Details

analyze132.0ms (1.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
0%	0%	50%	0.1%	0%	50%	0%	3
0%	0%	50%	0.1%	0%	50%	0%	4
25%	12.5%	37.5%	0.1%	0%	50%	0%	5
26.7%	12.5%	34.3%	0.1%	0%	53.1%	0%	6
37%	15.6%	26.5%	0.1%	1.6%	54.6%	1.6%	7
40.8%	15.6%	22.6%	0.1%	2.3%	57%	2.3%	8
49.4%	17.2%	17.6%	0.1%	3.5%	58.1%	3.5%	9
53.3%	17.2%	15%	0.1%	4.1%	59.5%	4.1%	10
59.5%	18%	12.2%	0.1%	4.8%	60.2%	4.8%	11
62.5%	18%	10.8%	0.1%	5.1%	60.9%	5.1%	12

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample2.6s (24.9%)

Results

1.3s	8256×	body	256	valid
759.0ms	1420×	body	1024	invalid
199.0ms	1609×	body	256	invalid
197.0ms	638×	body	512	invalid
81.0ms	475×	body	256	infinite
57.0ms	236×	body	256	unsamplable

Bogosity

preprocess61.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

752×	`*-commutative`
720×	`associate-/l*`
718×	`associate-/r*`
704×	`neg-mul-1`
660×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	98
1	55	86
2	118	86
3	272	86
4	740	86
5	1771	78
6	3517	78
7	6184	78
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 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 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 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 1/2 (/.f64 n 2))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (+.f64 1/2 (/.f64 n -2))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 2 (.f64 k (PI.f64))) (fma.f64 -1/2 n 1/2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 2 (.f64 k (PI.f64))) (fma.f64 n -1/2 1/2)) (sqrt.f64 n))

Compiler

Compiled 20 to 17 computations (15% saved)

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1058×	`associate-*r/`
1052×	`associate-/r*`
842×	`distribute-frac-neg`
792×	`associate-/l*`
672×	`*-commutative`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	35	43
2	69	43
3	151	43
4	399	43
5	948	39
6	1876	39
7	4291	39
8	7087	39

Stop Event

1×	node limit

Counts

1 → 6

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

eval2.0ms (0%)

Compiler: Compiled 88 to 57 computations (35.2% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	4	2	6
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	4	3	7

Error

0.3b

Counts

7 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 56 to 38 computations (32.1% saved)

series60.0ms (0.6%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
23.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
17.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
10.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
3.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite105.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1602×	`associate-*l/`
1006×	`associate-/l*`
986×	`associate-/r*`
366×	`add-sqr-sqrt`
352×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	102
1	363	98
2	4637	98

Stop Event

1×	node limit

Counts

4 → 191

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) 2) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 2 (PI.f64))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)) (sqrt.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 2) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)) (sqrt.f64 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 n) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)) (sqrt.f64 (.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2)) (pow.f64 (.f64 2 (PI.f64)) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 n) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))) (pow.f64 n (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (-.f64 1/2 (.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (-.f64 1/2 (.f64 k 1/2)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))))))
((#(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 (cbrt.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)) 3) 1/3)))) (#(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 2) (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x 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))))))))
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simplify143.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1030×	`distribute-frac-neg`
906×	`associate-/l*`
616×	`associate-r`
560×	`associate-/l/`
466×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	538	12237
1	1310	11371
2	5955	11317

Stop Event

1×	node limit

Counts

239 → 337

Calls

Call 1

Inputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
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(/.f64 (pow.f64 (PI.f64) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2)) (pow.f64 2 (-.f64 1/2 (.f64 k 1/2)))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2)) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 k 1/2)))))
(/.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2)) (pow.f64 (cbrt.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 k 1/2)))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2)))))
(/.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2)))))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k 1/4))) (pow.f64 k 1/4))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)))
(/.f64 (.f64 (/.f64 1 (cbrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) 1) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4)))))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) 2) 1) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))))))
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 k 1/2))) 1) (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2)))
(/.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) -1) 1) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) 1) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) 1) 1) (sqrt.f64 k))
(/.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 k 1/4)) 1) (pow.f64 k 1/4))
(/.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) (cbrt.f64 k)) 1) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) 1) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 k 1/4))) (pow.f64 k 1/4))
(/.f64 (.f64 (sqrt.f64 -1) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 k 1/4))) (sqrt.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (-.f64 1/2 (.f64 k 1/2)))) k))) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2) (pow.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (*.f64 k 1/2)))
(/.f64 (.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) (cbrt.f64 (sqrt.f64 k)))) (cbrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 k))) 1)
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (cbrt.f64 (sqrt.f64 k)))) (cbrt.f64 k))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) 2) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) (sqrt.f64 k))) 1)
(/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) 2) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) (pow.f64 k 1/4))) (pow.f64 k 1/4))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) 2) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k)))) (cbrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 k 1/2))) (/.f64 (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2) (sqrt.f64 k))) 1)
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 k 1/2))) (/.f64 (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2) (pow.f64 k 1/4))) (pow.f64 k 1/4))
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 k 1/2))) (/.f64 (pow.f64 (pow.f64 n (-.f64 1 k)) 1/2) (cbrt.f64 (sqrt.f64 k)))) (cbrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 (pow.f64 (cbrt.f64 k) 2))) (sqrt.f64 (cbrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 1 1/2)) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 (pow.f64 (cbrt.f64 k) 2) 1/2)) (pow.f64 (cbrt.f64 k) 1/2))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) -1) 1) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) -1) (pow.f64 k 1/4)) (neg.f64 (pow.f64 k 1/4)))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) -1) (cbrt.f64 k)) (neg.f64 (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) -1) -1) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) -1) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) (sqrt.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) -1) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 k))) (cbrt.f64 (neg.f64 (sqrt.f64 k))))) (cbrt.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) -1) (neg.f64 (pow.f64 k 1/4))) (pow.f64 k 1/4))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) -1) (neg.f64 (cbrt.f64 k))) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) 1) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) (pow.f64 k 1/4)) (neg.f64 (pow.f64 k 1/4)))
(/.f64 (/.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) (cbrt.f64 k)) (neg.f64 (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) -1) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) (sqrt.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 k))) (cbrt.f64 (neg.f64 (sqrt.f64 k))))) (cbrt.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) (neg.f64 (pow.f64 k 1/4))) (pow.f64 k 1/4))
(/.f64 (/.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) (neg.f64 (cbrt.f64 k))) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 1) 1) (sqrt.f64 k))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 1) (sqrt.f64 (pow.f64 (cbrt.f64 k) 2))) (sqrt.f64 (cbrt.f64 k)))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 1) (pow.f64 1 1/2)) (sqrt.f64 k))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 1) (pow.f64 (pow.f64 (cbrt.f64 k) 2) 1/2)) (pow.f64 (cbrt.f64 k) 1/2))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) 1) (pow.f64 k 1/4))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (pow.f64 k 1/4)))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (sqrt.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (sqrt.f64 (pow.f64 k 1/4))) (sqrt.f64 (pow.f64 k 1/4)))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (cbrt.f64 k)) 1) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (cbrt.f64 k)) (sqrt.f64 (cbrt.f64 (sqrt.f64 k)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (cbrt.f64 k)) (cbrt.f64 (cbrt.f64 k))) (cbrt.f64 (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) (cbrt.f64 k)) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (cbrt.f64 (sqrt.f64 k))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (cbrt.f64 k)) (cbrt.f64 (pow.f64 k 1/4))) (cbrt.f64 (pow.f64 k 1/4)))
(/.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) 1) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) (pow.f64 k 1/4)) (neg.f64 (pow.f64 k 1/4)))
(/.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) (cbrt.f64 k)) (neg.f64 (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) -1) (sqrt.f64 k))
(/.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) (sqrt.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2)))) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 k))) (cbrt.f64 (neg.f64 (sqrt.f64 k))))) (cbrt.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) (neg.f64 (pow.f64 k 1/4))) (pow.f64 k 1/4))
(/.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) (neg.f64 (cbrt.f64 k))) (cbrt.f64 (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k)) 1)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k 1/4)) 2)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k)) 3) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (-.f64 1/2 (.f64 k 1/2)))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k)) 3))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) 3) (/.f64 (pow.f64 k -1/2) k)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) 3)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (.f64 k 1/2))) (sqrt.f64 k))) 1))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))))

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

localize25.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 50 to 34 computations (32% saved)

series6.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

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

rewrite88.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1640×	`associate-/r*`
1608×	`associate-*l/`
360×	`add-sqr-sqrt`
348×	`*-un-lft-identity`
346×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	91
1	351	91
2	4655	91

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

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

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

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simplify142.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1758×	`distribute-lft-in`
1358×	`associate-*r/`
1066×	`associate-*l/`
912×	`associate-/r*`
728×	`associate-/l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	6798
1	725	5792
2	2870	5788

