Details

analyze406.0ms (7.6%)

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)

sample3.1s (58.1%)

Results

1.3s	8256×	body	128	valid
1.1s	1375×	body	1024	invalid
453.0ms	768×	body	512	invalid
171.0ms	1202×	body	128	invalid
107.0ms	351×	body	256	invalid

Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess34.0ms (0.6%)

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 (0.3%)

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

0.4b

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))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize9.0ms (0.2%)

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

series76.0ms (1.4%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
27.0ms	n	@	0	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
21.0ms	n	@	-inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
9.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
7.0ms	n	@	inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
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%)

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 exp.f64 (log.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (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 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 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 +.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 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))))) (#(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))))))))

simplify42.0ms (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)))

prune127.0ms (2.4%)

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
	0.6b	(.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)))
	0.5b	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	1.0b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
▶	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	21.1b	(/.f64 (-.f64 (+.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))))))) (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)))
	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)

Compiler

Compiled 2517 to 1720 computations (31.7% saved)

localize10.0ms (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))))
✓	0.2b	(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))

series28.0ms (0.5%)

Counts

4 → 24

Calls

18 calls:

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

rewrite63.0ms (1.2%)

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

simplify37.0ms (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))))

prune169.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	132	7	139

Error

Counts

139 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4)))
▶	0.3b	(/.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))))))))) (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)))
	0.3b	(.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)))
	1.0b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	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)

Compiler

Compiled 3197 to 2039 computations (36.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series61.0ms (1.1%)

Counts

4 → 16

Calls

21 calls:

Time	Variable		Point	Expression
46.0ms	k	@	0	(.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
2.0ms	n	@	-inf	(/.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))))))))) (sqrt.f64 k))
2.0ms	n	@	-inf	(.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)))))))))
1.0ms	n	@	0	(.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)))))))))
1.0ms	n	@	inf	(.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)))))))))

rewrite72.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

308×	`log1p-udef_binary64`
178×	`associate-r_binary64`
177×	`add-sqr-sqrt_binary64`
172×	`*-un-lft-identity_binary64`
172×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	87
1	367	75
2	4558	75

Stop Event

1×	node limit

Counts

4 → 95

Calls

Call 1

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

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

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
457×	`distribute-lft-neg-in_binary64`
454×	`distribute-rgt-neg-in_binary64`
425×	`associate-r_binary64`
356×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	444
1	158	396
2	497	368
3	3097	366

Stop Event

1×	node limit

Counts

111 → 107

Calls

Call 1

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

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

prune152.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	5	0	5
Picked	0	1	1
Done	0	1	1
Total	123	7	130

Error

Counts

130 → 7

Alt Table

Status	Error	Program
	0.4b	(pow.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 k))) 2)
✓	0.3b	(/.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))))))))) (sqrt.f64 k))
▶	0.3b	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))) (pow.f64 k -1/2))
	0.3b	(.f64 (.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 k -1/2)))
	0.3b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2)) (pow.f64 k -1/2)))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	11.9b	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 (PI.f64) 2)) (pow.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) -1/2) 2)) k))

Compiler

Compiled 3474 to 2268 computations (34.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series38.0ms (0.7%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
9.0ms	k	@	0	(.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))
5.0ms	k	@	0	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))) (pow.f64 k -1/2))
5.0ms	n	@	0	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))) (pow.f64 k -1/2))
3.0ms	n	@	inf	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))) (pow.f64 k -1/2))
2.0ms	k	@	inf	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))) (pow.f64 k -1/2))

rewrite61.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

778×	`log-prod_binary64`
255×	`expm1-udef_binary64`
255×	`log1p-udef_binary64`
250×	`log-pow_binary64`
147×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	76
1	301	58
2	3632	54

Stop Event

1×	node limit

Counts

4 → 88

Calls

Call 1

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

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

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
452×	`distribute-rgt-neg-in_binary64`
451×	`distribute-lft-neg-in_binary64`
420×	`associate-r_binary64`
350×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	548
1	124	516
2	449	488
3	2837	478

Stop Event

1×	node limit

Counts

112 → 98

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

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

prune148.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	120	7	127

Error

Counts

127 → 7

Alt Table

Status	Error	Program
	0.3b	(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k) (PI.f64))))) (pow.f64 k -1/2))
✓	0.3b	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))) (pow.f64 k -1/2))
	0.4b	(pow.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 k))) 2)
✓	0.3b	(/.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))))))))) (sqrt.f64 k))
	0.3b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k) -1/2)) (pow.f64 k -1/2)))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k))
	11.9b	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 (PI.f64) 2)) (pow.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) -1/2) 2)) k))

Compiler

Compiled 3004 to 2180 computations (27.4% saved)

regimes397.0ms (7.5%)

Accuracy

Total 0.3b remaining (86.2%)

Threshold costs 0.3b (86.2%)

Counts

159 → 1

Compiler

Compiled 3122 to 2077 computations (33.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	18	34

Stop Event

1×

saturated

Calls

Call 1

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

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

end133.0ms (2.5%)

Stop Event

1×

fuel

Compiler

Compiled 203 to 157 computations (22.7% saved)

Details

analyze406.0ms (7.6%)

sample3.1s (58.1%)

preprocess34.0ms (0.6%)

simplify18.0ms (0.3%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series76.0ms (1.4%)

rewrite54.0ms (1%)

simplify42.0ms (0.8%)

prune127.0ms (2.4%)

localize10.0ms (0.2%)

series28.0ms (0.5%)

rewrite63.0ms (1.2%)

simplify37.0ms (0.7%)

prune169.0ms (3.2%)

localize15.0ms (0.3%)

series61.0ms (1.1%)

rewrite72.0ms (1.4%)

simplify33.0ms (0.6%)

prune152.0ms (2.8%)

localize14.0ms (0.3%)

series38.0ms (0.7%)

rewrite61.0ms (1.1%)

simplify33.0ms (0.6%)

prune148.0ms (2.8%)

regimes397.0ms (7.5%)

simplify2.0ms (0%)

end133.0ms (2.5%)

Profiling