Details

analyze118.0ms (1.7%)

Algorithm

1×

Search

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

sample4.1s (59.1%)

Results

1.4s	1336×	body	1024	invalid
1.4s	7906×	body	64	valid
541.0ms	719×	body	512	invalid
279.0ms	1689×	body	64	invalid
173.0ms	350×	body	128	valid
165.0ms	325×	body	256	invalid
55.0ms	179×	body	128	invalid

preprocess53.0ms (0.8%)

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 18 to 15 computations (16.7% saved)

simplify28.0ms (0.4%)

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))

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.6b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series73.0ms (1.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
27.0ms	n	@	-inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
25.0ms	n	@	0	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
10.0ms	n	@	inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
2.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
2.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

rewrite62.0ms (0.9%)

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

simplify67.0ms (1%)

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)))

prune797.0ms (11.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	10	108

Error

0.0b

Counts

108 → 10

Alt Table

Status	Error	Program
	0.8b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	0.6b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
	0.7b	(/.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))
	0.7b	(.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)))
	25.4b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (.f64 1/8 (.f64 k k)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64)))))))))) (sqrt.f64 k))
	9.3b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	0.7b	(.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)))
	2.9b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/6)))
▶	0.6b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	9.1b	(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k))

Compiler

Compiled 2672 to 1848 computations (30.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series85.0ms (1.2%)

Counts

4 → 56

Calls

21 calls:

Time	Variable		Point	Expression
37.0ms	n	@	-inf	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
23.0ms	n	@	0	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
7.0ms	n	@	inf	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
4.0ms	k	@	-inf	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
3.0ms	k	@	0	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))

rewrite72.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

727×	`log-prod_binary64`
454×	`pow-unpow_binary64`
375×	`pow2_binary64`
256×	`pow1/3_binary64`
253×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	299	55
2	3700	55

Stop Event

1×	node limit

Counts

4 → 132

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.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 2 (PI.f64)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.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 2 (PI.f64)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.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 2 (PI.f64)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) -1/2) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) (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 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.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 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (PI.f64))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) -1/2) k) (sqrt.f64 (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 (.f64 k -1/2) 1)) (sqrt.f64 (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 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 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 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 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (PI.f64)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (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 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2)) (cbrt.f64 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 (fma.f64 k -1/2 1/2))) (sqrt.f64 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (cbrt.f64 (fma.f64 k -1/2 1/2))) (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2)) 1) (cbrt.f64 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2))) (cbrt.f64 (cbrt.f64 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2)) (cbrt.f64 (sqrt.f64 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (sqrt.f64 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 k -1/2 1/2))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)))) (sqrt.f64 (cbrt.f64 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 (fma.f64 k -1/2 1/2))) 1) (sqrt.f64 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 (fma.f64 k -1/2 1/2))) (cbrt.f64 (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 k -1/2 1/2)) 2))) (sqrt.f64 (cbrt.f64 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 (fma.f64 k -1/2 1/2))) (sqrt.f64 (sqrt.f64 (fma.f64 k -1/2 1/2)))) (sqrt.f64 (sqrt.f64 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) 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simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary64`
519×	`*-commutative_binary64`
363×	`distribute-lft-out_binary64`
292×	`distribute-rgt-in_binary64`
290×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	1684
1	422	1615
2	1465	1519
3	5225	1477
4	7282	1477

Stop Event

1×	node limit

Counts

188 → 167

Calls

Call 1

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

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

prune465.0ms (6.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	168	9	177

Error

0.0b

Counts

177 → 9

Alt Table

Status	Error	Program
	8.8b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (+.f64 (.f64 -1/2 (.f64 (*.f64 k (log.f64 n)) (sqrt.f64 n))) (sqrt.f64 n))) (sqrt.f64 k))
	0.7b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (pow.f64 n k) -1/2) (sqrt.f64 n))) (sqrt.f64 k))
	0.6b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
	0.7b	(/.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))
	0.7b	(.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)))
	1.0b	(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
	9.3b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
▶	0.5b	(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	0.7b	(.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)))

Compiler

Compiled 4626 to 3172 computations (31.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series8.0ms (0.1%)

