Details

analyze126.0ms (1.3%)

Algorithm

1×

Search

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.9s (39.4%)

Results

1.7s	8256×	body	256	valid
1.0s	1378×	body	1024	invalid
641.0ms	2253×	body	256	invalid
436.0ms	683×	body	512	invalid

preprocess64.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 20 to 17 computations (15% saved)

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
▶	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 33 to 27 computations (18.2% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 56 to 38 computations (32.1% saved)

series80.0ms (0.8%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
29.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
24.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
10.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
4.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
3.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite80.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 105

Calls

Call 1

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

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

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-+r+_binary64`
527×	`associate-+l+_binary64`
420×	`associate-r_binary64`
405×	`associate-l_binary64`
325×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1206
1	227	1124
2	748	969
3	4114	958

Stop Event

1×	node limit

Counts

153 → 125

Calls

Call 1

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

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

localize26.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 45 to 26 computations (42.2% saved)

series10.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

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

rewrite79.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 87

Calls

Call 1

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

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

Outputs

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

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

683×	`exp-sum_binary64`
401×	`associate-+r+_binary64`
394×	`associate-+l+_binary64`
390×	`associate-r_binary64`
369×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	1106
1	204	1024
2	643	901
3	3613	842
4	6902	842

Stop Event

1×	node limit

Counts

135 → 106

Calls

Call 1

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

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

eval96.0ms (1%)

Compiler: Compiled 4779 to 3247 computations (32.1% saved)

prune53.0ms (0.5%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	211	20	231
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	211	22	233

Error

0.0b

Counts

233 → 22

Alt Table

Click to see full alt table

Status	Error	Program
	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
	0.4b	(.f64 (pow.f64 k -1/4) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
	12.4b	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
▶	21.0b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	12.8b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (*.f64 (PI.f64) n))) 3) (/.f64 (-.f64 1 k) 2)))
	14.2b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	3.4b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
▶	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	21.1b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) 2)) (.f64 k (sqrt.f64 2))) (sqrt.f64 2))) (sqrt.f64 k))
▶	12.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	21.0b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	13.1b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (fma.f64 k -1/2 1/2) 3))) (sqrt.f64 k))
	3.4b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
	3.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))

Compiler

Compiled 773 to 637 computations (17.6% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 70 to 46 computations (34.3% saved)

series27.0ms (0.3%)

Counts

4 → 24

Calls

18 calls:

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

rewrite89.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`log-prod_binary64`
693×	`pow-unpow_binary64`
379×	`pow2_binary64`
261×	`pow1/3_binary64`
256×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	298	57
2	3816	53

Stop Event

1×	node limit

Counts

4 → 122

Calls

Call 1

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

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

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	598
1	123	572
2	410	513
3	2675	502
4	4213	495
5	5818	495
6	7276	495

Stop Event

1×	node limit

Counts

146 → 133

Calls

Call 1

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

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

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
✓	0.1b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)
	0.3b	(*.f64 (PI.f64) n)
✓	11.4b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Compiler

Compiled 50 to 28 computations (44% saved)

series16.0ms (0.2%)

Counts

3 → 60

Calls

18 calls:

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

rewrite82.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

656×	`log-prod_binary64`
453×	`pow-unpow_binary64`
332×	`pow2_binary64`
226×	`pow1/3_binary64`
222×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	259	50
2	3385	50

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) (#(struct:change #<rule egg-rr> (2) ((x 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simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	1569
1	241	1477
2	778	1289
3	4223	1184

Stop Event

1×	node limit

Counts

176 → 151

Calls

Call 1

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

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

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 41 to 21 computations (48.8% saved)

series9.0ms (0.1%)

Counts

3 → 0

Calls

12 calls:

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

rewrite70.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log-prod_binary64`
426×	`pow-prod-down_binary64`
296×	`pow2_binary64`
261×	`pow-unpow_binary64`
211×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	261	28
2	3012	28

Stop Event

1×	node limit

Counts

3 → 85

Calls

Call 1

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

Outputs

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

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

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

85 → 85

Calls

Call 1

Inputs

Outputs

localize43.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))
✓	0.7b	(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))

