
	0.3b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
	0.1b	(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2)
	0.1b	(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
✓	0.1b	(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2)
	0.3b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
	0.3b	(.f64 n (.f64 2 (PI.f64)))
✓	20.3b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)

series48.0ms (0.5%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
22.0ms	k	@	-inf	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
13.0ms	k	@	0	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
3.0ms	k	@	inf	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
2.0ms	n	@	0	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
2.0ms	n	@	inf	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)

rewrite61.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

740×	`log-prod_binary64`
397×	`pow2_binary64`
266×	`pow1/3_binary64`
264×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	334	39
2	4083	39

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

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

Outputs

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

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

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-def_binary64`
777×	`distribute-rgt-in_binary64`
754×	`distribute-lft-in_binary64`
281×	`associate-+l+_binary64`
217×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2702
1	532	2411
2	1964	2013

Stop Event

1×	node limit

Counts

99 → 85

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 7)) 1/9))))
(+.f64 (.f64 1/3 (.f64 (.f64 (pow.f64 k 2) (-.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 3/4 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 3/4 (.f64 (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 17)) 1/9) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))) (pow.f64 (/.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)) 1/3))) (+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 7)) 1/9)))))
(+.f64 (.f64 1/3 (.f64 (.f64 (pow.f64 k 3) (-.f64 (.f64 (+.f64 (.f64 -9/8 (.f64 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/4 (+.f64 (.f64 3 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (.f64 -9/16 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))) (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 -1 (.f64 (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 4)) 1/9) (.f64 (-.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 3/4 (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))) (.f64 3/4 (.f64 (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 17)) 1/9) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 -1/8 (.f64 (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 7)) 1/3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (pow.f64 (/.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)) 1/3))) (+.f64 (.f64 1/3 (.f64 (.f64 (pow.f64 k 2) (-.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 3/4 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 3/4 (.f64 (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 17)) 1/9) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))) (pow.f64 (/.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)) 1/3))) (+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 7)) 1/9))))))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k))))) 1/3)
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k))))) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
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(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
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Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
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(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
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(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
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(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))))
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(+.f64 (.f64 -3/2 (.f64 k (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 -3/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(fma.f64 -3/2 (.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))))
(.f64 (+.f64 (.f64 (.f64 k -3/2) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 1) (.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2)))
(+.f64 (.f64 -3/2 (.f64 k (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (pow.f64 k 2) (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 3/4 (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))))))
(+.f64 (fma.f64 -3/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (.f64 (.f64 (.f64 k k) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (fma.f64 3/4 (.f64 0 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 2) 9/8))))
(fma.f64 -3/2 (.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (fma.f64 (.f64 k k) (.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) (fma.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) 9/8 0)) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k)))))
(fma.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2) (.f64 (.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2)) (+.f64 (.f64 (.f64 k k) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) 9/8)) (.f64 (.f64 k -3/2) (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
(+.f64 (.f64 -3/2 (.f64 k (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 (pow.f64 k 2) (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 3/4 (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))) (.f64 (pow.f64 k 3) (.f64 (+.f64 (.f64 -9/16 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 -9/8 (.f64 (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/4 (+.f64 (.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 3 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))))) (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))))))
(+.f64 (fma.f64 -3/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (fma.f64 (.f64 k k) (.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (fma.f64 3/4 (.f64 0 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) 9/8))) (.f64 (pow.f64 k 3) (.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (fma.f64 -9/16 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (fma.f64 -9/8 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 0 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2))) (.f64 1/4 (fma.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) 2)))))))))
(+.f64 (fma.f64 (.f64 k k) (.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) (fma.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) 9/8 0)) (.f64 (fma.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) -9/16 (fma.f64 1/4 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) 0) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 0))) (.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) (pow.f64 k 3)))) (fma.f64 -3/2 (.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k)))))
(+.f64 (.f64 (.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2)) (+.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) -9/16)) (.f64 (.f64 k k) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) 9/8)))) (.f64 (+.f64 (.f64 (.f64 k -3/2) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 1) (.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 3/2))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 (log.f64 k))))
(pow.f64 (exp.f64 3/2) (fma.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (log.f64 k))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3/2) (pow.f64 k -3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 (log.f64 k))))
(pow.f64 (exp.f64 3/2) (fma.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (log.f64 k))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3/2) (pow.f64 k -3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 (log.f64 k))))
(pow.f64 (exp.f64 3/2) (fma.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (log.f64 k))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3/2) (pow.f64 k -3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 (log.f64 k))))
(pow.f64 (exp.f64 3/2) (fma.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (log.f64 k))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3/2) (pow.f64 k -3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (log.f64 (/.f64 -1 k))))
(.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (neg.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (log.f64 (/.f64 -1 k))))
(.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (neg.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (log.f64 (/.f64 -1 k))))
(.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (neg.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (log.f64 (/.f64 -1 k))))
(.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (neg.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3/2))

