Details

analyze117.0ms (1.1%)

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)

sample2.9s (27.1%)

Results

1.5s	8256×	body	256	valid
800.0ms	1315×	body	1024	invalid
388.0ms	2333×	body	256	invalid
249.0ms	689×	body	512	invalid

preprocess68.0ms (0.6%)

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)

simplify47.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 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
▶	0.3b	(/.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)

localize29.0ms (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 2 (PI.f64)) n)
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.2b	(/.f64 1 (sqrt.f64 k))

Compiler

Compiled 56 to 38 computations (32.1% saved)

series75.0ms (0.7%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
28.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
26.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
8.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
3.0ms	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 (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 105

Calls

Call 1

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

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

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-+r+_binary64`
527×	`associate-+l+_binary64`
424×	`associate-r_binary64`
407×	`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	4136	958

Stop Event

1×	node limit

Counts

153 → 126

Calls

Call 1

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

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

localize23.0ms (0.2%)

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))
✓	0.2b	(*.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
2.0ms	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))
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	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))

rewrite76.0ms (0.7%)

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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Outputs

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

simplify80.0ms (0.7%)

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

eval95.0ms (0.9%)

Compiler: Compiled 4792 to 3255 computations (32.1% saved)

prune89.0ms (0.8%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	213	19	232
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	213	21	234

Error

0.0b

Counts

234 → 21

Alt Table

Click to see full alt table

Status	Error	Program
	3.2b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 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))
▶	12.2b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	10.7b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
	23.4b	(/.f64 (.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))))))))) (sqrt.f64 k))
	0.3b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	13.5b	(/.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 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.3b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (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)))
▶	10.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	0.5b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
	0.7b	(.f64 (.f64 (/.f64 1 (cbrt.f64 k)) (cbrt.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	28.0b	(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 k 3/2)) 1/3)
▶	23.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
▶	3.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	20.3b	(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
	0.5b	(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	23.2b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))

Compiler

Compiled 803 to 647 computations (19.4% saved)

localize56.0ms (0.5%)

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))
✓	0.2b	(.f64 (PI.f64) (.f64 n 2))

Compiler

Compiled 70 to 46 computations (34.3% saved)

series43.0ms (0.4%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
6.0ms	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))
5.0ms	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))
4.0ms	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	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))
3.0ms	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))

rewrite116.0ms (1.1%)

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

simplify234.0ms (2.2%)

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)))

localize38.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)
✓	0.1b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
	0.2b	(*.f64 (PI.f64) n)
✓	9.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Compiler

Compiled 50 to 28 computations (44% saved)

series28.0ms (0.3%)

Counts

3 → 60

Calls

18 calls:

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

rewrite111.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) 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simplify155.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

176 → 151

Calls

Call 1

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

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

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) n)
	0.2b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
✓	0.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))

Compiler

Compiled 41 to 21 computations (48.8% saved)

series45.0ms (0.4%)

Counts

2 → 0

Calls

9 calls:

Time	Variable		Point	Expression
34.0ms	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
2.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
2.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
2.0ms	n	@	-inf	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
1.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))

rewrite102.0ms (1%)

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	25
1	261	23
2	3012	23

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

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

Outputs

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

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

simplify43.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

58 → 58

Calls

Call 1

Inputs

Outputs

localize77.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) n)
✓	0.5b	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
✓	3.2b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	9.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Compiler

Compiled 77 to 45 computations (41.6% saved)

series217.0ms (2%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
104.0ms	n	@	inf	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
60.0ms	n	@	-inf	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
36.0ms	n	@	0	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
5.0ms	k	@	0	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
4.0ms	k	@	-inf	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))

rewrite144.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 87

Calls

Call 1

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

Outputs

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

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

111 → 95

Calls

Call 1

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

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

localize79.0ms (0.7%)

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 2 (PI.f64)) n)
✓	0.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	3.2b	(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))

Compiler

Compiled 64 to 47 computations (26.6% saved)

series73.0ms (0.7%)

Counts

2 → 24

Calls

9 calls:

Time	Variable		Point	Expression
39.0ms	k	@	inf	(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))
17.0ms	k	@	-inf	(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))
12.0ms	k	@	0	(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))
1.0ms	n	@	0	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	k	@	-inf	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite67.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

761×	`log-prod_binary64`
407×	`pow2_binary64`
279×	`pow1/3_binary64`
276×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	328	27
2	4000	26