Compiler

Compiled 80 to 58 computations (27.5% saved)

series104.0ms (1.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
48.0ms	n	@	0	(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))
27.0ms	n	@	-inf	(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))
9.0ms	n	@	inf	(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))
5.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
3.0ms	k	@	0	(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))

rewrite84.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`log-prod_binary64`
296×	`expm1-udef_binary64`
296×	`log1p-udef_binary64`
290×	`log-pow_binary64`
185×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	53
1	353	53
2	4575	47

Stop Event

1×	node limit

Counts

3 → 88

Calls

Call 1

Inputs

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

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

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

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

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

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-def_binary64`
448×	`*-commutative_binary64`
404×	`fma-neg_binary64`
355×	`distribute-lft-out_binary64`
297×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1714
1	398	1471
2	1349	1387
3	5214	1348
4	7721	1348

Stop Event

1×	node limit

Counts

136 → 116

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

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

localize40.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (fma.f64 k -1/2 1/2) 3))) (sqrt.f64 k))
	0.3b	(.f64 (PI.f64) (.f64 n 2))
✓	0.3b	(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (fma.f64 k -1/2 1/2) 3))
✓	12.6b	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (fma.f64 k -1/2 1/2) 3)))

Compiler

Compiled 70 to 51 computations (27.1% saved)

series46.0ms (0.5%)

Counts

3 → 60

Calls

18 calls:

Time	Variable		Point	Expression
8.0ms	k	@	inf	(/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (fma.f64 k -1/2 1/2) 3))) (sqrt.f64 k))
8.0ms	k	@	0	(/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (fma.f64 k -1/2 1/2) 3))) (sqrt.f64 k))
5.0ms	k	@	0	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (fma.f64 k -1/2 1/2) 3)))
4.0ms	n	@	inf	(/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (fma.f64 k -1/2 1/2) 3))) (sqrt.f64 k))
3.0ms	n	@	0	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (fma.f64 k -1/2 1/2) 3)))

rewrite87.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`log-prod_binary64`
593×	`pow-unpow_binary64`
404×	`pow2_binary64`
277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	63
1	335	53
2	3978	53

Stop Event

1×	node limit

Counts

3 → 133

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

864×	`times-frac_binary64`
572×	`distribute-rgt-in_binary64`
570×	`distribute-lft-in_binary64`
510×	`fma-def_binary64`
450×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	2424
1	507	2209
2	1978	1846

Stop Event

1×	node limit

Counts

193 → 166

Calls

Call 1

Inputs
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1/3)
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6) (sqrt.f64 1))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6) (sqrt.f64 1))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/3 (/.f64 (.f64 (pow.f64 k 2) (-.f64 (.f64 9/8 (.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6) (.f64 (sqrt.f64 1) (.f64 (pow.f64 (sqrt.f64 8) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))) (.f64 1/2 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6) (.f64 (sqrt.f64 1) (.f64 (pow.f64 (sqrt.f64 8) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))))))) (.f64 (pow.f64 (sqrt.f64 2) 2) (*.f64 n (PI.f64)))))))
(+.f64 (.f64 1/3 (/.f64 (.f64 (-.f64 (.f64 -9/16 (.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))) (+.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 (.f64 (pow.f64 n 2) (.f64 1 (pow.f64 (PI.f64) 2))) (pow.f64 (sqrt.f64 2) 5)) 1/3) (.f64 (-.f64 (.f64 9/8 (.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6) (.f64 (sqrt.f64 1) (.f64 (pow.f64 (sqrt.f64 8) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))) (.f64 1/2 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6) (.f64 (sqrt.f64 1) (.f64 (pow.f64 (sqrt.f64 8) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))))) (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 -1/8 (.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 8) 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7))))))) (pow.f64 k 3)) (.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 n (PI.f64))))) (+.f64 (.f64 -1/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6) (sqrt.f64 1))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/3 (/.f64 (.f64 (pow.f64 k 2) (-.f64 (.f64 9/8 (.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6) (.f64 (sqrt.f64 1) (.f64 (pow.f64 (sqrt.f64 8) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))) (.f64 1/2 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6) (.f64 (sqrt.f64 1) (.f64 (pow.f64 (sqrt.f64 8) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))))))) (.f64 (pow.f64 (sqrt.f64 2) 2) (*.f64 n (PI.f64))))))))
(pow.f64 (exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 3 (.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 3 (.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 3 (.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 3 (.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 3 (.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 3 (.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 3 (.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 3 (.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 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (sqrt.f64 8))
(+.f64 (.f64 -3/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))) (.f64 (sqrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (sqrt.f64 8)))
(+.f64 (.f64 9/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))) (+.f64 (.f64 -3/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))) (.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (sqrt.f64 8))))
(+.f64 (.f64 9/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))) (+.f64 (.f64 -3/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))) (+.f64 (.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (sqrt.f64 8)) (.f64 -9/16 (.f64 (.f64 (pow.f64 k 3) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))))))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) 1/3))
(.f64 (pow.f64 (.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1) 1/3) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1) 1/3) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1) 1/3) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1) 1/3) (sqrt.f64 (/.f64 1 k)))