eval291.0ms (3%)

Compiler: Compiled 14041 to 9016 computations (35.8% saved)

prune128.0ms (1.3%)

Pruning

44 alts after pruning (34 fresh and 10 done)

	Pruned	Kept	Total
New	726	16	742
Fresh	8	18	26
Picked	0	1	1
Done	0	9	9
Total	734	44	778

Error

Counts

778 → 44

Alt Table

Click to see full alt table

Status	Error	Program
	39.7b	(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))
	41.1b	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 2 k) n)) 3/2) 1/3)
	33.3b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
	0.6b	(.f64 (.f64 (pow.f64 k -1/4) (pow.f64 k -1/4)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	41.1b	(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)
	0.7b	(.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
	33.6b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2))) 3/2)
	35.2b	(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1/2))
	33.3b	(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
	12.2b	(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2)
	21.2b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
✓	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	21.1b	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
	0.7b	(pow.f64 (.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 4))) 2)
	0.5b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
	33.3b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
✓	32.9b	(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
✓	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
	21.1b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))
	35.6b	(pow.f64 (pow.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))) 1/6) 3)
	32.8b	(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
	0.5b	(/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (-.f64 1 k))))))
	34.6b	(/.f64 (sqrt.f64 2) (exp.f64 (.f64 (log.f64 (/.f64 k (.f64 n (PI.f64)))) 1/2)))
✓	12.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	32.9b	(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
	33.0b	(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))
	21.1b	(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
✓	14.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
✓	12.6b	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))
	12.6b	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)) k))
	35.2b	(sqrt.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))))))
	33.5b	(.f64 (sqrt.f64 (.f64 (/.f64 2 k) n)) (sqrt.f64 (PI.f64)))
	35.6b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
✓	21.4b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	33.6b	(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
	12.9b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 2)
	33.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)))
✓	41.1b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
	21.1b	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
✓	0.3b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
	48.0b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)
	33.3b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
✓	33.3b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	32.8b	(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)

Compiler

Compiled 610 to 497 computations (18.5% saved)

regimes234.0ms (2.4%)

Counts

84 → 1

Calls

Call 1

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

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

Calls

5 calls:

46.0ms	n
43.0ms	(.f64 (.f64 2 (PI.f64)) n)
42.0ms	(.f64 (.f64 2 (PI.f64)) n)
41.0ms	k
24.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

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

Compiler

Compiled 1199 to 778 computations (35.1% saved)

regimes234.0ms (2.4%)

Counts

80 → 1

Calls

Call 1

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

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

Calls

5 calls:

59.0ms	(.f64 (.f64 2 (PI.f64)) n)
41.0ms	(.f64 (.f64 2 (PI.f64)) n)
39.0ms	n
38.0ms	k
24.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

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

Compiler

Compiled 1084 to 708 computations (34.7% saved)

regimes166.0ms (1.7%)

Counts

74 → 1

Calls

Call 1

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

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

Calls

4 calls:

40.0ms	k
37.0ms	(.f64 (.f64 2 (PI.f64)) n)
36.0ms	n
23.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.4b	1	`k`
0.4b	1	`n`
0.4b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 971 to 626 computations (35.5% saved)

regimes56.0ms (0.6%)

Counts

39 → 1

Calls

Call 1

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

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

Calls

2 calls:

22.0ms	n
21.0ms	k

Results

Error	Segments	Branch
0.5b	1	`k`
0.5b	1	`n`

Compiler

Compiled 406 to 243 computations (40.1% saved)

regimes167.0ms (1.7%)