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 k -1/2) 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 (+.f64 (pow.f64 k -1/2) 1) 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 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 3) 1) (+.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 2) (+.f64 1 (*.f64 (+.f64 (pow.f64 k -1/2) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 k -1/2) 1) 2) 1) (+.f64 (+.f64 (pow.f64 k -1/2) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 k k) -1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 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 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))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (pow.f64 k -1/2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 k -1/2) 1)) 2) (cbrt.f64 (+.f64 (pow.f64 k -1/2) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 k -1/4)) (hypot.f64 1 (pow.f64 k -1/4)) -1)))))

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

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

846×	`exp-sum_binary64`
661×	`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	1320	440
4	5691	352

Stop Event

1×	node limit

Counts

76 → 59

Calls

Call 1

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

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

eval364.0ms (3.4%)

Compiler: Compiled 13929 to 8916 computations (36% saved)

prune137.0ms (1.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	683	17	700
Fresh	14	0	14
Picked	1	0	1
Done	5	1	6
Total	703	18	721

Error

Counts

721 → 18

Alt Table

Click to see full alt table

Status	Error	Program
▶	33.0b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
▶	23.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
▶	0.3b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	18.8b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
	9.3b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
	10.2b	(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 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))
▶	23.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
	12.2b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1/2))
✓	10.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	23.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/4) 2))
	20.3b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2) 1/3)
	10.1b	(sqrt.f64 (/.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) n)) k))
	33.0b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
	10.2b	(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
	23.1b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
▶	23.2b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
	23.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))

Compiler

Compiled 518 to 423 computations (18.3% saved)

localize43.0ms (0.4%)

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

Compiler

Compiled 53 to 38 computations (28.3% saved)

series9.0ms (0.1%)

Counts

2 → 24

Calls

9 calls:

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

rewrite91.0ms (0.9%)

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))))))

simplify54.0ms (0.5%)

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)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 n k) (.f64 2 (PI.f64)))
✓	9.5b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))

Compiler

Compiled 27 to 14 computations (48.1% saved)

series12.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

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

rewrite68.0ms (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)))))))))

simplify23.0ms (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)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))
	0.2b	(*.f64 (PI.f64) n)
✓	0.3b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
✓	0.4b	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))

Compiler

Compiled 43 to 22 computations (48.8% saved)

series10.0ms (0.1%)

Counts

3 → 0

Calls

15 calls:

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

rewrite76.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

619×	`log-prod_binary64`
364×	`pow-prod-down_binary64`
289×	`pow2_binary64`
248×	`pow-unpow_binary64`
205×	`pow-to-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	249	36
2	3095	36

Stop Event

1×	node limit

Counts

3 → 152

Calls

Call 1

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

Outputs

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

152 → 152

Calls

Call 1

Inputs

Outputs

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 (PI.f64) n))
	0.2b	(*.f64 (PI.f64) n)
✓	0.3b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
✓	0.5b	(/.f64 (sqrt.f64 k) (sqrt.f64 2))

Compiler

Compiled 32 to 16 computations (50% saved)

series7.0ms (0.1%)

Counts

3 → 0

Calls

12 calls:

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

rewrite78.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log-prod_binary64`
349×	`pow-prod-down_binary64`
284×	`pow2_binary64`
232×	`pow-unpow_binary64`
200×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	233	26
2	3028	26

Stop Event

1×	node limit

Counts

3 → 138

Calls

Call 1

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

Outputs

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

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

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

138 → 138

Calls

Call 1

Inputs

Outputs

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))
	0.2b	(*.f64 (PI.f64) n)
✓	0.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4))
✓	0.4b	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4)) (pow.f64 k 1/4))

Compiler

Compiled 48 to 28 computations (41.7% saved)

series54.0ms (0.5%)

Counts

2 → 12

Calls

12 calls:

Time	Variable		Point	Expression
29.0ms	k	@	inf	(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4))
9.0ms	k	@	-inf	(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4))
9.0ms	k	@	0	(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4))
2.0ms	n	@	0	(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4))
1.0ms	n	@	-inf	(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4))

rewrite74.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

656×	`log-prod_binary64`
381×	`pow-prod-down_binary64`
314×	`pow2_binary64`
254×	`pow-unpow_binary64`
219×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	258	28
2	3259	28