Outputs
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2))))))
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 -1/2 k 1/2) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(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 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2))))))
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 -1/2 k 1/2) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(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 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2))))))
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 -1/2 k 1/2) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(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 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2))))))
(cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 -1/2 k 1/2) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(+.f64 (.f64 -1/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6) (sqrt.f64 1))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(fma.f64 -1/2 (.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k (sqrt.f64 8))) (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6)) (cbrt.f64 1/2)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(fma.f64 (.f64 (cbrt.f64 1/2) (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6)) (.f64 (.f64 -1/2 k) (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(+.f64 (.f64 -1/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6) (sqrt.f64 1))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/3 (/.f64 (.f64 (pow.f64 k 2) (-.f64 (.f64 9/8 (.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6) (.f64 (sqrt.f64 1) (.f64 (pow.f64 (sqrt.f64 8) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))) (.f64 1/2 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3) (.f64 (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6) (.f64 (sqrt.f64 1) (.f64 (pow.f64 (sqrt.f64 8) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))))))) (.f64 (pow.f64 (sqrt.f64 2) 2) (*.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/3 (.f64 (/.f64 (.f64 k k) (pow.f64 (sqrt.f64 2) 2)) (/.f64 (-.f64 (.f64 9/8 (.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)))) (.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 2))) (.f64 (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (pow.f64 (sqrt.f64 8) 2)))) 3/4)) (*.f64 (PI.f64) n))))))
(fma.f64 -1/2 (.f64 (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k (sqrt.f64 8))) (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6)) (cbrt.f64 1/2)) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/6 (/.f64 (.f64 k (.f64 k (fma.f64 9/8 (.f64 (sqrt.f64 8) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))) (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) 8) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 2))) (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6))) -3/4)))) (.f64 (PI.f64) n)))))
(fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 8) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (cbrt.f64 1/2) (pow.f64 (.f64 (pow.f64 n 7) (pow.f64 (PI.f64) 7)) 1/6))))) (fma.f64 1/6 (/.f64 (fma.f64 9/8 (.f64 (sqrt.f64 8) (.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2))) (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 2))) (pow.f64 (.f64 (pow.f64 n 17) (pow.f64 (PI.f64) 17)) 1/6)) 8) (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) -3/4)) (.f64 (/.f64 (PI.f64) k) (/.f64 n k))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))
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(pow.f64 (exp.f64 3) (.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 3) (.f64 (fma.f64 -1/2 k 1/2) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (sqrt.f64 8))
(.f64 (sqrt.f64 8) (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))
(+.f64 (.f64 -3/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))) (.f64 (sqrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (sqrt.f64 8)))
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(.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (+.f64 (sqrt.f64 8) (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 8))) -3/2)))
(.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (fma.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) -3/2 (sqrt.f64 8)))
(+.f64 (.f64 9/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))) (+.f64 (.f64 -3/2 (.f64 (.f64 k (.f64 (sqrt.f64 8) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))))) (.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (sqrt.f64 8))))
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(.f64 (sqrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) (+.f64 (fma.f64 9/8 (.f64 (.f64 k k) (.f64 (sqrt.f64 8) (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2))) (.f64 (.f64 -3/2 (.f64 k (sqrt.f64 8))) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (sqrt.f64 8)))
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(pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
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(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
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(exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
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(pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 3)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 3)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 3)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 3)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 3)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 3)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 3)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 1 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) 1/3))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 3)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1) 1/3) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 -1/2 k 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(.f64 (pow.f64 (.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1) 1/3) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 -1/2 k 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(.f64 (pow.f64 (.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1) 1/3) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 -1/2 k 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(.f64 (pow.f64 (.f64 (exp.f64 (.f64 3 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) 1) 1/3) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 k -1/2 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (exp.f64 3) (.f64 (fma.f64 -1/2 k 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))

eval338.0ms (3.5%)

