Details

analyze108.0ms (1%)

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)

sample2.5s (22.9%)

Results

1.2s	8256×	body	256	valid
726.0ms	1375×	body	1024	invalid
214.0ms	687×	body	512	invalid
177.0ms	1509×	body	256	invalid
85.0ms	473×	body	256	infinite
63.0ms	261×	body	256	unsamplable

Bogosity

preprocess65.0ms (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)

simplify72.0ms (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

0.6b

Counts

7 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.7b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.7b	(.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)

localize28.0ms (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 (.f64 2 (PI.f64)) n)
✓	0.4b	(/.f64 1 (sqrt.f64 k))
✓	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

Compiler

Compiled 56 to 38 computations (32.1% saved)

series61.0ms (0.5%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
25.0ms	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))
6.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
6.0ms	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)))

rewrite106.0ms (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 1 (sqrt.f64 k))
(.f64 (.f64 2 (PI.f64)) n)
(.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 (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 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.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 -1 (/.f64 -1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 k 1/4) -1) (pow.f64 (pow.f64 k 1/4) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 k) -1) (pow.f64 (cbrt.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 (sqrt.f64 k) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)))) (#(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 sqrt.f64 (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.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 (log.f64 (sqrt.f64 k)) -1))))) (#(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)))))))
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k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.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 2 (.f64 (PI.f64) n)) (-.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 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))))))))

simplify152.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

906×	`associate-/l*`
618×	`associate-r`
560×	`associate-/l/`
466×	`times-frac`
456×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	538	12237
1	1310	11371
2	5961	11317

Stop Event

1×	node limit

Counts

239 → 335

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

localize24.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite90.0ms (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 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (PI.f64) (.f64 2 n))

Outputs
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((#(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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((#(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))))))))

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1758×	`distribute-lft-in`
1356×	`associate-*r/`
1058×	`associate-*l/`
912×	`associate-/r*`
728×	`associate-/l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	6798
1	725	5792
2	2872	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 (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)))))
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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 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(-.f64 (exp.f64 (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))))
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(.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 (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))))
(-.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))))

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

eval213.0ms (1.9%)

Compiler: Compiled 12747 to 8536 computations (33% saved)

prune112.0ms (1%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	504	20	524
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	504	22	526

Error

Counts

526 → 22

Alt Table

Click to see full alt table

Status	Error	Program
	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)
	1.3b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 3)
✓	0.7b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4)))))
	0.9b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 n (-.f64 1 k)))))
▶	0.7b	(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))) (sqrt.f64 k))
▶	3.6b	(/.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (*.f64 k 1/2)))))
	0.8b	(/.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))
	0.9b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) 2) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (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))
	20.9b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	3.6b	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
	3.6b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
	0.8b	(.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	17.2b	(.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)))
	0.7b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
✓	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
▶	14.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (*.f64 k -1))) k))

Compiler

Compiled 812 to 662 computations (18.5% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 70 to 46 computations (34.3% saved)

series15.0ms (0.1%)

Counts

3 → 24

Calls

15 calls:

Time	Variable		Point	Expression
3.0ms	k	@	inf	(/.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))
2.0ms	k	@	0	(/.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))
2.0ms	n	@	-inf	(/.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))
2.0ms	n	@	0	(/.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))
1.0ms	k	@	-inf	(/.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))

rewrite89.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1724×	`associate-/l*`
1040×	`associate-*r/`
876×	`associate-*l/`
354×	`add-sqr-sqrt`
344×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	107
1	353	89
2	4524	89

Stop Event

1×	node limit

Counts

3 → 90

Calls

Call 1

Inputs

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

(/.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))

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

Outputs

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

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

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1490×	`associate-*r/`
960×	`*-commutative`
906×	`unswap-sqr`
778×	`distribute-lft-in`
738×	`associate-/r*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	264	4668
1	618	4386
2	2353	4378

