Details

analyze341.0ms (6.9%)

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
18.3%	9.3%	72.4%	13
18.3%	8.5%	73.1%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.0s (60.7%)

Results

1.3s	8256×	body	128	valid
1.0s	1413×	body	1024	invalid
340.0ms	658×	body	512	invalid
170.0ms	1105×	body	128	invalid
151.0ms	354×	body	256	invalid

Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess35.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

421×	`div-sub_binary64`
418×	`associate-/l*_binary64`
293×	`associate-l_binary64`
268×	`associate-/r*_binary64`
224×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-/l*_binary64`
544×	`associate-/r*_binary64`
257×	`associate-*l/_binary64`
214×	`unswap-sqr_binary64`
214×	`div-sub_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	140	22
4	354	22
5	958	20
6	2187	20

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series78.0ms (1.6%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
29.0ms	n	@	0	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
26.0ms	n	@	-inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
8.0ms	n	@	inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
3.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
3.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

rewrite54.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`log-prod_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
212×	`log-pow_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 82

Calls

Call 1

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

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

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

simplify41.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
433×	`associate-r_binary64`
373×	`associate-l_binary64`
176×	`distribute-rgt-in_binary64`
172×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1144
1	183	984
2	587	828
3	3441	826

Stop Event

1×	node limit

Counts

130 → 99

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

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

prune133.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	7	101

Error

0.0b

Counts

101 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	1.0b	(/.f64 (.f64 (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)) (sqrt.f64 k))
	0.5b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
▶	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))
	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	0.6b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))

Compiler

Compiled 2415 to 1660 computations (31.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series43.0ms (0.9%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
14.0ms	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))
6.0ms	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))
5.0ms	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))
3.0ms	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))
2.0ms	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))

rewrite63.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`
251×	`log-pow_binary64`
146×	`add-sqr-sqrt_binary64`
142×	`pow1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	298	57
2	3814	53

Stop Event

1×	node limit

Counts

4 → 103

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

simplify34.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
451×	`distribute-rgt-neg-in_binary64`
449×	`distribute-lft-neg-in_binary64`
438×	`associate-r_binary64`
371×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	604
1	127	572
2	460	512
3	2920	510

Stop Event

1×	node limit

Counts

127 → 114

Calls

Call 1

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

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

prune147.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	132	7	139

Error

Counts

139 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	0.7b	(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (cbrt.f64 (sqrt.f64 k))))
	0.5b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	9.4b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 2 (.f64 (PI.f64) n))))))
	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
▶	0.3b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))

Compiler

Compiled 3189 to 2029 computations (36.4% saved)

localize12.0ms (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 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 k -1/2)) (sqrt.f64 k))
✓	0.2b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))
	0.3b	(*.f64 (PI.f64) n)

series14.0ms (0.3%)

Counts

3 → 12

Calls

15 calls:

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

rewrite56.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`
250×	`log-pow_binary64`
146×	`add-sqr-sqrt_binary64`
142×	`pow1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	298	51
2	3758	49

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

Inputs

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

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

(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))

Outputs

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

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

simplify28.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
382×	`distribute-rgt-in_binary64`
316×	`distribute-lft-in_binary64`
279×	`exp-sum_binary64`
228×	`exp-prod_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	348
1	77	348
2	183	348
3	574	324
4	1799	276

Stop Event

1×	node limit

Counts

101 → 94

Calls

Call 1

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

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

prune156.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	132	7	139

Error

Counts

139 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	0.7b	(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (cbrt.f64 (sqrt.f64 k))))
	0.5b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	9.4b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 2 (.f64 (PI.f64) n))))))
▶	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
✓	0.3b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))

Compiler

Compiled 3251 to 2043 computations (37.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.2%)

Counts

2 → 0

Calls

9 calls:

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

rewrite60.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

298×	`log1p-udef_binary64`
172×	`add-sqr-sqrt_binary64`
168×	`pow1_binary64`
167×	`*-un-lft-identity_binary64`
166×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	41
1	360	39
2	4530	39

Stop Event

1×	node limit

Counts

2 → 64

Calls

Call 1

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

Outputs

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

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

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

64 → 64

Calls

Call 1

Inputs

Outputs

prune124.0ms (2.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	101	7	108

Error

Counts

108 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	0.7b	(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (cbrt.f64 (sqrt.f64 k))))
	0.5b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	9.4b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 2 (.f64 (PI.f64) n))))))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))) (sqrt.f64 k))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
✓	0.3b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))

Compiler

Compiled 2589 to 1709 computations (34% saved)

regimes327.0ms (6.6%)

Accuracy

Total 0.3b remaining (89.6%)

Threshold costs 0.3b (89.6%)

Counts

148 → 1

Compiler

Compiled 2903 to 1890 computations (34.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	18	31

Stop Event

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))

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))

end124.0ms (2.5%)

Stop Event

1×

fuel

Compiler

Compiled 203 to 154 computations (24.1% saved)

Details

analyze341.0ms (6.9%)

sample3.0s (60.7%)

preprocess35.0ms (0.7%)

simplify18.0ms (0.4%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series78.0ms (1.6%)

rewrite54.0ms (1.1%)

simplify41.0ms (0.8%)

prune133.0ms (2.7%)

localize9.0ms (0.2%)

series43.0ms (0.9%)

rewrite63.0ms (1.3%)

simplify34.0ms (0.7%)

prune147.0ms (3%)

localize12.0ms (0.2%)

series14.0ms (0.3%)

rewrite56.0ms (1.1%)

simplify28.0ms (0.6%)

prune156.0ms (3.2%)

localize12.0ms (0.3%)

series10.0ms (0.2%)

rewrite60.0ms (1.2%)

simplify9.0ms (0.2%)

prune124.0ms (2.5%)

regimes327.0ms (6.6%)

simplify2.0ms (0%)

end124.0ms (2.5%)

Profiling