Compiler: Compiled 17147 to 10589 computations (38.2% saved)

prune171.0ms (1.7%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	751	20	771
Fresh	13	2	15
Picked	1	0	1
Done	5	1	6
Total	770	23	793

Error

Counts

793 → 23

Alt Table

Click to see full alt table

Status	Error	Program
	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
	21.0b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
	12.1b	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
	33.0b	(sqrt.f64 (.f64 (.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (.f64 -2 (log.f64 (.f64 n (*.f64 2 (PI.f64))))))))
	21.0b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
	33.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 3/2)))
	21.0b	(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
▶	14.2b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))
	32.5b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
▶	32.5b	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))
▶	34.6b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
▶	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	21.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4) 2))
	22.0b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 1/3)
✓	12.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	21.0b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
	21.0b	(.f64 (pow.f64 k -1/2) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	21.0b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 k))
	12.2b	(sqrt.f64 (.f64 (neg.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
▶	12.2b	(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
	21.1b	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	10.9b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))

Compiler

Compiled 662 to 539 computations (18.6% saved)

localize59.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 53 to 38 computations (28.3% saved)

series31.0ms (0.3%)

Counts

2 → 24

Calls

9 calls:

Time	Variable		Point	Expression
9.0ms	k	@	inf	(pow.f64 k -1/2)
9.0ms	k	@	0	(pow.f64 k -1/2)
9.0ms	k	@	-inf	(pow.f64 k -1/2)
1.0ms	k	@	-inf	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	n	@	0	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite69.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	307	27
2	3794	26

Stop Event

1×	node limit

Counts

2 → 41

Calls

Call 1

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

Outputs

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

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

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

846×	`exp-sum_binary64`
656×	`exp-prod_binary64`
486×	`distribute-rgt-in_binary64`
472×	`distribute-lft-in_binary64`
458×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	508
1	117	496
2	367	472
3	1326	440
4	5685	352

Stop Event

1×	node limit

Counts

65 → 49

Calls

Call 1

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

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

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (PI.f64) k) (.f64 n 2))
✓	0.3b	(/.f64 (PI.f64) k)
✓	11.2b	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))

Compiler

Compiled 27 to 14 computations (48.1% saved)

series9.0ms (0.1%)

Counts

3 → 24

Calls

15 calls:

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

rewrite66.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

956×	`pow1_binary64`
885×	`add-log-exp_binary64`
885×	`log1p-expm1-u_binary64`
885×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	189	29
2	2398	29

Stop Event

1×	node limit

Counts

3 → 83

Calls

Call 1

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

Outputs

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

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

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

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

107 → 85

Calls

Call 1

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

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

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
✓	0.1b	(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
✓	0.4b	(/.f64 (PI.f64) (/.f64 -1 n))
✓	11.4b	(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))

Compiler

Compiled 64 to 45 computations (29.7% saved)

series8.0ms (0.1%)

Counts

4 → 72

Calls

21 calls:

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

rewrite92.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

767×	`log-prod_binary64`
265×	`pow1/3_binary64`
260×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
246×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	67
1	309	63
2	4186	63

Stop Event

1×	node limit

Counts

4 → 162

Calls

Call 1

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

Outputs
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simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1653
1	247	1561
2	794	1373
3	4258	1268

Stop Event

1×	node limit

Counts

234 → 199

Calls

Call 1

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

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

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 2 (.f64 n (PI.f64))) k)
	0.3b	(*.f64 n (PI.f64))
✓	4.7b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
✓	11.2b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))

Compiler

Compiled 48 to 25 computations (47.9% saved)

series7.0ms (0.1%)