Stop Event

1×	node limit

Counts

114 → 168

Calls

Call 1

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

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

localize27.0ms (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)))
✓	13.2b	(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	n	@	0	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (*.f64 k -1))) k))
1.0ms	n	@	0	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 (*.f64 k -1)))
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 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simplify123.0ms (1.1%)

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

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 59 to 41 computations (30.5% saved)

series15.0ms (0.1%)

Counts

3 → 12

Calls

15 calls:

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

rewrite87.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1404×	`associate-/r*`
1144×	`associate-*r/`
874×	`associate-*l/`
364×	`add-sqr-sqrt`
352×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	103
1	369	87
2	4685	87

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1510×	`associate-/l*`
934×	`unswap-sqr`
768×	`distribute-rgt-in`
762×	`distribute-lft-in`
578×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	4524
1	548	4406
2	2082	4310

Stop Event

1×	node limit

Counts

104 → 175

Calls

Call 1

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

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

localize43.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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)))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	23.5b	(pow.f64 (/.f64 (pow.f64 k -1/2) k) 1/3)

Compiler

Compiled 70 to 50 computations (28.6% saved)

series10.0ms (0.1%)

Counts

2 → 12

Calls

9 calls:

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

rewrite82.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1690×	`associate-*l/`
1194×	`associate-/r*`
414×	`add-sqr-sqrt`
390×	`*-un-lft-identity`
386×	`add-cbrt-cube`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	72
1	418	52
2	5327	52

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(pow.f64 (/.f64 (pow.f64 k -1/2) 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)))

Outputs

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

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

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1078×	`associate-*r/`
1020×	`associate-/l/`
914×	`associate-/r/`
900×	`associate-*l/`
606×	`unswap-sqr`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	2333
1	389	2325
2	1317	2097
3	4904	2095

Stop Event

1×	node limit

Counts

63 → 91

Calls

Call 1

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

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

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (PI.f64) (.f64 2 n))
✓	0.3b	(/.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.5b	(pow.f64 (exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (-.f64 1/2 (/.f64 k 2)))
✓	5.6b	(exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))))

Compiler

Compiled 67 to 47 computations (29.9% saved)

series3.0ms (0%)

Counts

3 → 48

Calls

15 calls:

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

rewrite97.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1614×	`associate-*l/`
1402×	`associate-/r*`
374×	`add-sqr-sqrt`
362×	`*-un-lft-identity`
358×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	91
1	377	91
2	4772	91

Stop Event

1×	node limit

Counts

3 → 109

Calls

Call 1

Inputs

(exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))

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

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

Outputs

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

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

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1648×	`distribute-lft-in`
1256×	`associate-*r/`
952×	`associate-*l/`
836×	`associate-/r*`
632×	`associate-/l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	6901
1	810	5935
2	3121	5931

Stop Event

1×	node limit

Counts

157 → 211

Calls

Call 1

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

eval430.0ms (3.9%)

Compiler: Compiled 24847 to 16430 computations (33.9% saved)

prune269.0ms (2.4%)

Pruning

28 alts after pruning (23 fresh and 5 done)

	Pruned	Kept	Total
New	1110	16	1126
Fresh	8	7	15
Picked	0	1	1
Done	2	4	6
Total	1120	28	1148

Error

Counts

1148 → 28

Alt Table

Click to see full alt table

Status	Error	Program
	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)
	21.5b	(/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/4) (+.f64 2 (*.f64 2 k))) (sqrt.f64 k))
✓	0.7b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	14.0b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (cbrt.f64 (pow.f64 k 3/2)))
	21.6b	(/.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))))
	21.4b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 (+.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (*.f64 (+.f64 1 k) 1/2))))
✓	0.7b	(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))) (sqrt.f64 k))
	3.6b	(/.f64 (pow.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 1/2)) (+.f64 1 (.f64 k -1))) (sqrt.f64 k))
✓	3.6b	(/.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.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))
	20.8b	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) 1) (sqrt.f64 k))
	20.9b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	3.6b	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
▶	3.6b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
▶	34.6b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 k)))))
✓	17.2b	(.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)))
	0.7b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 (.f64 k -1/2) 1/2)) (pow.f64 k -1/2))
✓	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	14.0b	(.f64 (/.f64 1 (cbrt.f64 (pow.f64 k 3/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.7b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	14.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	34.6b	(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))
	34.4b	(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
	34.4b	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
▶	34.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
	41.8b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 k)) k) 3/2))