Stop Event

1×	node limit

Counts

2 → 97

Calls

Call 1

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

Outputs

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

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

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

946×	`unswap-sqr_binary64`
764×	`fma-neg_binary64`
392×	`associate-l_binary64`
368×	`*-commutative_binary64`
255×	`associate-r_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	23	252
1	50	252
2	96	252
3	213	252
4	540	252
5	1653	216
6	2899	216
7	7316	216

Stop Event

1×	node limit

Counts

109 → 100

Calls

Call 1

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

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

eval225.0ms (2.1%)

Compiler: Compiled 10177 to 6483 computations (36.3% saved)

prune128.0ms (1.2%)

Pruning

32 alts after pruning (30 fresh and 2 done)

	Pruned	Kept	Total
New	620	23	643
Fresh	5	7	12
Picked	1	0	1
Done	3	2	5
Total	629	32	661

Error

Counts

661 → 32

Alt Table

Click to see full alt table

Status	Error	Program
	32.1b	(pow.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))) -1/2)
	23.1b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
	32.2b	(pow.f64 (pow.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))) 1/4) -2)
	33.0b	(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
	20.3b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2) 1/3)
▶	33.0b	(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
	34.6b	(pow.f64 (pow.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))) 1/6) -3)
	10.1b	(sqrt.f64 (/.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) n)) k))
	23.1b	(/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k 1/2)))
	34.5b	(pow.f64 (pow.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))) -1/6) 3)
	33.1b	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 2))
	40.9b	(pow.f64 (pow.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))) 3/2) -1/3)
	23.2b	(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
	33.2b	(.f64 (sqrt.f64 (.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
	23.3b	(/.f64 1 (.f64 (pow.f64 2 -1/2) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) n)))))
▶	33.2b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
✓	33.0b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
	33.0b	(sqrt.f64 (/.f64 (.f64 (PI.f64) n) (.f64 k 1/2)))
	32.1b	(/.f64 1 (sqrt.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n)))))
	40.4b	(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))) 3/2))
	40.4b	(cbrt.f64 (pow.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))) -3/2))
	18.8b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
▶	9.3b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
	26.0b	(/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (exp.f64 (.f64 (log.f64 (*.f64 k 1/2)) 1/2)))
	12.2b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))
	23.1b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))
	41.9b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))) 3/2) 1/3)
▶	34.1b	(exp.f64 (.f64 (log.f64 (.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))) -1/2))
	12.2b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1/2))
	23.2b	(/.f64 1 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) -1/2) (sqrt.f64 k)))
✓	10.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
▶	10.2b	(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))

Compiler

Compiled 808 to 665 computations (17.7% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))
✓	0.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
	0.2b	(.f64 (PI.f64) (.f64 n 2))
✓	8.6b	(sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))

Compiler

Compiled 64 to 43 computations (32.8% saved)

series17.0ms (0.2%)

Counts

3 → 48

Calls

18 calls:

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

rewrite78.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	58
1	285	55
2	3753	55

Stop Event

1×	node limit

Counts

3 → 114

Calls

Call 1

Inputs

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

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (/.f64 1 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1/4) (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 2))) (sqrt.f64 (cbrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1/4) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 k)) (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 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simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-neg_binary64`
370×	`associate-r_binary64`
366×	`associate-l_binary64`
315×	`fma-def_binary64`
293×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	1285
1	257	1211
2	959	1123
3	5717	1051