Stop Event

1×	node limit

Counts

140 → 189

Calls

Call 1

Inputs
(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 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 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 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 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 n)) (-.f64 1/2 (.f64 1/2 k)))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))))) 1)
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) 1)
(.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) 2))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 2) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2)))
(.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 n) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (pow.f64 (.f64 2 n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (pow.f64 1 (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (+.f64 1/2 (*.f64 k -1/2))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) (+.f64 1/2 (*.f64 k -1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n)))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 k)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) 1) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 k)))
(/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))) 1) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 k))))
(/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 k))))
(/.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))) (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 2)) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 k))))
(/.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 2 n) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (PI.f64) (.f64 1/2 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 n)) (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 2 n) (*.f64 1/2 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) 1) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 k)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 k))))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 k))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 k))))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 k))))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (.f64 k -1/2) -2))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (.f64 k -1/2) -2)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (PI.f64) (.f64 1/2 k))) (pow.f64 (.f64 2 n) (*.f64 1/2 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 2 n) (.f64 1/2 k))) (pow.f64 (PI.f64) (*.f64 1/2 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 1 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 1/2 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 1/2 k))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 1/2 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2) (.f64 1/2 k))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 1/2 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) 2) (.f64 1/2 k))) (pow.f64 n (*.f64 1/2 k)))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n)))))
(exp.f64 (.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 1))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (.f64 2 n)))) 1)
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) 1)
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2)
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 2))
(log.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (.f64 2 n)))))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 3))
(cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (.f64 2 n) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 n) 3) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (.f64 (PI.f64) (.f64 2 n))))
(exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 1))
(log1p.f64 (expm1.f64 (.f64 (PI.f64) (.f64 2 n))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))) 1)
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 k -1/2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 -1 (sqrt.f64 k)))
(.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (.f64 (pow.f64 (.f64 2 n) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 k -1/2)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) 1) (/.f64 (pow.f64 (.f64 2 n) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 n) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 2)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) -1)
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) 1))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))

Outputs
(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 k -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))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -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))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -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))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
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(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 -1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (.f64 (pow.f64 (.f64 2 n) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 k -1/2)))
(.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (.f64 (pow.f64 (.f64 n 2) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 k -1/2)))
(.f64 (pow.f64 (.f64 n 2) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (+.f64 n n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 k 1/4) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 k 1/4) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2)))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) 2) (cbrt.f64 k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 k)))
(.f64 (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) 1) (/.f64 (pow.f64 (.f64 2 n) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (pow.f64 (.f64 n 2) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n 2) (fma.f64 k -1/2 1/2))))
(*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (+.f64 n n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n 2) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n 2) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(*.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (+.f64 n n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 n) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n 2) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n 2) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 (+.f64 n n) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 3)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3) 1/3)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))) -1)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 2 (.f64 k -1/2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (*.f64 k -1))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) 1))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

eval413.0ms (4%)

Compiler: Compiled 12770 to 8551 computations (33% saved)

prune126.0ms (1.2%)

Pruning

29 alts after pruning (27 fresh and 2 done)

	Pruned	Kept	Total
New	499	27	526
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	499	29	528

Error

Counts

528 → 29

Alt Table

Click to see full alt table

Status	Error	Program
	18.4b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3) 1/3)
	0.9b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k 1/4)) 2)
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 2)
✓	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 (-.f64 1 k))) (.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))))
▶	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (.f64 (pow.f64 k 1/4) (pow.f64 k 1/4)))
	0.6b	(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))) (sqrt.f64 k))
	3.2b	(/.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.5b	(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.5b	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 k))) (sqrt.f64 k))
	0.5b	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2))) (sqrt.f64 k))
	0.5b	(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)))
	24.1b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	3.3b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
▶	10.3b	(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) 3)) (sqrt.f64 k))
	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
	0.5b	(.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	15.7b	(.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) k) 1/3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
	0.5b	(.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (pow.f64 (.f64 n 2) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
	24.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	3.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (-.f64 1/2 (.f64 k 1/2)) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (exp.f64 (log.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	9.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (*.f64 k -1))) k))
	3.2b	(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))

Compiler

Compiled 1052 to 864 computations (17.9% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 53 to 38 computations (28.3% saved)

series51.0ms (0.5%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
27.0ms	k	@	-inf	(pow.f64 k -1/2)
11.0ms	k	@	0	(pow.f64 k -1/2)
8.0ms	k	@	inf	(pow.f64 k -1/2)
1.0ms	n	@	0	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
1.0ms	n	@	0	(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))

rewrite83.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1108×	`swap-sqr`
620×	`distribute-rgt-in`
576×	`distribute-lft-in`
550×	`associate-*r/`
354×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	85
1	346	77
2	4341	77

Stop Event

1×	node limit

Counts

3 → 59

Calls

Call 1

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

Outputs

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

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

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

simplify98.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1182×	`unswap-sqr`
1040×	`distribute-lft-in`
986×	`distribute-rgt-in`
918×	`*-commutative`
796×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	4537
1	565	3775
2	1819	3505
3	6860	3505

Stop Event

1×	node limit

Counts

107 → 111

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k))))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k))))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k))))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)))) 1)
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) 1)
(.f64 1 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (.f64 -1/4 k))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (*.f64 -1/4 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))))
(.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 2 n) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 2 n) (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
(.f64 (.f64 (pow.f64 1 (+.f64 1/4 (.f64 -1/4 k))) (pow.f64 1 (+.f64 1/4 (.f64 -1/4 k)))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2) (+.f64 1/4 (.f64 -1/4 k))) (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2) (+.f64 1/4 (.f64 -1/4 k)))) (.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) (+.f64 1/4 (.f64 -1/4 k))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) (+.f64 1/4 (*.f64 -1/4 k)))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) 2) (+.f64 1/4 (.f64 -1/4 k))) (pow.f64 (.f64 (PI.f64) 2) (+.f64 1/4 (.f64 -1/4 k)))) (.f64 (pow.f64 n (+.f64 1/4 (.f64 -1/4 k))) (pow.f64 n (+.f64 1/4 (*.f64 -1/4 k)))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 2 (fma.f64 k -1/2 1/2))))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n)))))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 2 n)))) 1))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 1)
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 1)
(pow.f64 (.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (.f64 -1/4 k)))) 2)
(pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3)
(pow.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) 1/3)
(sqrt.f64 (.f64 (pow.f64 k -1) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2)))))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) 3)))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))
(exp.f64 (log.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 1))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)
(*.f64 (pow.f64 k -1/2) 1)
(*.f64 1 (pow.f64 k -1/2))
(*.f64 (pow.f64 k -1/4) (pow.f64 k -1/4))
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1)))
(*.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2)))
(*.f64 (pow.f64 1 -1/2) (pow.f64 k -1/2))
(*.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2))
(.f64 (.f64 (pow.f64 1 -1/4) (pow.f64 1 -1/4)) (pow.f64 k -1/2))
(.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/4) (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/4)) (*.f64 (pow.f64 (cbrt.f64 k) -1/4) (pow.f64 (cbrt.f64 k) -1/4)))
(sqrt.f64 (pow.f64 k -1))
(log.f64 (exp.f64 (pow.f64 k -1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))
(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))
(exp.f64 (log.f64 (pow.f64 k -1/2)))
(exp.f64 (*.f64 (log.f64 (pow.f64 k -1/2)) 1))
(log1p.f64 (expm1.f64 (pow.f64 k -1/2)))

Outputs
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 2))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 (sqrt.f64 2) (.f64 k k)))) (sqrt.f64 2))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 1/8 (.f64 (.f64 k k) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (sqrt.f64 2)) (.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 3))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 2)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 (sqrt.f64 2) (.f64 k k)))) (.f64 (.f64 -1/48 (.f64 (sqrt.f64 2) (pow.f64 k 3))) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 -1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
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(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 1)
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 1)
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(pow.f64 (.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (.f64 -1/4 k)))) 2)
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3)
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(pow.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) 1/3)
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(sqrt.f64 (.f64 (pow.f64 k -1) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 (fma.f64 -1/2 k 1/2) 2)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 (*.f64 -1/2 k) 2 1)) k))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) 3)))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(exp.f64 (log.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 1))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)) (pow.f64 k -1/2))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(*.f64 (pow.f64 k -1/2) 1)
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(*.f64 1 (pow.f64 k -1/2))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(*.f64 (pow.f64 k -1/4) (pow.f64 k -1/4))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1)))
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))
(*.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2)))
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 1 -1/2) (pow.f64 k -1/2))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(*.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))
(pow.f64 (sqrt.f64 k) -1)
(/.f64 1 (sqrt.f64 k))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2))
(.f64 (.f64 (pow.f64 1 -1/4) (pow.f64 1 -1/4)) (pow.f64 k -1/2))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/4) (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/4)) (*.f64 (pow.f64 (cbrt.f64 k) -1/4) (pow.f64 (cbrt.f64 k) -1/4)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2))
(sqrt.f64 (pow.f64 k -1))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(log.f64 (exp.f64 (pow.f64 k -1/2)))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(exp.f64 (log.f64 (pow.f64 k -1/2)))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(exp.f64 (*.f64 (log.f64 (pow.f64 k -1/2)) 1))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(log1p.f64 (expm1.f64 (pow.f64 k -1/2)))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (*.f64 k -1))) k)
✓	0.2b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (*.f64 k -1)))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	8.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (*.f64 k -1))) k))

Compiler

Compiled 62 to 44 computations (29% saved)

series10.0ms (0.1%)

Counts

4 → 72

Calls

21 calls:

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

rewrite96.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1724×	`associate-/l*`
1376×	`associate-*r/`
1012×	`associate-*l/`
352×	`add-sqr-sqrt`
340×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	130
1	353	112
2	4625	112