Counts

3 → 24

Calls

18 calls:

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

rewrite82.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

562×	`log-prod_binary64`
425×	`exp-prod_binary64`
312×	`pow-prod-down_binary64`
260×	`pow2_binary64`
209×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	213	37
2	2674	37

Stop Event

1×	node limit

Counts

3 → 200

Calls

Call 1

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

Outputs

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

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

224 → 145

Calls

Call 1

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

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

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k)
	0.3b	(*.f64 (PI.f64) n)
✓	3.8b	(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))
✓	11.4b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))

Compiler

Compiled 72 to 43 computations (40.3% saved)

series7.0ms (0.1%)

Counts

3 → 60

Calls

18 calls:

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

rewrite94.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	285	50
2	3532	50

Stop Event

1×	node limit

Counts

3 → 158

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	1377
1	242	1349
2	779	1289
3	4231	1184

Stop Event

1×	node limit

Counts

218 → 192

Calls

Call 1

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

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

eval320.0ms (3.3%)

Compiler: Compiled 14808 to 10088 computations (31.9% saved)

prune154.0ms (1.6%)

Pruning

25 alts after pruning (20 fresh and 5 done)

	Pruned	Kept	Total
New	761	13	774
Fresh	10	7	17
Picked	0	1	1
Done	1	4	5
Total	772	25	797

Error

Counts

797 → 25

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
	21.0b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
	12.1b	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
	32.5b	(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
	33.0b	(sqrt.f64 (.f64 (.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (.f64 -2 (log.f64 (.f64 n (*.f64 2 (PI.f64))))))))
	33.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 3/2)))
	32.5b	(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
	21.0b	(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
✓	14.2b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))
✓	32.5b	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))
	32.4b	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
✓	34.6b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
✓	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	40.5b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 3/2))
▶	32.6b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
	41.9b	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 3/2) 1/3)
	32.5b	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n 2)) k))
	22.0b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
✓	12.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
▶	32.6b	(sqrt.f64 (/.f64 1 (/.f64 k (.f64 (PI.f64) (.f64 n 2)))))
▶	21.0b	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
	21.0b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
	20.9b	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2)))
	32.6b	(sqrt.f64 (.f64 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (neg.f64 k))) (*.f64 n 2)))
▶	32.7b	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4) 2)

Compiler

Compiled 589 to 478 computations (18.8% saved)

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 50 to 25 computations (50% saved)

series9.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

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

rewrite80.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

725×	`log-prod_binary64`
600×	`prod-diff_binary64`
246×	`fma-def_binary64`
245×	`expm1-udef_binary64`
245×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	296	43
2	4189	43

Stop Event

1×	node limit

Counts

3 → 110

Calls

Call 1

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

Outputs

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

simplify80.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

410×	`associate-r_binary64`
401×	`associate-+r+_binary64`
395×	`associate-+l+_binary64`
386×	`associate-l_binary64`
344×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	1206
1	210	1060
2	660	937
3	3767	878
4	7610	878

Stop Event

1×	node limit

Counts

158 → 130

Calls

Call 1

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

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

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 n k) (.f64 2 (PI.f64)))
✓	11.2b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))

Compiler

Compiled 27 to 14 computations (48.1% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

12 calls:

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

rewrite57.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

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

Outputs

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

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

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

75 → 52

Calls

Call 1

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

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

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 k (.f64 (PI.f64) (.f64 n 2)))
✓	0.3b	(/.f64 1 (/.f64 k (.f64 (PI.f64) (.f64 n 2))))
	0.3b	(.f64 (PI.f64) (.f64 n 2))
✓	11.2b	(sqrt.f64 (/.f64 1 (/.f64 k (.f64 (PI.f64) (.f64 n 2)))))

Compiler

Compiled 41 to 27 computations (34.1% saved)

series9.0ms (0.1%)

Counts

3 → 48

Calls

18 calls:

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

rewrite82.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

589×	`log-prod_binary64`
449×	`exp-prod_binary64`
347×	`pow-prod-down_binary64`
276×	`pow2_binary64`
232×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	230	35
2	2964	35