Stop Event

1×	node limit

Counts

162 → 139

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
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Outputs
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(.f64 1/2 (fma.f64 (/.f64 k (/.f64 n k)) (/.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (PI.f64)) (/.f64 k (.f64 n (PI.f64)))))
(.f64 (/.f64 1/2 (PI.f64)) (+.f64 (/.f64 k n) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 (/.f64 k n) k))))
(+.f64 (.f64 -1 (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 n (PI.f64)))) (.f64 1/4 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 n (PI.f64))))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 k 2) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 n (PI.f64)))) (.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))))
(fma.f64 -1 (.f64 (pow.f64 k 3) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 n (PI.f64))) -1/4)) (.f64 1/2 (+.f64 (/.f64 (.f64 k k) (/.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (/.f64 k (*.f64 n (PI.f64))))))
(-.f64 (.f64 1/2 (fma.f64 (/.f64 k (/.f64 n k)) (/.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (PI.f64)) (/.f64 k (.f64 n (PI.f64))))) (.f64 (pow.f64 k 3) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (*.f64 n (PI.f64))) -1/4)))
(fma.f64 (pow.f64 k 3) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) n) (/.f64 1/4 (PI.f64))) (.f64 (/.f64 1/2 (PI.f64)) (+.f64 (/.f64 k n) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (/.f64 k n) k)))))
(fma.f64 (/.f64 1/2 (PI.f64)) (+.f64 (/.f64 k n) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (/.f64 k n) k))) (.f64 (/.f64 1/4 n) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (PI.f64)) (pow.f64 k 3))))
(+.f64 (.f64 -1 (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 n (PI.f64)))) (.f64 1/4 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 n (PI.f64))))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 k 2) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 n (PI.f64)))) (+.f64 (.f64 1/2 (/.f64 k (.f64 n (PI.f64)))) (.f64 -1 (.f64 (pow.f64 k 4) (+.f64 (.f64 -1/12 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (.f64 n (PI.f64)))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (.f64 n (PI.f64)))) (.f64 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 n (PI.f64)))) (.f64 1/4 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 n (PI.f64))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))))))
(fma.f64 -1 (.f64 (pow.f64 k 3) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 n (PI.f64))) -1/4)) (fma.f64 1/2 (/.f64 (.f64 k k) (/.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 1/2 (/.f64 k (.f64 n (PI.f64))) (neg.f64 (.f64 (pow.f64 k 4) (fma.f64 -1/12 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (.f64 n (PI.f64))) (fma.f64 1/4 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 n (PI.f64))) -1/4)))))))))
(-.f64 (-.f64 (.f64 1/2 (fma.f64 (/.f64 k (/.f64 n k)) (/.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (PI.f64)) (/.f64 k (.f64 n (PI.f64))))) (.f64 (pow.f64 k 4) (+.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 n (PI.f64))) -1/4)) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 n (PI.f64))) 1/6)))) (.f64 (pow.f64 k 3) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (*.f64 n (PI.f64))) -1/4)))
(-.f64 (fma.f64 (pow.f64 k 3) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) n) (/.f64 1/4 (PI.f64))) (.f64 (/.f64 1/2 (PI.f64)) (+.f64 (/.f64 k n) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (/.f64 k n) k))))) (.f64 (pow.f64 k 4) (fma.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 n (PI.f64))) -1/4 (.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 n (PI.f64))) 1/6))))
(-.f64 (.f64 (/.f64 1/2 (PI.f64)) (+.f64 (/.f64 k n) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (/.f64 k n) k)))) (fma.f64 (pow.f64 k 4) (fma.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 n (PI.f64))) -1/4 (.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 n (PI.f64))) 1/6)) (.f64 (pow.f64 k 3) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) n) (/.f64 -1/4 (PI.f64))))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(/.f64 k (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(/.f64 k (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(/.f64 k (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)))
(/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(/.f64 k (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)))

localize26.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 k (*.f64 2 (PI.f64)))
✓	0.3b	(/.f64 n (/.f64 k (*.f64 2 (PI.f64))))
✓	9.5b	(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))

Compiler

Compiled 29 to 18 computations (37.9% saved)

series12.0ms (0.1%)

Counts

3 → 36

Calls

15 calls:

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

rewrite103.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 176

Calls

Call 1

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

Outputs

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

simplify35.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

212 → 179

Calls

Call 1

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

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

localize27.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
✓	1.0b	(sqrt.f64 (*.f64 2 (PI.f64)))
✓	9.5b	(sqrt.f64 (/.f64 n k))

Compiler

Compiled 29 to 15 computations (48.3% saved)

series14.0ms (0.1%)

Counts

3 → 0

Calls

12 calls:

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

rewrite101.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

986×	`pow1_binary64`
911×	`add-log-exp_binary64`
911×	`log1p-expm1-u_binary64`
911×	`expm1-log1p-u_binary64`
101×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	207	26
2	2525	26

Stop Event

1×	node limit

Counts

3 → 69

Calls

Call 1

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

Outputs

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

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

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

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

69 → 69

Calls

Call 1

Inputs

Outputs

localize39.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) n)
✓	0.2b	(/.f64 k (*.f64 (PI.f64) n))
✓	4.7b	(exp.f64 (.f64 (log.f64 (.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))) -1/2))
✓	8.7b	(log.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))))