Stop Event

1×	node limit

Counts

4 → 151

Calls

Call 1

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

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

simplify125.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

898×	`associate-r`
850×	`associate-/r/`
816×	`associate-/l/`
654×	`associate-l`
590×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	423	9967
1	1036	9313
2	4383	9177

Stop Event

1×	node limit

Counts

223 → 300

Calls

Call 1

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

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

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))
✓	0.2b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
	0.2b	(.f64 (PI.f64) (.f64 2 n))
✓	3.0b	(exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n)))))

Compiler

Compiled 73 to 52 computations (28.8% saved)

series10.0ms (0.1%)

Counts

3 → 60

Calls

18 calls:

Time	Variable		Point	Expression
5.0ms	k	@	0	(.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))
0.0ms	k	@	0	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
0.0ms	n	@	-inf	(exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n)))))
0.0ms	n	@	-inf	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
0.0ms	k	@	inf	(.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))

rewrite99.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1240×	`associate-*r/`
998×	`associate-*l/`
768×	`associate-/r*`
388×	`add-sqr-sqrt`
374×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	129
1	388	101
2	4734	101

Stop Event

1×	node limit

Counts

3 → 135

Calls

Call 1

Inputs

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

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

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

Outputs

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

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simplify119.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1560×	`associate-*r/`
1240×	`associate-*l/`
642×	`associate-+l+`
562×	`associate-+r+`
550×	`+-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	406	9661
1	1036	9305
2	4543	9237

Stop Event

1×	node limit

Counts

195 → 219

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(+.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(+.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(+.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
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(/.f64 (.f64 (-.f64 (.f64 (log.f64 (PI.f64)) (log.f64 (PI.f64))) (.f64 (log.f64 (.f64 2 n)) (log.f64 (.f64 2 n)))) (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n))))
(/.f64 (.f64 (+.f64 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3)) (fma.f64 k -1/2 1/2)) (-.f64 (+.f64 (.f64 (log.f64 (PI.f64)) (log.f64 (PI.f64))) (.f64 (log.f64 (.f64 2 n)) (log.f64 (.f64 2 n)))) (.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n)))))
(/.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1/4 (pow.f64 (.f64 k -1/2) 2))) 1) (-.f64 1/2 (.f64 k -1/2)))
(/.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (+.f64 1/8 (.f64 -1/8 (pow.f64 k 3)))) 1) (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2))))
(/.f64 (.f64 (.f64 (-.f64 1/4 (pow.f64 (.f64 k -1/2) 2)) (log.f64 (.f64 (PI.f64) (.f64 2 n)))) 1) (-.f64 1/2 (.f64 k -1/2)))
(/.f64 (.f64 (.f64 (+.f64 1/8 (.f64 -1/8 (pow.f64 k 3))) (log.f64 (.f64 (PI.f64) (.f64 2 n)))) 1) (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2))))
(/.f64 (.f64 (sqrt.f64 (+.f64 1/8 (.f64 -1/8 (pow.f64 k 3)))) (.f64 (sqrt.f64 (fma.f64 k -1/2 1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 1/4 (pow.f64 (.f64 k -1/2) 2))) (.f64 (sqrt.f64 (fma.f64 k -1/2 1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 (-.f64 1/2 (.f64 k -1/2))))
(/.f64 (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1/4 (pow.f64 (.f64 k -1/2) 2))) 1) (-.f64 1/2 (*.f64 k -1/2)))
(/.f64 (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1/4 (pow.f64 (.f64 k -1/2) 2))) (sqrt.f64 (-.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 (-.f64 1/2 (.f64 k -1/2))))
(/.f64 (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (-.f64 1/4 (pow.f64 (.f64 k -1/2) 2))) (.f64 (cbrt.f64 (-.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (-.f64 1/2 (.f64 k -1/2))))) (cbrt.f64 (-.f64 1/2 (.f64 k -1/2))))
(/.f64 (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (+.f64 1/8 (.f64 -1/8 (pow.f64 k 3)))) 1) (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (+.f64 1/8 (.f64 -1/8 (pow.f64 k 3)))) (sqrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2))))) (sqrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (+.f64 1/8 (.f64 -1/8 (pow.f64 k 3)))) (.f64 (cbrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2)))) (cbrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2)))))) (cbrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (.f64 k -1/2) 2)) (log.f64 (.f64 (PI.f64) (.f64 2 n)))) 1) (-.f64 1/2 (*.f64 k -1/2)))
(/.f64 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (.f64 k -1/2) 2)) (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (sqrt.f64 (-.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 (-.f64 1/2 (.f64 k -1/2))))
(/.f64 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (.f64 k -1/2) 2)) (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (.f64 (cbrt.f64 (-.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (-.f64 1/2 (.f64 k -1/2))))) (cbrt.f64 (-.f64 1/2 (.f64 k -1/2))))
(/.f64 (/.f64 (.f64 (+.f64 1/8 (.f64 -1/8 (pow.f64 k 3))) (log.f64 (.f64 (PI.f64) (.f64 2 n)))) 1) (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (*.f64 k -1/2) 1/2))))
(/.f64 (/.f64 (.f64 (+.f64 1/8 (.f64 -1/8 (pow.f64 k 3))) (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (sqrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2))))) (sqrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2)))))
(/.f64 (/.f64 (.f64 (+.f64 1/8 (.f64 -1/8 (pow.f64 k 3))) (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (.f64 (cbrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2)))) (cbrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2)))))) (cbrt.f64 (+.f64 1/4 (.f64 (.f64 k -1/2) (-.f64 (.f64 k -1/2) 1/2)))))
(pow.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 1)
(pow.f64 (sqrt.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))) 2)
(pow.f64 (cbrt.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))) 3)
(pow.f64 (pow.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 3) 1/3)
(sqrt.f64 (pow.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 2))
(log.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)))
(log.f64 (+.f64 1 (-.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 1)))
(cbrt.f64 (pow.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 3))
(cbrt.f64 (.f64 (pow.f64 (fma.f64 k -1/2 1/2) 3) (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 3)))
(cbrt.f64 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 3) (pow.f64 (fma.f64 k -1/2 1/2) 3)))
(expm1.f64 (log1p.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))
(exp.f64 (log.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) 1))
(log1p.f64 (-.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 1))

Outputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 (sqrt.f64 2)) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (.f64 k k)) (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 (sqrt.f64 2) (.f64 k k)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (.f64 k k)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 -1/48 (.f64 (sqrt.f64 2) (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 (sqrt.f64 2)) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 (sqrt.f64 2) (.f64 k k)))) (.f64 -1/48 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(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 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(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 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(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 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(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 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(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 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(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 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(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 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(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 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
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(log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (fma.f64 -1/2 k 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(log.f64 (+.f64 1 (-.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 1)))
(log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (fma.f64 -1/2 k 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(cbrt.f64 (pow.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 3))
(log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (fma.f64 -1/2 k 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(cbrt.f64 (.f64 (pow.f64 (fma.f64 k -1/2 1/2) 3) (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 3)))
(log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (fma.f64 -1/2 k 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(cbrt.f64 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 3) (pow.f64 (fma.f64 k -1/2 1/2) 3)))
(log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (fma.f64 -1/2 k 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(expm1.f64 (log1p.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))
(log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (fma.f64 -1/2 k 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(exp.f64 (log.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))
(log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (fma.f64 -1/2 k 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) 1))
(log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (fma.f64 -1/2 k 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(log1p.f64 (-.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 1))
(log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (fma.f64 -1/2 k 1/2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 64 to 42 computations (34.4% saved)

series3.0ms (0%)

Counts

4 → 32

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (.f64 (pow.f64 k 1/4) (pow.f64 k 1/4)))
0.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (.f64 (pow.f64 k 1/4) (pow.f64 k 1/4)))
0.0ms	k	@	0	(*.f64 (pow.f64 k 1/4) (pow.f64 k 1/4))
0.0ms	k	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (.f64 (pow.f64 k 1/4) (pow.f64 k 1/4)))
0.0ms	n	@	-inf	(*.f64 n (PI.f64))

rewrite92.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1818×	`associate-*r/`
1472×	`associate-*l/`
380×	`add-sqr-sqrt`
368×	`*-un-lft-identity`
364×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	94
1	380	90
2	5084	90

Stop Event

1×	node limit

Counts

4 → 111

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 k)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 k (sqrt.f64 k)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 k k) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 k)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 k (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 k) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/4 (log.f64 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 k)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 k k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 k)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))))))) (#(struct:change #<rule 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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 2)) (pow.f64 2 (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 1 (+.f64 1/2 (.f64 k -1/2))) 1) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 1 (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 1 (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) 1) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))))) (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 2 (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 2 (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k 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((#(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 (cbrt.f64 (.f64 n (PI.f64))) 3)))) (#(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 sqrt.f64 (pow.f64 (.f64 n (PI.f64)) 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 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 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) 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simplify93.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1690×	`associate-/r*`
1582×	`associate-*r/`
1268×	`associate-*l/`
1166×	`distribute-lft-in`
610×	`associate-/l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	320	6649
1	741	5649
2	2876	5645