Stop Event

1×	node limit

Counts

3 → 193

Calls

Call 1

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

Outputs

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

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

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

26×	`associate-/l*_binary64`
21×	`*-commutative_binary64`
17×	`associate-/r/_binary64`
12×	`associate-*r/_binary64`
10×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	528
1	22	528
2	51	528
3	100	528
4	144	528
5	158	528

Stop Event

1×

saturated

Counts

241 → 197

Calls

Call 1

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

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

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 31 to 19 computations (38.7% saved)

series3.0ms (0%)

Counts

1 → 0

Calls

6 calls:

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

rewrite58.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

546×	`log-prod_binary64`
399×	`exp-prod_binary64`
322×	`pow-prod-down_binary64`
255×	`pow2_binary64`
203×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	208	13
2	2622	13

Stop Event

1×	node limit

Counts

1 → 60

Calls

Call 1

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

Outputs

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

60 → 60

Calls

Call 1

Inputs

Outputs

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (/.f64 (PI.f64) k) (.f64 n 2))
	0.3b	(/.f64 (PI.f64) k)
✓	0.5b	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4) 2)
✓	11.3b	(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4)

Compiler

Compiled 40 to 23 computations (42.5% saved)

series152.0ms (1.6%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
76.0ms	n	@	0	(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4)
21.0ms	n	@	-inf	(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4)
17.0ms	k	@	-inf	(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4)
16.0ms	k	@	0	(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4)
10.0ms	k	@	inf	(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4)

rewrite68.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

585×	`log-prod_binary64`
428×	`exp-prod_binary64`
353×	`pow-prod-down_binary64`
292×	`pow2_binary64`
244×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	243	27
2	2985	27

Stop Event

1×	node limit

Counts

2 → 66

Calls

Call 1

Inputs
(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4)
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4) 2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/12) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (PI.f64) k) 1/4) (pow.f64 (+.f64 n n) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 n n) 1/4) (pow.f64 (/.f64 (PI.f64) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/8) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) n) 1/4) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/12)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/8 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1/2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1/8) 2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (PI.f64) k) 1/4) (pow.f64 (*.f64 (+.f64 n n) (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/8) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/8) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 5/6) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) (/.f64 (PI.f64) k)) 1/4) (pow.f64 (+.f64 n n) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 1) 1))))))

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

692×	`exp-sum_binary64`
322×	`div-sub_binary64`
320×	`sub-neg_binary64`
316×	`fma-def_binary64`
305×	`exp-diff_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1080
1	160	1032
2	393	888
3	1230	648
4	4760	648

Stop Event

1×	node limit

Counts

114 → 80

Calls

Call 1

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

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

eval178.0ms (1.8%)

Compiler: Compiled 9979 to 4546 computations (54.4% saved)

prune114.0ms (1.2%)

Pruning

40 alts after pruning (31 fresh and 9 done)

	Pruned	Kept	Total
New	631	23	654
Fresh	7	8	15
Picked	0	1	1
Done	1	8	9
Total	639	40	679

Error

Counts

679 → 40

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
	12.1b	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
	32.5b	(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
	33.0b	(sqrt.f64 (.f64 (.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (.f64 -2 (log.f64 (.f64 n (*.f64 2 (PI.f64))))))))
	41.9b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))) 3/2) 1/3)
	21.0b	(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
✓	14.2b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))
✓	32.5b	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)))
	31.2b	(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
	32.4b	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
	32.5b	(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
	32.6b	(sqrt.f64 (/.f64 1 (.f64 (/.f64 1 (.f64 (PI.f64) n)) (/.f64 k 2))))
✓	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	34.8b	(pow.f64 (exp.f64 1/2) (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))
	33.6b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3/2)) (sqrt.f64 k))
	32.6b	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
	32.6b	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k (PI.f64)) (/.f64 1 (+.f64 n n)))))
	33.3b	(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
	32.9b	(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
	32.5b	(.f64 (sqrt.f64 (.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
✓	32.7b	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 1/4) 2)
	32.5b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
	31.6b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
	33.6b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/6) 3)
	20.9b	(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
✓	32.6b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
	41.9b	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n 2)) 3/2) 1/3)
	49.4b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
	20.9b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
	32.5b	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n 2)) k))
	22.0b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	35.0b	(pow.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))) 1/6) 3)
	40.5b	(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
✓	12.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	32.6b	(sqrt.f64 (.f64 (.f64 (/.f64 1 k) (PI.f64)) (+.f64 n n)))
✓	32.6b	(sqrt.f64 (/.f64 1 (/.f64 k (.f64 (PI.f64) (.f64 n 2)))))
✓	21.0b	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
	32.5b	(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
	32.5b	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) 1) (/.f64 2 k)))
	31.3b	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))