Compiler

Compiled 51 to 23 computations (54.9% saved)

series158.0ms (1.5%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
85.0ms	k	@	0	(log.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))))
20.0ms	n	@	-inf	(log.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))))
18.0ms	k	@	-inf	(log.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))))
15.0ms	n	@	0	(log.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))))
7.0ms	k	@	inf	(log.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))))

rewrite83.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`log-prod_binary64`
337×	`pow-prod-down_binary64`
303×	`pow2_binary64`
224×	`pow-unpow_binary64`
213×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	243	35
2	3034	35

Stop Event

1×	node limit

Counts

3 → 192

Calls

Call 1

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

Outputs

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

simplify82.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-def_binary64`
467×	`exp-sum_binary64`
308×	`div-sub_binary64`
299×	`associate--r+_binary64`
293×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	1064
1	134	1056
2	327	984
3	865	912
4	2660	912

Stop Event

1×	node limit

Counts

264 → 209

Calls

Call 1

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

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

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
✓	0.1b	(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
✓	0.3b	(/.f64 (PI.f64) (/.f64 -1 n))
✓	9.5b	(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	k	@	0	(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
1.0ms	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	(/.f64 (PI.f64) (/.f64 -1 n))
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))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 -2 (.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 -2 (.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))) (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 -2 (.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 -2 (.f64 (PI.f64) (neg.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) (neg.f64 n))) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 -2 (.f64 (PI.f64) (neg.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) (neg.f64 n))) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (neg.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n))) (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (neg.f64 n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (PI.f64) (neg.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 (PI.f64) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 n (.f64 (PI.f64) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) (neg.f64 n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (PI.f64) (neg.f64 n)))))) (#(struct:change #<rule egg-rr> 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simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-+l+_binary64`
473×	`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	246	1561
2	793	1373
3	4249	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)))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64))))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 k 2) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)

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

eval303.0ms (2.8%)

Compiler: Compiled 14509 to 8930 computations (38.5% saved)

prune150.0ms (1.4%)

Pruning

43 alts after pruning (36 fresh and 7 done)

	Pruned	Kept	Total
New	816	21	837
Fresh	10	15	25
Picked	0	1	1
Done	0	6	6
Total	826	43	869

Error

Counts

869 → 43

Alt Table

Click to see full alt table

Status	Error	Program
	23.1b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
	41.8b	(pow.f64 (*.f64 1/4 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) -2)) -1/4)
	33.1b	(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
	33.0b	(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
	20.3b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2) 1/3)
✓	33.0b	(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
	33.1b	(*.f64 (pow.f64 1/2 -1/2) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))
	34.6b	(pow.f64 (pow.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))) 1/6) -3)
	10.1b	(sqrt.f64 (/.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) k) n)) k))
	32.1b	(pow.f64 (*.f64 (/.f64 1/2 (PI.f64)) (/.f64 k n)) -1/2)
	33.0b	(sqrt.f64 (.f64 (.f64 2 (/.f64 (PI.f64) k)) n))
	23.2b	(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
	33.1b	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 2))
	9.3b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)))))
	40.9b	(pow.f64 (pow.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))) 3/2) -1/3)
	23.2b	(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
	33.2b	(.f64 (sqrt.f64 (.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
	32.2b	(/.f64 1 (sqrt.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))))
	23.3b	(/.f64 1 (.f64 (pow.f64 2 -1/2) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) n)))))
✓	33.2b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
✓	33.0b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
	33.0b	(sqrt.f64 (/.f64 (.f64 (PI.f64) n) (.f64 k 1/2)))
	32.1b	(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
	23.1b	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
✓	10.2b	(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
	32.2b	(pow.f64 (pow.f64 (*.f64 (/.f64 1/2 (PI.f64)) (/.f64 k n)) -1/4) 2)
	12.2b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) k))
	23.1b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))
	35.4b	(pow.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
	34.5b	(pow.f64 (pow.f64 (*.f64 (/.f64 1/2 (PI.f64)) (/.f64 k n)) -1/6) 3)
	33.3b	(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
	32.4b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 1/2 (PI.f64)) (/.f64 k n))) -3/2)
	35.1b	(sqrt.f64 (/.f64 n (exp.f64 (log.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))))
	9.3b	(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2)
	32.1b	(/.f64 1 (sqrt.f64 (*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))))
✓	34.1b	(exp.f64 (.f64 (log.f64 (.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))) -1/2))
	12.2b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1/2))
	23.2b	(/.f64 1 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) -1/2) (sqrt.f64 k)))
✓	10.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	33.0b	(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
	40.4b	(cbrt.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 3/2))
	46.5b	(pow.f64 (pow.f64 (*.f64 (/.f64 1/2 (PI.f64)) (/.f64 k n)) 3) -1/6)
✓	9.3b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))