Stop Event

1×	node limit

Counts

143 → 198

Calls

Call 1

Inputs
(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 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
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(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 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 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 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 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
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(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) 1)
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(.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 1 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)))
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(.f64 (pow.f64 (.f64 2 n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k))
(/.f64 (.f64 1 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))
(/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (.f64 n (PI.f64)) (*.f64 k 1/2)))
(/.f64 (.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 2)) (pow.f64 2 (.f64 k 1/2)))
(/.f64 (.f64 (pow.f64 1 (+.f64 1/2 (.f64 k -1/2))) 1) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 (.f64 (pow.f64 1 (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k))
(/.f64 (.f64 (pow.f64 1 (+.f64 1/2 (.f64 k -1/2))) (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))
(/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) 1) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))))) (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))
(/.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 2 (.f64 k 1/2)))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 2 (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 (.f64 n (PI.f64)) (*.f64 k 1/2)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))))
(log.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(exp.f64 (.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 1))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)
(pow.f64 (*.f64 n (PI.f64)) 1)
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 2)
(pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 2))
(log.f64 (pow.f64 (exp.f64 n) (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 n (PI.f64)))))
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3))
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))
(expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))
(exp.f64 (log.f64 (*.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (.f64 n (PI.f64))) 1))
(log1p.f64 (expm1.f64 (*.f64 n (PI.f64))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))) 1)
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k -1/2)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)) (/.f64 1 (pow.f64 k 1/4)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 k -1/2)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) 1) (/.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 2)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) -1)
(neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) 3) (.f64 k (sqrt.f64 k))))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) 1))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))

Outputs
(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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (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))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (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))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (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))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (+.f64 1/2 (.f64 k -1/2)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (+.f64 1/2 (.f64 k -1/2)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (+.f64 1/2 (.f64 k -1/2)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (+.f64 1/2 (.f64 k -1/2)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 2))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 k (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (*.f64 k k)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 k (sqrt.f64 2)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2)))))
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(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 2 (.f64 k -1/2)))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (.f64 k -1))) k)))
(.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 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1 (.f64 k -1))) k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 2 (.f64 k -1/2))))) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (*.f64 k -1)))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1 (*.f64 k -1)))) (pow.f64 k -1/2)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)) (/.f64 1 (pow.f64 k 1/4)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 k -1/2)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 k 1/4)))
(/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 2 (.f64 k -1/2))))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 k 1/4))) (pow.f64 k 1/4))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (.f64 k -1)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1 (.f64 k -1)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)))
(/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 2 (.f64 k -1/2))))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 k 1/4))) (pow.f64 k 1/4))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (.f64 k -1)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1 (.f64 k -1)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 2 (.f64 k -1/2))))) (cbrt.f64 k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (.f64 k -1)))) (cbrt.f64 k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1 (.f64 k -1)))) (cbrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) 1) (/.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 3)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3) 1/3)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) -1)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.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 2 (.f64 n (PI.f64))) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 2 (.f64 k -1/2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (*.f64 k -1))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1 (*.f64 k -1))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.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 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) 3) (.f64 k (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) 1))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

localize38.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (PI.f64) (.f64 2 n))
	0.3b	(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2)))
✓	0.3b	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) 3)
✓	9.9b	(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) 3))

Compiler

Compiled 82 to 60 computations (26.8% saved)

series15.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
8.0ms	k	@	0	(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) 3))
3.0ms	k	@	0	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) 3)
1.0ms	n	@	0	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) 3)
1.0ms	n	@	inf	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) 3)
1.0ms	n	@	-inf	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) 3)

rewrite84.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`distribute-rgt-in`
608×	`distribute-lft-in`
588×	`associate-*r/`
410×	`associate-*l/`
368×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	72
1	386	64
2	4506	64

Stop Event

1×	node limit

Counts

2 → 69

Calls

Call 1

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

Outputs

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

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

simplify137.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

950×	`associate-*r/`
878×	`associate-r`
714×	`associate-l`
526×	`distribute-lft-out`
488×	`associate-+r+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	10139
1	945	6577
2	3883	6243
3	6990	6243

Stop Event

1×	node limit

Counts

117 → 151

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
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(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (.f64 -1/4 k)))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (*.f64 -1/4 k))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2))) (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))) (pow.f64 (.f64 2 n) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (.f64 -1/4 k))) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (*.f64 -1/4 k))) 3))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2)))) 3) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2)) 3))
(.f64 (pow.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 (.f64 2 n) (fma.f64 k -1/2 1/2)) 3))
(.f64 (pow.f64 (PI.f64) (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 (.f64 2 n) (.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 (.f64 2 n) (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 (PI.f64) (.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 1 (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (*.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2) (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) (*.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 n (.f64 (fma.f64 k -1/2 1/2) 3)))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 6)))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3))))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 2 n))))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 (fma.f64 k -1/2 1/2) 3)))
(exp.f64 (.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))) 1))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3))))

Outputs
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (PI.f64) (*.f64 n 2))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (*.f64 n 2))))) 1) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2)))) (sqrt.f64 (*.f64 n (PI.f64))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k (.f64 k (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2))))) 1) (sqrt.f64 2)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (.f64 (sqrt.f64 2) (*.f64 k k))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (pow.f64 k 3)) (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 n 2))) 3)))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k (.f64 k (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2))))) (.f64 -1/48 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 3)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2))))) 1) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 3))) (.f64 1/8 (.f64 k (.f64 k (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 n 2))) 2))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 -1/2 k 1/2))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 2))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 2))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 2))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 2))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(pow.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))) 3)
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(pow.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))) 3)
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
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(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2))) (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2)))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 k))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 -1/2 k 1/2)))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))) (pow.f64 (.f64 2 n) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (.f64 n 2) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 -1/2 k 1/2))) (.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) (pow.f64 (.f64 n 2) (fma.f64 -1/2 k 1/2))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (.f64 -1/4 k))) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (*.f64 -1/4 k))) 3))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 2 (fma.f64 k -1/2 1/2)))) 3) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2)) 3))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 k)) 3))
(.f64 (pow.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 (.f64 2 n) (fma.f64 k -1/2 1/2)) 3))
(.f64 (pow.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 (.f64 n 2) (fma.f64 k -1/2 1/2)) 3))
(.f64 (pow.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) 3) (pow.f64 (pow.f64 (.f64 n 2) (fma.f64 -1/2 k 1/2)) 3))
(.f64 (pow.f64 (pow.f64 (PI.f64) (fma.f64 k -1/4 1/4)) 6) (pow.f64 (pow.f64 (.f64 n 2) (fma.f64 -1/2 k 1/2)) 3))
(.f64 (pow.f64 (PI.f64) (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 (.f64 2 n) (.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 (PI.f64) (.f64 3 (fma.f64 k -1/2 1/2))) (pow.f64 (.f64 n 2) (.f64 3 (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 (PI.f64) (.f64 3 (fma.f64 -1/2 k 1/2))) (pow.f64 (.f64 n 2) (.f64 3 (fma.f64 -1/2 k 1/2))))
(.f64 (pow.f64 (.f64 2 n) (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 (PI.f64) (.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 (PI.f64) (.f64 3 (fma.f64 k -1/2 1/2))) (pow.f64 (.f64 n 2) (.f64 3 (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 (PI.f64) (.f64 3 (fma.f64 -1/2 k 1/2))) (pow.f64 (.f64 n 2) (.f64 3 (fma.f64 -1/2 k 1/2))))
(.f64 (pow.f64 1 (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (*.f64 (fma.f64 k -1/2 1/2) 3)))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 2 (.f64 3 (fma.f64 k -1/2 1/2))))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 (fma.f64 -1/2 k 1/2) 6))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2) (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) (*.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (.f64 3 (fma.f64 k -1/2 1/2))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 3 (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (.f64 3 (fma.f64 -1/2 k 1/2))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 3 (fma.f64 -1/2 k 1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 n (.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 3 (fma.f64 k -1/2 1/2))) (pow.f64 n (.f64 3 (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 3 (fma.f64 -1/2 k 1/2))) (pow.f64 n (.f64 3 (fma.f64 -1/2 k 1/2))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 6)))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3))))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3)) 3))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3))))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(exp.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 2 n))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 (fma.f64 k -1/2 1/2) 3)))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(exp.f64 (.f64 (.f64 3 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))) 1))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 (fma.f64 k -1/2 1/2) 3))))
(.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 3 (fma.f64 -1/2 k 1/2)))

eval493.0ms (4.7%)

Compiler: Compiled 27821 to 19105 computations (31.3% saved)

prune253.0ms (2.4%)

Pruning

32 alts after pruning (28 fresh and 4 done)

	Pruned	Kept	Total
New	1080	18	1098
Fresh	12	10	22
Picked	1	0	1
Done	2	4	6
Total	1095	32	1127