Counts

35 → 2

Calls

Call 1

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

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

Calls

2 calls:

124.0ms	n
33.0ms	k

Results

Error	Segments	Branch
0.5b	2	`k`
6.5b	8	`n`

Compiler

Compiled 350 to 204 computations (41.7% saved)

bsearch35.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
34.0ms	2.557724295753228e-50	1.4047469740588824e-49

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes159.0ms (1.6%)

Counts

34 → 2

Calls

Call 1

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

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

Calls

2 calls:

118.0ms	n
30.0ms	k

Results

Error	Segments	Branch
0.6b	2	`k`
6.9b	8	`n`

Compiler

Compiled 337 to 196 computations (41.8% saved)

bsearch33.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
33.0ms	4.099557307751841e-12	9.241908060648496e-11

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes85.0ms (0.9%)

Counts

33 → 2

Calls

Call 1

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

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

Calls

2 calls:

45.0ms	n
30.0ms	k

Results

Error	Segments	Branch
17.4b	2	`k`
20.0b	3	`n`

Compiler

Compiled 325 to 188 computations (42.2% saved)

bsearch57.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
56.0ms	2.2686164303828526e+146	3.879678674408656e+151

Compiler

Compiled 266 to 226 computations (15% saved)

regimes42.0ms (0.4%)

Counts

31 → 1

Calls

Call 1

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

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

Calls

2 calls:

16.0ms	k
16.0ms	n

Results

Error	Segments	Branch
21.1b	1	`k`
21.1b	1	`n`

Compiler

Compiled 303 to 175 computations (42.2% saved)

regimes27.0ms (0.3%)

Counts

20 → 1

Calls

Call 1

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

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

Calls

2 calls:

11.0ms	n
10.0ms	k

Results

Error	Segments	Branch
21.1b	1	`k`
21.1b	1	`n`

Compiler

Compiled 184 to 104 computations (43.5% saved)

regimes22.0ms (0.2%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	n
8.0ms	k

Results

Error	Segments	Branch
32.8b	1	`k`
32.8b	1	`n`

Compiler

Compiled 146 to 83 computations (43.2% saved)

regimes15.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	n
6.0ms	k

Results

Error	Segments	Branch
33.3b	1	`k`
33.3b	1	`n`

Compiler

Compiled 80 to 45 computations (43.8% saved)

regimes12.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.3%)

Threshold costs -0.1b (-0.3%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	n
5.0ms	k

Results

Error	Segments	Branch
33.3b	1	`k`
33.3b	1	`n`

Compiler

Compiled 56 to 33 computations (41.1% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	310
1	100	310
2	104	310
3	106	310
4	107	310

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(if (<=.f64 k 689561106027824512/26959946667150639794667015087019630673637144422540572481103610249216) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 k -1/2)) (pow.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 324800392615102848/79228162514264337593543950336) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 k -1/2)) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 38000000000000000362010740996030570265764272365158915667926303816832894685975084924058266377513288763869254360760036547885329637985186250334770636521472) (.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2)) (pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6))
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))

Outputs
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 (*.f64 k -1/2) 1/2)) (sqrt.f64 k))
(if (<=.f64 k 689561106027824512/26959946667150639794667015087019630673637144422540572481103610249216) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 k -1/2)) (pow.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 5387196140842379/210624583337114373395836055367340864637790190801098222508621955072) (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k -1/2)) (pow.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 324800392615102848/79228162514264337593543950336) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 k -1/2)) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 2537503067305491/618970019642690137449562112) (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k -1/2)) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 38000000000000000362010740996030570265764272365158915667926303816832894685975084924058266377513288763869254360760036547885329637985186250334770636521472) (.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2)) (pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6))
(if (<=.f64 k 38000000000000000362010740996030570265764272365158915667926303816832894685975084924058266377513288763869254360760036547885329637985186250334770636521472) (.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (pow.f64 k -1/2)) (pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6))
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (pow.f64 k -1/2))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))

end128.0ms (1.3%)

Stop Event

1×

fuel

Compiler

Compiled 418 to 302 computations (27.8% saved)