Compiler

Compiled 510 to 402 computations (21.2% saved)

regimes232.0ms (2.4%)

Counts

78 → 1

Calls

Call 1

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

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

Calls

5 calls:

47.0ms	(.f64 (.f64 2 (PI.f64)) n)
46.0ms	k
46.0ms	n
43.0ms	(.f64 (.f64 2 (PI.f64)) n)
22.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

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

Compiler

Compiled 1011 to 611 computations (39.6% saved)

regimes181.0ms (1.8%)

Counts

75 → 1

Calls

Call 1

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

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

Calls

4 calls:

42.0ms	n
41.0ms	(.f64 (.f64 2 (PI.f64)) n)
36.0ms	k
35.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

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

Compiler

Compiled 943 to 565 computations (40.1% saved)

regimes54.0ms (0.5%)

Counts

42 → 1

Calls

Call 1

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

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

Calls

2 calls:

21.0ms	n
21.0ms	k

Results

Error	Segments	Branch
0.4b	1	`k`
0.4b	1	`n`

Compiler

Compiled 435 to 237 computations (45.5% saved)

regimes172.0ms (1.8%)

Counts

39 → 2

Calls

Call 1

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

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

Calls

2 calls:

120.0ms	n
41.0ms	k

Results

Error	Segments	Branch
0.6b	2	`k`
8.5b	7	`n`

Compiler

Compiled 393 to 212 computations (46.1% saved)

bsearch35.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
35.0ms	1.0254190527390609e-34	3.568531536937689e-34

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes67.0ms (0.7%)

Counts

38 → 2

Calls

Call 1

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

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

Calls

2 calls:

35.0ms	k
21.0ms	n

Results

Error	Segments	Branch
17.3b	2	`k`
20.9b	1	`n`

Compiler

Compiled 381 to 205 computations (46.2% saved)

bsearch42.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
42.0ms	1.400440661881221e+139	8.352657732837975e+142

Compiler

Compiled 231 to 179 computations (22.5% saved)

regimes42.0ms (0.4%)

Counts

32 → 1

Calls

Call 1

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

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

Calls

2 calls:

17.0ms	n
16.0ms	k

Results

Error	Segments	Branch
20.9b	1	`k`
20.9b	1	`n`

Compiler

Compiled 315 to 171 computations (45.7% saved)

regimes29.0ms (0.3%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

2 calls:

11.0ms	k
11.0ms	n

Results

Error	Segments	Branch
31.2b	1	`k`
31.2b	1	`n`

Compiler

Compiled 187 to 111 computations (40.6% saved)

regimes13.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.4%)

Threshold costs -0.1b (-0.4%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	n
5.0ms	k

Results

Error	Segments	Branch
32.5b	1	`k`
32.5b	1	`n`

Compiler

Compiled 64 to 42 computations (34.4% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	209
1	72	209
2	76	209
3	78	209
4	79	209

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(if (<=.f64 k 4795685198491011/46768052394588893382517914646921056628989841375232) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n))) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 81999999999999996315140137226485455788856138541313166767561319713832050907409038827141034033541783318658357069941371507889162614579981411418112) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n))) (pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))

Outputs
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (.f64 k -1/2) 1/2)) (sqrt.f64 k))
(if (<=.f64 k 4795685198491011/46768052394588893382517914646921056628989841375232) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n))) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 81999999999999996315140137226485455788856138541313166767561319713832050907409038827141034033541783318658357069941371507889162614579981411418112) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n))) (pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))

Compiler

Compiled 149 to 110 computations (26.2% saved)

soundness97.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Compiler

Compiled 350 to 293 computations (16.3% saved)

end72.0ms (0.7%)

Compiler: Compiled 133 to 70 computations (47.4% saved)