Error

Counts

1127 → 32

Alt Table

Click to see full alt table

Status	Error	Program
	34.1b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1 k)) k) 1/4) 2)
	0.9b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k 1/4)) 2)
	0.7b	(/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (*.f64 -1/4 k))) 2) (sqrt.f64 k))
✓	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	25.0b	(/.f64 (pow.f64 (.f64 n 2) (.f64 (+.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (PI.f64) (*.f64 (+.f64 1 k) 1/2))))
	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (pow.f64 k 1/4) 2))
	14.9b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 k (sqrt.f64 k)) 1/3))
	0.9b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (cbrt.f64 (sqrt.f64 k)) 3))
▶	3.2b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (exp.f64 (.f64 (log.f64 k) 1/2)))
	13.2b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (cbrt.f64 (pow.f64 k 3/2)))
	0.6b	(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))) (sqrt.f64 k))
	3.2b	(/.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.5b	(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.5b	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 k))) (sqrt.f64 k))
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))) (sqrt.f64 k))
	0.5b	(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)))
	24.1b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
✓	3.3b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
▶	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
	32.6b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 k)))))
	15.7b	(.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) k) 1/3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
▶	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (/.f64 1 k)))
	3.2b	(.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	9.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	33.4b	(sqrt.f64 (/.f64 (.f64 (PI.f64) (+.f64 (.f64 (.f64 k -2) (.f64 n (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (*.f64 n 2))) k))
	34.0b	(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1 k)) (/.f64 1 k)))
	33.2b	(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
	33.1b	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
▶	33.2b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
	3.2b	(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))

Compiler

Compiled 1061 to 861 computations (18.9% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 67 to 41 computations (38.8% saved)

series11.0ms (0.1%)

Counts

4 → 60

Calls

21 calls:

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

rewrite101.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1604×	`associate-*l/`
1454×	`associate-/l*`
394×	`add-sqr-sqrt`
380×	`*-un-lft-identity`
378×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	134
1	388	128
2	5059	128

Stop Event

1×	node limit

Counts

4 → 148

Calls

Call 1

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

Outputs
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simplify121.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1358×	`distribute-rgt-in`
1358×	`distribute-lft-in`
1182×	`associate-/r/`
1088×	`associate-/l/`
420×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	420	10998
1	1011	9182
2	3563	9136

Stop Event

1×	node limit

Counts

208 → 332

Calls

Call 1

Inputs
(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 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))))
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(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 3)))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) 1))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))) 1)
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
(.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) 1)
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k 1/4)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 2))
(.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) 2) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (neg.f64 (+.f64 1/2 (.f64 k -1/2)))) -1))
(.f64 -1 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) -1))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 k))) (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) 1) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2)))) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (+.f64 1/2 (.f64 k -1/2))))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (.f64 k -1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (pow.f64 (/.f64 (pow.f64 k 1/4) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4)))) -1) (pow.f64 (/.f64 (pow.f64 k 1/4) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4)))) -1))
(.f64 (pow.f64 (cbrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (+.f64 1/2 (.f64 k -1/2)))))) -1) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) -1))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))) -1)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k 1/4)) 2)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3) 1/3)
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 2))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(exp.f64 (-.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) (log.f64 (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) -1))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) 1))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))

Outputs
(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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (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))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (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))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (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))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (+.f64 1/2 (.f64 k -1/2)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (+.f64 1/2 (.f64 k -1/2)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (+.f64 1/2 (.f64 k -1/2)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (+.f64 1/2 (.f64 k -1/2)))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 (sqrt.f64 2)) (.f64 k (log.f64 (.f64 n (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 k (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 k k)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 k (sqrt.f64 2)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (sqrt.f64 2) (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 (sqrt.f64 2)) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)) (.f64 (.f64 -1/48 (sqrt.f64 2)) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 k (sqrt.f64 2)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (.f64 -1/48 (.f64 (sqrt.f64 2) (pow.f64 k 3))) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 3)) (.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2)))))
(pow.f64 (.f64 2 (.f64 n (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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (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 k -1/2))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
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(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(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)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (-.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) (log.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) -1))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) 1))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 n k) (PI.f64))
✓	8.9b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series7.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	n	@	0	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
1.0ms	k	@	-inf	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
1.0ms	k	@	0	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
1.0ms	n	@	-inf	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
0.0ms	n	@	inf	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))

rewrite73.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1260×	`associate-*r/`
1040×	`associate-*l/`
906×	`associate-/r*`
810×	`swap-sqr`
622×	`associate-/l*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	245	40
2	3045	40

Stop Event

1×	node limit

Counts

2 → 141

Calls

Call 1

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

Outputs

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

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

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1246×	`associate-+r-`
890×	`associate-/l*`
574×	`associate-/l/`
554×	`+-commutative`
440×	`unswap-sqr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	366	3955
1	850	3943
2	3612	3935
3	6976	3935

Stop Event

1×	node limit

Counts

165 → 196

Calls

Call 1

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

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

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 59 to 43 computations (27.1% saved)

series5.0ms (0%)

Counts

2 → 12

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	k	@	-inf	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (/.f64 1 k)))
0.0ms	k	@	0	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (/.f64 1 k)))
0.0ms	k	@	-inf	(sqrt.f64 (/.f64 1 k))
0.0ms	n	@	-inf	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (/.f64 1 k)))
0.0ms	k	@	inf	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (/.f64 1 k)))

rewrite80.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1084×	`associate-*r/`
732×	`associate-*l/`
610×	`distribute-lft-in`
396×	`add-sqr-sqrt`
378×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	60
1	397	46
2	4837	46

Stop Event

1×	node limit

Counts

2 → 86

Calls

Call 1

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

Outputs

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

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

simplify82.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1410×	`associate-+r+`
992×	`associate-/l*`
622×	`times-frac`
620×	`*-commutative`
608×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	3454
1	533	3426
2	1640	3206
3	6697	3206

Stop Event

1×	node limit

Counts

98 → 133

Calls

Call 1

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

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

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (exp.f64 (.f64 (log.f64 k) 1/2)))
	0.2b	(*.f64 n (PI.f64))
	0.3b	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
✓	5.0b	(exp.f64 (*.f64 (log.f64 k) 1/2))

Compiler

Compiled 62 to 38 computations (38.7% saved)

series2.0ms (0%)

Counts

2 → 12

Calls

9 calls:

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

rewrite82.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1412×	`associate-*r/`
1366×	`associate-/r*`
1056×	`associate-*l/`
394×	`add-sqr-sqrt`
382×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	384	48
2	5027	48

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

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

Outputs

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

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

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1670×	`associate-/r*`
1482×	`associate-/l*`
1036×	`unswap-sqr`
1020×	`associate-*r/`
748×	`associate-*l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2941
1	422	2675
2	1716	2661

Stop Event

1×	node limit

Counts

73 → 97

Calls

Call 1

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

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

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 67 to 47 computations (29.9% saved)

series58.0ms (0.6%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
13.0ms	n	@	0	(/.f64 (pow.f64 (.f64 n 2) (.f64 (+.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (PI.f64) (*.f64 (+.f64 1 k) 1/2))))
12.0ms	n	@	-inf	(pow.f64 (.f64 n 2) (.f64 (+.f64 1 k) 1/2))
11.0ms	n	@	0	(pow.f64 (.f64 n 2) (.f64 (+.f64 1 k) 1/2))
9.0ms	n	@	inf	(pow.f64 (.f64 n 2) (.f64 (+.f64 1 k) 1/2))
3.0ms	k	@	0	(/.f64 (sqrt.f64 k) (pow.f64 (PI.f64) (*.f64 (+.f64 1 k) 1/2)))

rewrite101.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1894×	`associate-*l/`
724×	`associate-/r/`
390×	`add-sqr-sqrt`
378×	`*-un-lft-identity`
374×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	138
1	385	116
2	5148	116

Stop Event

1×	node limit

Counts

4 → 166

Calls

Call 1

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

Outputs
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simplify131.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1266×	`unswap-sqr`
636×	`*-commutative`
624×	`associate-r`
474×	`associate-l`
440×	`associate-+r+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	477	10802
1	1245	10212
2	4988	10096