Compiler

Compiled 547 to 449 computations (17.9% saved)

regimes244.0ms (2.3%)

Counts

82 → 1

Calls

Call 1

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

54.0ms	(.f64 (.f64 2 (PI.f64)) n)
50.0ms	n
45.0ms	(.f64 (.f64 2 (PI.f64)) n)
42.0ms	k
20.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.2b	1	`k`
0.2b	1	`n`
0.2b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.2b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.2b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1080 to 692 computations (35.9% saved)

regimes228.0ms (2.1%)

Counts

78 → 1

Calls

Call 1

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

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

Calls

5 calls:

48.0ms	(.f64 (.f64 2 (PI.f64)) n)
46.0ms	n
42.0ms	k
40.0ms	(.f64 (.f64 2 (PI.f64)) n)
24.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

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

Compiler

Compiled 967 to 619 computations (36% saved)

regimes130.0ms (1.2%)

Counts

60 → 1

Calls

Call 1

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

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

Calls

4 calls:

34.0ms	k
30.0ms	(.f64 (.f64 2 (PI.f64)) n)
29.0ms	n
16.0ms	(.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)`

Compiler

Compiled 676 to 420 computations (37.9% saved)

regimes105.0ms (1%)

Counts

52 → 1

Calls

Call 1

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

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

Calls

3 calls:

30.0ms	(.f64 (.f64 2 (PI.f64)) n)
30.0ms	k
29.0ms	n

Results

Error	Segments	Branch
0.3b	1	`k`
0.3b	1	`n`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 559 to 345 computations (38.3% saved)

regimes275.0ms (2.6%)

Counts

48 → 2

Calls

Call 1

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

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

Calls

2 calls:

216.0ms	n
44.0ms	k

Results

Error	Segments	Branch
0.3b	2	`k`
6.2b	7	`n`

Compiler

Compiled 490 to 294 computations (40% saved)

bsearch34.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
33.0ms	2.7489459935190213e-47	1.202414458904683e-45

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes130.0ms (1.2%)

Counts

45 → 2

Calls

Call 1

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

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

Calls

2 calls:

70.0ms	n
45.0ms	k

Results

Error	Segments	Branch
0.3b	2	`k`
7.9b	3	`n`

Compiler

Compiled 449 to 266 computations (40.8% saved)

bsearch35.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
34.0ms	2.7489459935190213e-47	1.202414458904683e-45

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes120.0ms (1.1%)

Counts

44 → 2

Calls

Call 1

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

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

Calls

2 calls:

60.0ms	n
46.0ms	k

Results

Error	Segments	Branch
17.8b	2	`k`
21.9b	3	`n`

Compiler

Compiled 437 to 259 computations (40.7% saved)

bsearch87.0ms (0.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
87.0ms	4.998315169762851e+145	8.629697315955726e+160

Compiler

Compiled 283 to 239 computations (15.5% saved)

regimes92.0ms (0.9%)

Counts

34 → 2

Calls

Call 1

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

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

Calls

2 calls:

49.0ms	n
33.0ms	k

Results

Error	Segments	Branch
19.8b	2	`k`
21.9b	3	`n`

Compiler

Compiled 326 to 196 computations (39.9% saved)

bsearch59.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
59.0ms	1.2742718600162848e+132	2.4706865406340115e+133

Compiler

Compiled 205 to 173 computations (15.6% saved)

regimes43.0ms (0.4%)

Counts

30 → 1

Calls

Call 1

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

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

Calls

2 calls:

18.0ms	n
17.0ms	k

Results

Error	Segments	Branch
23.1b	1	`k`
23.1b	1	`n`

Compiler

Compiled 282 to 169 computations (40.1% saved)

regimes24.0ms (0.2%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	k
9.0ms	n