Counts

2 → 12

Calls

9 calls:

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

rewrite55.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

695×	`log-prod_binary64`
451×	`pow-unpow_binary64`
371×	`pow2_binary64`
338×	`pow-pow_binary64`
252×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	46
1	297	39
2	3466	39

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

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

Outputs

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

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

simplify37.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

934×	`unswap-sqr_binary64`
730×	`fma-def_binary64`
640×	`times-frac_binary64`
556×	`associate-l_binary64`
441×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	408
1	81	360
2	238	360
3	928	360
4	3835	360

Stop Event

1×	node limit

Counts

54 → 46

Calls

Call 1

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

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

prune267.0ms (3.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	112	9	121

Error

0.0b

Counts

121 → 9

Alt Table

Status	Error	Program
	1.0b	(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
▶	0.3b	(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1))))
	0.6b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
	0.7b	(/.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))
	9.3b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
✓	0.5b	(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	0.7b	(.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)))
	8.8b	(.f64 (+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 n))) (sqrt.f64 n)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	0.6b	(.f64 (.f64 (pow.f64 n (.f64 (.f64 k -1/2) 1)) (sqrt.f64 n)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))

Compiler

Compiled 3225 to 2446 computations (24.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.3%)

Counts

3 → 24

Calls

12 calls:

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

rewrite71.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

797×	`log-prod_binary64`
603×	`pow-unpow_binary64`
425×	`pow2_binary64`
290×	`pow1/3_binary64`
288×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	77
1	353	68
2	4046	68

Stop Event

1×	node limit

Counts

3 → 70

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

simplify35.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

902×	`fma-def_binary64`
761×	`distribute-rgt-in_binary64`
738×	`distribute-lft-in_binary64`
409×	`*-commutative_binary64`
197×	`associate-+r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	715
1	157	715
2	461	611
3	2084	561

Stop Event

1×	node limit

Counts

94 → 84

Calls

Call 1

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

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

prune288.0ms (4.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	118	9	127

Error

0.0b

Counts

127 → 9

Alt Table

Status	Error	Program
	1.0b	(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
✓	0.3b	(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1))))
	0.6b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
	0.7b	(/.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))
	9.3b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
✓	0.5b	(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	0.7b	(.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)))
	8.8b	(.f64 (+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 n))) (sqrt.f64 n)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	0.6b	(.f64 (.f64 (pow.f64 n (.f64 (.f64 k -1/2) 1)) (sqrt.f64 n)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))

Compiler

Compiled 3350 to 2569 computations (23.3% saved)

regimes46.0ms (0.7%)

Accuracy

Total -35.5b remaining (-10199.4%)

Threshold costs -35.5b (-10199.4%)

Counts

19 → 1

Calls

Call 1

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

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

Results

10.0ms	0.3b	`k`
10.0ms	0.3b	`n`
6.0ms	0.3b	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
11.0ms	0.3b	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 431 to 296 computations (31.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	33
1	21	33

Stop Event

1×

saturated

Calls

Call 1

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

Outputs

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

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

end34.0ms (0.5%)

Stop Event

1×

fuel

Compiler

Compiled 48 to 40 computations (16.7% saved)

Details

analyze118.0ms (1.7%)

sample4.1s (59.1%)

preprocess53.0ms (0.8%)

simplify28.0ms (0.4%)

prune3.0ms (0.1%)

localize9.0ms (0.1%)

series73.0ms (1.1%)

rewrite62.0ms (0.9%)

simplify67.0ms (1%)

prune797.0ms (11.6%)

localize11.0ms (0.2%)

series85.0ms (1.2%)

rewrite72.0ms (1.1%)

simplify90.0ms (1.3%)

prune465.0ms (6.8%)

localize14.0ms (0.2%)

series8.0ms (0.1%)

rewrite55.0ms (0.8%)

simplify37.0ms (0.5%)

prune267.0ms (3.9%)

localize13.0ms (0.2%)

series17.0ms (0.3%)

rewrite71.0ms (1%)

simplify35.0ms (0.5%)

prune288.0ms (4.2%)

regimes46.0ms (0.7%)

simplify2.0ms (0%)

end34.0ms (0.5%)

Profiling