Stop Event

1×	node limit

Counts

214 → 310

Calls

Call 1

Inputs
(sqrt.f64 (PI.f64))
(+.f64 (sqrt.f64 (PI.f64)) (.f64 1/2 (.f64 (*.f64 k (log.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))
(+.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (PI.f64)) 2)) (sqrt.f64 (PI.f64)))) (.f64 1/2 (.f64 (.f64 k (log.f64 (PI.f64))) (sqrt.f64 (PI.f64))))))
(+.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (PI.f64)) 3)) (sqrt.f64 (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (PI.f64)) 2)) (sqrt.f64 (PI.f64)))) (.f64 1/2 (.f64 (*.f64 k (log.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (PI.f64)) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (PI.f64)) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (PI.f64)) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (PI.f64)) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 (*.f64 -1 k)) (log.f64 (PI.f64)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 (*.f64 -1 k)) (log.f64 (PI.f64)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 (*.f64 -1 k)) (log.f64 (PI.f64)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 (*.f64 -1 k)) (log.f64 (PI.f64)))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (log.f64 n)) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (log.f64 n)) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (log.f64 n)) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (log.f64 n)) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -2)) (+.f64 k 1))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -2)) (+.f64 k 1))))
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(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (sqrt.f64 k)) 1) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (sqrt.f64 k)) 1) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) 1))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (sqrt.f64 k)) (/.f64 1 (pow.f64 (PI.f64) (.f64 1/4 (+.f64 1 k))))) (pow.f64 (PI.f64) (.f64 1/4 (+.f64 1 k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (sqrt.f64 k)) (/.f64 1 (cbrt.f64 (pow.f64 (PI.f64) (+.f64 1 k))))) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (sqrt.f64 k)) -1) (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))))
(.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k)))) -1) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (sqrt.f64 k)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k)))) (neg.f64 (neg.f64 (sqrt.f64 k)))) (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 n) (+.f64 1 k)) (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) (pow.f64 (sqrt.f64 2) (+.f64 1 k)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) 1) 1) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) 1) 1) (/.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (sqrt.f64 k)) 1))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) 1) (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (pow.f64 k 1/4)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) 1) (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) 1) (neg.f64 (sqrt.f64 k))) (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) 1) (/.f64 (sqrt.f64 k) 1)) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) 1) (/.f64 (sqrt.f64 k) (pow.f64 (PI.f64) (.f64 1/4 (+.f64 1 k))))) (pow.f64 (PI.f64) (.f64 1/4 (+.f64 1 k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) 1) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (PI.f64) (+.f64 1 k))))) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) 1) -1) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) 1) (neg.f64 (neg.f64 (sqrt.f64 k)))) (neg.f64 (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))) 1) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) (sqrt.f64 (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (cbrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) 1) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (cbrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n 2) (+.f64 1 k))) (cbrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) (cbrt.f64 (neg.f64 (sqrt.f64 k)))) (cbrt.f64 (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) 1)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))) 3)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))) (sqrt.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)))) -1)
(neg.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k))) (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 2) (+.f64 1 k)) (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))) 1)
(*.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))
(*.f64 1 (/.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))) 1))
(*.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (PI.f64) (+.f64 1 k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))) 1)
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(.f64 (pow.f64 k 1/4) (.f64 (pow.f64 k 1/4) (pow.f64 (pow.f64 (PI.f64) (+.f64 1 k)) -1/2)))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))
(*.f64 (cbrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(.f64 (cbrt.f64 k) (.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 (pow.f64 (PI.f64) (+.f64 1 k)) -1/2)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) (+.f64 1 k)) -1/2) (sqrt.f64 k))
(*.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))))
(.f64 (/.f64 1 (pow.f64 (PI.f64) (.f64 1/4 (+.f64 1 k)))) (/.f64 (sqrt.f64 k) (pow.f64 (PI.f64) (*.f64 1/4 (+.f64 1 k)))))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (PI.f64) (+.f64 1 k)))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))))
(*.f64 -1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(*.f64 (/.f64 1 (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 k 1/4) 1) (/.f64 (pow.f64 k 1/4) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))))
(*.f64 (/.f64 (pow.f64 k 1/4) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))) (pow.f64 k 1/4))
(*.f64 (/.f64 (pow.f64 k 1/4) (cbrt.f64 (pow.f64 (PI.f64) (+.f64 1 k)))) (/.f64 (pow.f64 k 1/4) (cbrt.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))))
(*.f64 (/.f64 (cbrt.f64 k) 1) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))))
(.f64 (/.f64 (cbrt.f64 k) (pow.f64 (PI.f64) (.f64 1/4 (+.f64 1 k)))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 (PI.f64) (*.f64 1/4 (+.f64 1 k)))))
(*.f64 (/.f64 (cbrt.f64 k) (cbrt.f64 (pow.f64 (PI.f64) (+.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(*.f64 (/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (pow.f64 k 1/4))) (pow.f64 k 1/4))
(*.f64 (/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (cbrt.f64 k))) (cbrt.f64 (sqrt.f64 k)))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (pow.f64 (pow.f64 (PI.f64) (+.f64 1 k)) -1/2))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))) (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(*.f64 (/.f64 1 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(*.f64 (/.f64 (cbrt.f64 k) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))) (cbrt.f64 (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))) 1)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) 3)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))) 3) 1/3)
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (sqrt.f64 k)) -1)
(neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))) 3))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))

Outputs
(sqrt.f64 (PI.f64))
(+.f64 (sqrt.f64 (PI.f64)) (.f64 1/2 (.f64 (*.f64 k (log.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))
(+.f64 (sqrt.f64 (PI.f64)) (.f64 1/2 (.f64 (sqrt.f64 (PI.f64)) (*.f64 k (log.f64 (PI.f64))))))
(.f64 (+.f64 (.f64 1/2 (*.f64 k (log.f64 (PI.f64)))) 1) (sqrt.f64 (PI.f64)))
(.f64 (+.f64 1 (.f64 1/2 (*.f64 k (log.f64 (PI.f64))))) (sqrt.f64 (PI.f64)))
(+.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (PI.f64)) 2)) (sqrt.f64 (PI.f64)))) (.f64 1/2 (.f64 (.f64 k (log.f64 (PI.f64))) (sqrt.f64 (PI.f64))))))
(+.f64 (sqrt.f64 (PI.f64)) (fma.f64 1/8 (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 k k) (pow.f64 (log.f64 (PI.f64)) 2))) (.f64 1/2 (.f64 (sqrt.f64 (PI.f64)) (.f64 k (log.f64 (PI.f64)))))))
(+.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1/2 (.f64 k (log.f64 (PI.f64)))) (.f64 (.f64 1/8 (.f64 k k)) (pow.f64 (log.f64 (PI.f64)) 2)))))
(.f64 (sqrt.f64 (PI.f64)) (+.f64 (+.f64 1 (.f64 1/2 (.f64 k (log.f64 (PI.f64))))) (.f64 (.f64 1/8 (.f64 k k)) (pow.f64 (log.f64 (PI.f64)) 2))))
(+.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (PI.f64)) 3)) (sqrt.f64 (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (PI.f64)) 2)) (sqrt.f64 (PI.f64)))) (.f64 1/2 (.f64 (*.f64 k (log.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))))
(+.f64 (sqrt.f64 (PI.f64)) (fma.f64 1/48 (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (PI.f64)) 3))) (fma.f64 1/8 (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 k k) (pow.f64 (log.f64 (PI.f64)) 2))) (.f64 1/2 (.f64 (sqrt.f64 (PI.f64)) (.f64 k (log.f64 (PI.f64))))))))
(+.f64 (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (PI.f64)) 3))) (.f64 (.f64 1/8 (.f64 k k)) (pow.f64 (log.f64 (PI.f64)) 2)))) (.f64 (+.f64 (.f64 1/2 (*.f64 k (log.f64 (PI.f64)))) 1) (sqrt.f64 (PI.f64))))
(+.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1/2 (.f64 k (log.f64 (PI.f64)))) (+.f64 (.f64 (.f64 1/8 (.f64 k k)) (pow.f64 (log.f64 (PI.f64)) 2)) (.f64 1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (PI.f64)) 3)))))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (PI.f64)) (+.f64 k 1))))
(pow.f64 (pow.f64 (PI.f64) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (PI.f64) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (PI.f64)) (+.f64 k 1))))
(pow.f64 (pow.f64 (PI.f64) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (PI.f64) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (PI.f64)) (+.f64 k 1))))
(pow.f64 (pow.f64 (PI.f64) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (PI.f64) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (PI.f64)) (+.f64 k 1))))
(pow.f64 (pow.f64 (PI.f64) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (PI.f64) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 (*.f64 -1 k)) (log.f64 (PI.f64)))))
(pow.f64 (pow.f64 (PI.f64) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (PI.f64) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 (*.f64 -1 k)) (log.f64 (PI.f64)))))
(pow.f64 (pow.f64 (PI.f64) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (PI.f64) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 (*.f64 -1 k)) (log.f64 (PI.f64)))))
(pow.f64 (pow.f64 (PI.f64) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (PI.f64) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 (*.f64 -1 k)) (log.f64 (PI.f64)))))
(pow.f64 (pow.f64 (PI.f64) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (PI.f64) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (log.f64 n)) (+.f64 k 1))))
(pow.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (log.f64 n)) (+.f64 k 1))))
(pow.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (log.f64 n)) (+.f64 k 1))))
(pow.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (log.f64 n)) (+.f64 k 1))))
(pow.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 k 1))))
(pow.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 k 1))))
(pow.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 k 1))))
(pow.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)))
(exp.f64 (.f64 1/2 (.f64 (+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 k 1))))
(pow.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)) 1/2)
(sqrt.f64 (pow.f64 (*.f64 2 n) (+.f64 k 1)))
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(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (pow.f64 (pow.f64 (PI.f64) (+.f64 1 k)) -1/2))
(*.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (PI.f64) (+.f64 k 1)) -1/2))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))) (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(*.f64 (/.f64 1 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(*.f64 (cbrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))))
(*.f64 (/.f64 (cbrt.f64 k) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k))) (cbrt.f64 (sqrt.f64 k)))
(*.f64 (cbrt.f64 (sqrt.f64 k)) (/.f64 (cbrt.f64 k) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 k 1))))
(/.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 k 1)))
(/.f64 (cbrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 k 1)) (cbrt.f64 (sqrt.f64 k))))
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))) 1)
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) 2)
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) 3)
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))) 3) 1/3)
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) (sqrt.f64 k)) -1)
(/.f64 (*.f64 (neg.f64 (sqrt.f64 k)) 1) (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 k 1))))
(*.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 k 1))))
(neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 k)) 1) (neg.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 k 1))))
(*.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 k 1))))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))))))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k)))) 3))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 1 k)) 3)))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) (+.f64 k 1)) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))) 1))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 1 k))))))
(sqrt.f64 (/.f64 k (pow.f64 (PI.f64) (+.f64 k 1))))

eval492.0ms (4.7%)