Results

Error	Segments	Branch
23.1b	1	`k`
23.1b	1	`n`

Compiler

Compiled 149 to 94 computations (36.9% saved)

regimes23.0ms (0.2%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	k
9.0ms	n

Results

Error	Segments	Branch
23.2b	1	`k`
23.2b	1	`n`

Compiler

Compiled 140 to 90 computations (35.7% saved)

regimes22.0ms (0.2%)

Counts

14 → 1

Calls

Call 1

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

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

Calls

2 calls:

8.0ms	n
8.0ms	k

Results

Error	Segments	Branch
32.1b	1	`k`
32.1b	1	`n`

Compiler

Compiled 131 to 84 computations (35.9% saved)

regimes16.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	n
6.0ms	k

Results

Error	Segments	Branch
32.1b	1	`k`
32.1b	1	`n`

Compiler

Compiled 82 to 53 computations (35.4% saved)

regimes14.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	k
5.0ms	n

Results

Error	Segments	Branch
33.0b	1	`k`
33.0b	1	`n`

Compiler

Compiled 64 to 42 computations (34.4% saved)

regimes10.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	k
4.0ms	n

Results

Error	Segments	Branch
33.0b	1	`k`
33.0b	1	`n`

Compiler

Compiled 40 to 27 computations (32.5% saved)

regimes10.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	k
4.0ms	n

Results

Error	Segments	Branch
33.0b	1	`k`
33.0b	1	`n`

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
2×	`+-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	87	368
1	110	368
2	114	368
3	116	368
4	117	368

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 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(if (<=.f64 k 5654253950206775/205688069665150755269371147819668813122841983204197482918576128) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 5654253950206775/205688069665150755269371147819668813122841983204197482918576128) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 84999999999999998213603245593805083795683535920658541195366571638195986967256819992309064720081154714209333698972015804276677658957652836441586904062511412150272) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (/.f64 1/2 (PI.f64)) (/.f64 k n)) 3) -1/6))
(if (<=.f64 k 23999999999999998519045419372047302735549329194983996125066556781529766265629002332961933727766258123613933919902619079587651404169216) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 1/4 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) -2)) -1/4))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(pow.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))) -1/2)
(pow.f64 (*.f64 (/.f64 1/2 (PI.f64)) (/.f64 k n)) -1/2)
(sqrt.f64 (/.f64 (.f64 (PI.f64) n) (.f64 k 1/2)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (.f64 (.f64 2 (/.f64 (PI.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 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (/.f64 (-.f64 1 k) 2)) (pow.f64 k -1/2))
(if (<=.f64 k 5654253950206775/205688069665150755269371147819668813122841983204197482918576128) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 5654253950206775/205688069665150755269371147819668813122841983204197482918576128) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)) (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 5654253950206775/205688069665150755269371147819668813122841983204197482918576128) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 5654253950206775/205688069665150755269371147819668813122841983204197482918576128) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 84999999999999998213603245593805083795683535920658541195366571638195986967256819992309064720081154714209333698972015804276677658957652836441586904062511412150272) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (/.f64 1/2 (PI.f64)) (/.f64 k n)) 3) -1/6))
(if (<=.f64 k 84999999999999998213603245593805083795683535920658541195366571638195986967256819992309064720081154714209333698972015804276677658957652836441586904062511412150272) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (/.f64 1/2 (PI.f64)) (/.f64 k n)) 3) -1/6))
(if (<=.f64 k 23999999999999998519045419372047302735549329194983996125066556781529766265629002332961933727766258123613933919902619079587651404169216) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 1/4 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) -2)) -1/4))
(if (<=.f64 k 23999999999999998519045419372047302735549329194983996125066556781529766265629002332961933727766258123613933919902619079587651404169216) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)) (pow.f64 (*.f64 1/4 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) -2)) -1/4))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(pow.f64 (.f64 1/2 (/.f64 k (.f64 (PI.f64) n))) -1/2)
(pow.f64 (*.f64 (/.f64 1/2 (PI.f64)) (/.f64 k n)) -1/2)
(sqrt.f64 (/.f64 (.f64 (PI.f64) n) (.f64 k 1/2)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) 2))))
(sqrt.f64 (.f64 (.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))

Compiler

Compiled 263 to 206 computations (21.7% saved)

soundness106.0ms (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)

end138.0ms (1.3%)

Compiler: Compiled 233 to 148 computations (36.5% saved)