Compiler: Compiled 27969 to 18397 computations (34.2% saved)

prune329.0ms (3.2%)

Pruning

43 alts after pruning (36 fresh and 7 done)

	Pruned	Kept	Total
New	1229	22	1251
Fresh	9	14	23
Picked	1	0	1
Done	1	7	8
Total	1240	43	1283

Error

Counts

1283 → 43

Alt Table

Click to see full alt table

Status	Error	Program
	40.5b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)
	33.3b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 1/4) 2)
	0.9b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k 1/4)) 2)
	0.7b	(/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/4 (*.f64 -1/4 k))) 2) (sqrt.f64 k))
✓	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	25.0b	(/.f64 (pow.f64 (.f64 n 2) (.f64 (+.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (PI.f64))))
▶	14.9b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 k (sqrt.f64 k)) 1/3))
	3.5b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (exp.f64 1/2) (log.f64 k)))
✓	3.2b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (.f64 1/2 k))) (exp.f64 (.f64 (log.f64 k) 1/2)))
	13.2b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (cbrt.f64 (pow.f64 k 3/2)))
	3.2b	(/.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))) (sqrt.f64 k))
	24.1b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (sqrt.f64 k))
	0.5b	(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)))
	0.5b	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 k -1/2))))
	24.1b	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
✓	3.3b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
	3.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (*.f64 k 1/2)))))
	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 (*.f64 1/2 k) -1/2)))))
▶	0.4b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 (.f64 1/2 k) -1/2))))
	15.7b	(.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) k) 1/3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
✓	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (/.f64 1 k)))
	3.2b	(.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	33.3b	(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
	33.3b	(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 2 (/.f64 k n))))
▶	33.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))
▶	9.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	33.4b	(sqrt.f64 (/.f64 (.f64 (PI.f64) (+.f64 (.f64 (.f64 k -2) (.f64 n (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (*.f64 n 2))) k))
	33.2b	(sqrt.f64 (*.f64 (PI.f64) (/.f64 2 (/.f64 k n))))
	33.2b	(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) (/.f64 1 n)) k)))
	33.2b	(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
	33.2b	(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
	33.2b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	33.1b	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
	33.2b	(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 n (PI.f64))))))
✓	33.2b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
▶	33.2b	(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))
	35.1b	(exp.f64 (.f64 (log.f64 (.f64 (/.f64 n k) (*.f64 (PI.f64) 2))) 1/2))
	3.2b	(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
	39.2b	(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2))
	39.1b	(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 2 (/.f64 k n))) 3/2))

Compiler

Compiled 1220 to 996 computations (18.4% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 68 to 47 computations (30.9% saved)

series52.0ms (0.5%)

Counts

3 → 48

Calls

18 calls:

Time	Variable		Point	Expression
37.0ms	k	@	-inf	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 (*.f64 1/2 k) -1/2))
3.0ms	k	@	0	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 (.f64 1/2 k) -1/2))))
2.0ms	k	@	-inf	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 (.f64 1/2 k) -1/2))))
2.0ms	k	@	0	(.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 (.f64 1/2 k) -1/2)))
1.0ms	n	@	inf	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 (.f64 1/2 k) -1/2))))

rewrite100.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1120×	`associate-*r/`
850×	`associate-*l/`
806×	`associate-/r*`
400×	`add-sqr-sqrt`
382×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	113
1	400	109
2	4906	109

Stop Event

1×	node limit

Counts

3 → 140

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

simplify126.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1694×	`distribute-rgt-in`
1690×	`distribute-lft-in`
1458×	`associate-/r/`
1348×	`associate-/l/`
414×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	409	12012
1	931	10892
2	3540	10886

Stop Event

1×	node limit

Counts

188 → 275

Calls

Call 1

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

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

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 n (/.f64 (PI.f64) k))
✓	0.3b	(/.f64 (PI.f64) k)
✓	8.9b	(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series3.0ms (0%)

Counts

3 → 24

Calls

15 calls:

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

rewrite78.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1402×	`associate-*r/`
1106×	`associate-*l/`
910×	`associate-/r*`
614×	`associate-/l*`
252×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	245	49
2	3044	49

Stop Event

1×	node limit

Counts

3 → 193

Calls

Call 1

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

Outputs

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

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1252×	`associate-/l*`
676×	`distribute-lft-in`
672×	`distribute-rgt-in`
568×	`distribute-frac-neg`
496×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	454	4783
1	1085	4741
2	4857	4741

Stop Event

1×	node limit

Counts

217 → 274

Calls

Call 1

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

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

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (PI.f64) (/.f64 k n))
✓	0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))
✓	8.9b	(sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))

Compiler

Compiled 31 to 12 computations (61.3% saved)

series6.0ms (0.1%)

Counts

3 → 24

Calls

18 calls:

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

rewrite79.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1802×	`associate-*l/`
1552×	`associate-/l*`
624×	`associate-/r/`
282×	`associate-/l/`
270×	`add-sqr-sqrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	59
1	269	59
2	3448	59

Stop Event

1×	node limit

Counts

3 → 159

Calls

Call 1

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

Outputs

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

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

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1080×	`associate-/r/`
1050×	`distribute-rgt-in`
1042×	`distribute-lft-in`
496×	`associate-r`
440×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	373	4719
1	910	4583
2	3243	4583

Stop Event

1×	node limit

Counts

183 → 238

Calls

Call 1

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

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

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
✓	0.2b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	8.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 50 to 33 computations (34% saved)

series5.0ms (0%)

Counts

3 → 60

Calls

18 calls:

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

rewrite92.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1718×	`associate-*r/`
1496×	`associate-/r*`
1416×	`associate-*l/`
320×	`add-sqr-sqrt`
310×	`*-un-lft-identity`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	97
1	315	97
2	4097	97

Stop Event

1×	node limit

Counts

3 → 160

Calls

Call 1

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

Outputs

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simplify122.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1518×	`distribute-lft-in`
1514×	`distribute-rgt-in`
1080×	`associate-/r/`
658×	`associate-/l*`
592×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	437	11558
1	1082	10166
2	4356	10166

Stop Event

1×	node limit

Counts

220 → 268

Calls

Call 1

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

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

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 k (sqrt.f64 k))
	0.2b	(*.f64 n (PI.f64))
	0.3b	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
✓	22.6b	(pow.f64 (*.f64 k (sqrt.f64 k)) 1/3)

Compiler

Compiled 65 to 36 computations (44.6% saved)

series5.0ms (0%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	k	@	0	(pow.f64 (*.f64 k (sqrt.f64 k)) 1/3)
1.0ms	k	@	-inf	(pow.f64 (*.f64 k (sqrt.f64 k)) 1/3)
1.0ms	k	@	inf	(pow.f64 (*.f64 k (sqrt.f64 k)) 1/3)
0.0ms	k	@	-inf	(*.f64 k (sqrt.f64 k))
0.0ms	k	@	0	(*.f64 k (sqrt.f64 k))

rewrite50.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1196×	`add-sqr-sqrt`
1166×	`*-un-lft-identity`
1102×	`add-cube-cbrt`
1096×	`pow1`
1092×	`add-cbrt-cube`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	167	12
2	1671	12

Stop Event

1×	node limit

Counts

2 → 30

Calls

Call 1

Inputs
(pow.f64 (*.f64 k (sqrt.f64 k)) 1/3)
(*.f64 k (sqrt.f64 k))

Outputs

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

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

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1046×	`associate--l+`
726×	`*-commutative`
550×	`log-prod`
518×	`associate-+r-`
444×	`+-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	576
1	142	414
2	356	248
3	1325	224
4	3686	224
5	6702	224

Stop Event

1×	node limit

Counts

30 → 40

Calls

Call 1

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

Outputs
(-.f64 (+.f64 1 (sqrt.f64 k)) 1)
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(*.f64 (sqrt.f64 k) 1)
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(*.f64 1 (sqrt.f64 k))
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(*.f64 (pow.f64 k 1/4) (pow.f64 k 1/4))
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(*.f64 (pow.f64 k 1/6) (cbrt.f64 k))
(*.f64 (cbrt.f64 k) (pow.f64 k 1/6))
(*.f64 (pow.f64 k 1/6) (cbrt.f64 k))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 k) 2)) (sqrt.f64 (cbrt.f64 k)))
(*.f64 (fabs.f64 (cbrt.f64 k)) (sqrt.f64 (cbrt.f64 k)))
(*.f64 (cbrt.f64 k) (sqrt.f64 (cbrt.f64 k)))
(pow.f64 (cbrt.f64 k) 3/2)
(*.f64 (pow.f64 1 1/2) (sqrt.f64 k))
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) 1/2) (pow.f64 (cbrt.f64 k) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 k) 2)) (sqrt.f64 (cbrt.f64 k)))
(*.f64 (fabs.f64 (cbrt.f64 k)) (sqrt.f64 (cbrt.f64 k)))
(*.f64 (cbrt.f64 k) (sqrt.f64 (cbrt.f64 k)))
(pow.f64 (cbrt.f64 k) 3/2)
(*.f64 (pow.f64 1 1/3) (sqrt.f64 k))
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 k 3/2)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 k 3/2)) 1/3))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 k 3/2))) (cbrt.f64 (sqrt.f64 (pow.f64 k 3/2))))
(*.f64 (cbrt.f64 (pow.f64 k 3/4)) (cbrt.f64 (pow.f64 k 3/4)))
(pow.f64 (pow.f64 (pow.f64 k 3/4) 1/6) 4)
(sqrt.f64 k)
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(fabs.f64 (sqrt.f64 k))
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(log.f64 (exp.f64 (sqrt.f64 k)))
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(cbrt.f64 (pow.f64 k 3/2))
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(expm1.f64 (log1p.f64 (sqrt.f64 k)))
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(exp.f64 (log.f64 (sqrt.f64 k)))
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(log1p.f64 (expm1.f64 (sqrt.f64 k)))
(+.f64 1 (-.f64 (sqrt.f64 k) 1))
(+.f64 (sqrt.f64 k) 0)
(sqrt.f64 k)
(-.f64 (+.f64 1 (pow.f64 k 3/2)) 1)
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)
(pow.f64 k 3/2)
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 (sqrt.f64 k) 3)
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)
(pow.f64 (pow.f64 k 3/2) 1)
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)
(pow.f64 (sqrt.f64 (pow.f64 k 3/2)) 2)
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)
(pow.f64 (pow.f64 (pow.f64 k 3/2) 3) 1/3)
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)
(sqrt.f64 (pow.f64 k 3))
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)
(log.f64 (exp.f64 (pow.f64 k 3/2)))
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)
(cbrt.f64 (pow.f64 (pow.f64 k 3/2) 3))
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)
(expm1.f64 (log1p.f64 (pow.f64 k 3/2)))
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)
(exp.f64 (log.f64 (pow.f64 k 3/2)))
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)
(log1p.f64 (expm1.f64 (pow.f64 k 3/2)))
(+.f64 1 (-.f64 (pow.f64 k 3/2) 1))
(+.f64 (pow.f64 k 3/2) 0)
(pow.f64 k 3/2)

eval440.0ms (4.2%)

Compiler: Compiled 25313 to 15624 computations (38.3% saved)

prune303.0ms (2.9%)

Pruning

42 alts after pruning (33 fresh and 9 done)

	Pruned	Kept	Total
New	1223	20	1243
Fresh	18	13	31
Picked	1	0	1
Done	2	9	11
Total	1244	42	1286

Error

Counts

1286 → 42

Alt Table

Click to see full alt table

Status	Error	Program
	18.4b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	40.5b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)
	40.5b	(pow.f64 (pow.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))) 3/2) 1/3)
✓	0.4b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	37.4b	(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) (-.f64 (+.f64 1 (sqrt.f64 k)) 1))
	0.5b	(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 1/2 k -1/2)))
	24.0b	(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 (*.f64 1/2 k) -1/2)))))
✓	0.4b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 (.f64 1/2 k) -1/2))))
	8.1b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
✓	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
✓	0.4b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (/.f64 1 k)))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	24.1b	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2)))
	33.3b	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
	33.3b	(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
	33.3b	(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 2 (/.f64 k n))))
✓	33.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))
✓	9.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	9.4b	(sqrt.f64 (/.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) n)) k))
	9.4b	(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))
	33.2b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
	33.2b	(sqrt.f64 (*.f64 (PI.f64) (/.f64 2 (/.f64 k n))))
	33.2b	(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
	33.2b	(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) (/.f64 1 n)) k)))
	33.2b	(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
	33.2b	(sqrt.f64 (*.f64 2 (/.f64 (/.f64 n (/.f64 1 (PI.f64))) k)))
	33.2b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	33.1b	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
	33.2b	(sqrt.f64 (*.f64 2 (/.f64 1 (/.f64 (/.f64 k (PI.f64)) n))))
	33.2b	(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 n (PI.f64))))))
✓	33.2b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
✓	33.2b	(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))
	33.2b	(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
	33.2b	(sqrt.f64 (*.f64 2 (fabs.f64 (/.f64 (PI.f64) (/.f64 k n)))))
	11.5b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
	35.1b	(exp.f64 (.f64 (log.f64 (.f64 (/.f64 n k) (*.f64 (PI.f64) 2))) 1/2))
	17.0b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2))
	39.2b	(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2))
	39.1b	(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 2 (/.f64 k n))) 3/2))
	39.1b	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2))
	39.1b	(cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2))

Compiler

Compiled 566 to 463 computations (18.2% saved)

regimes176.0ms (1.7%)

Counts

89 → 1

Calls

Call 1

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

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

Calls

4 calls:

44.0ms	(.f64 (.f64 2 (PI.f64)) n)
42.0ms	n
39.0ms	k
19.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

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

Compiler

Compiled 1284 to 849 computations (33.9% saved)

regimes56.0ms (0.5%)

Counts

34 → 2

Calls

Call 1

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

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

Calls

2 calls:

30.0ms	k
18.0ms	n

Results

Error	Segments	Branch
0.4b	2	`k`
8.1b	1	`n`

Compiler

Compiled 347 to 214 computations (38.3% saved)

bsearch16.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
16.0ms	2.0140507178398204e-53	1.0510557035636933e-52

Results

15.0ms

96×

body

256

valid

Compiler

Compiled 185 to 151 computations (18.4% saved)

regimes46.0ms (0.4%)

Counts

29 → 2

Calls

Call 1

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

Outputs
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2))

Calls

2 calls:

25.0ms	k
14.0ms	n

Results

Error	Segments	Branch
22.6b	2	`k`
24.0b	1	`n`

Compiler

Compiled 279 to 166 computations (40.5% saved)

bsearch4.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
3.0ms	2.4110517791502025e+113	6.382955145250321e+114

Results

2.0ms	16×	body	256	valid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	256	infinite

Compiler

Compiled 48 to 40 computations (16.7% saved)

regimes36.0ms (0.4%)

Counts

22 → 2

Calls

Call 1

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

Outputs
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2))

Calls

2 calls:

20.0ms	k
11.0ms	n

Results

Error	Segments	Branch
22.6b	2	`k`
24.0b	1	`n`

Compiler

Compiled 205 to 120 computations (41.5% saved)

bsearch4.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
4.0ms	6.382955145250321e+114	2.6060963649547375e+115

Results

2.0ms	16×	body	256	valid
1.0ms	7×	body	256	infinite

Compiler

Compiled 48 to 40 computations (16.7% saved)

regimes27.0ms (0.3%)

Counts

21 → 1

Calls

Call 1

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

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

Calls

2 calls:

12.0ms	n
11.0ms	k

Results

Error	Segments	Branch
24.0b	1	`k`
24.0b	1	`n`

Compiler

Compiled 195 to 115 computations (41% saved)

regimes25.0ms (0.2%)

Counts

20 → 1

Calls

Call 1

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

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

Calls

2 calls:

10.0ms	n
10.0ms	k

Results

Error	Segments	Branch
24.1b	1	`k`
24.1b	1	`n`

Compiler

Compiled 186 to 110 computations (40.9% saved)

regimes27.0ms (0.3%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

2 calls:

11.0ms	n
10.0ms	k

Results

Error	Segments	Branch
33.1b	1	`k`
33.1b	1	`n`

Compiler

Compiled 177 to 105 computations (40.7% saved)

regimes7.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	n
3.0ms	k

Results

Error	Segments	Branch
33.2b	1	`k`
33.2b	1	`n`

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative`
8×	`sub-neg`
8×	`+-commutative`
4×	`neg-mul-1`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	364
1	75	364
2	83	364
3	87	364
4	89	364

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 6039028053441743/215679573337205118357336120696157045389097155380324579848828881993728) (/.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 400000000000000006223766451786737209707280558768424573347908232172333512465902281305994155966018979070482512347136) (/.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2)))
(if (<=.f64 k 10000000000000000155594161294668430242682013969210614333697705804308337811647557032649853899150474476762062808678400) (/.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2)))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))

Outputs
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 6039028053441743/215679573337205118357336120696157045389097155380324579848828881993728) (/.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 6039028053441743/215679573337205118357336120696157045389097155380324579848828881993728) (/.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (-.f64 1 k)) k)))
(if (<=.f64 k 400000000000000006223766451786737209707280558768424573347908232172333512465902281305994155966018979070482512347136) (/.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2)))
(if (<=.f64 k 400000000000000006223766451786737209707280558768424573347908232172333512465902281305994155966018979070482512347136) (/.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 k (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2)))
(if (<=.f64 k 10000000000000000155594161294668430242682013969210614333697705804308337811647557032649853899150474476762062808678400) (/.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)))
(if (<=.f64 k 10000000000000000155594161294668430242682013969210614333697705804308337811647557032649853899150474476762062808678400) (/.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 k (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 2 n)) (sqrt.f64 (/.f64 k (PI.f64))))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2)))
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))

Compiler

Compiled 135 to 104 computations (23% saved)

soundness127.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1058×	`associate-*r/`
1052×	`associate-/r*`
842×	`distribute-frac-neg`
792×	`associate-/l*`
672×	`*-commutative`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	35	43
2	69	43
3	151	43
4	399	43
5	948	39
6	1876	39
7	4291	39
8	7087	39

Stop Event

1×	node limit

Compiler

Compiled 150 to 104 computations (30.7% saved)

end65.0ms (0.6%)

Compiler: Compiled 121 to 75 computations (38% saved)