Compiler

Compiled 882 to 722 computations (18.1% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 70 to 46 computations (34.3% saved)

series42.0ms (0.4%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
32.0ms	n	@	inf	(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 k))
2.0ms	k	@	0	(/.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))
1.0ms	n	@	0	(/.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))
1.0ms	n	@	-inf	(/.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))
1.0ms	k	@	-inf	(/.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))

rewrite124.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1736×	`associate-*l/`
480×	`associate-/l/`
442×	`associate-/r/`
374×	`distribute-rgt-in`
358×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	84
1	358	66
2	4732	66

Stop Event

1×	node limit

Counts

2 → 85

Calls

Call 1

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

Outputs

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

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1800×	`associate-/l*`
1276×	`associate-*r/`
1244×	`associate-/r*`
962×	`*-commutative`
904×	`associate-*l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	5237
1	672	5041
2	2357	5009

Stop Event

1×	node limit

Counts

109 → 175

Calls

Call 1

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

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

localize35.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 n k) (PI.f64))
✓	13.3b	(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	k	@	0	(*.f64 (/.f64 n k) (PI.f64))
1.0ms	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	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))))

rewrite104.0ms (0.9%)

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

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(/.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))))))))

simplify122.0ms (1.1%)

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

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 k)))))
✓	0.2b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 k))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	12.8b	(sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (+.f64 1 k))))

Compiler

Compiled 64 to 43 computations (32.8% saved)

series13.0ms (0.1%)

Counts

3 → 48

Calls

18 calls:

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

rewrite100.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1742×	`associate-*r/`
1516×	`associate-/l*`
1362×	`associate-*l/`
346×	`add-sqr-sqrt`
334×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	107
1	341	101
2	4474	101

Stop Event

1×	node limit

Counts

3 → 136

Calls

Call 1

Inputs

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

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simplify123.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1466×	`distribute-lft-in`
1458×	`distribute-rgt-in`
1266×	`associate-/r*`
1124×	`associate-/l*`
716×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	368	10290
1	833	9482
2	2823	9468

Stop Event

1×	node limit

Counts

184 → 267

Calls

Call 1

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

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

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log.f64 (.f64 (PI.f64) (.f64 2 n)))
	0.2b	(.f64 (PI.f64) (.f64 2 n))
✓	0.3b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
✓	3.4b	(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)

series5.0ms (0%)

Counts

3 → 48

Calls

15 calls:

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

rewrite94.0ms (0.8%)

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	111
1	388	87
2	4734	87

Stop Event

1×	node limit

Counts

3 → 109

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))

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

Outputs

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

simplify97.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1304×	`associate-*r/`
1110×	`associate-+l+`
1108×	`associate-+r+`
1020×	`associate-*l/`
838×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	330	6531
1	776	6081
2	3502	6081

Stop Event

1×	node limit

Counts

157 → 201

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 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))
(+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))
(+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))
(+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))
(+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))
(+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))
(+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))
(+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))
(-.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 (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))))
(.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 (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))))
(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)) (fma.f64 k -1/2 1/2)) 1)
(pow.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) 2)
(pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) 3)
(pow.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 3) 1/3)
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))
(pow.f64 (exp.f64 1) (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 2 n)))))
(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))))))
(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))))))
(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)))))
(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)))))
(sqrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 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))))
(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)) (sqrt.f64 k)))) 1)
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 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)) 2) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2))) (/.f64 -1 (sqrt.f64 k)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.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)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) -1)
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 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))
(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 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 0)
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) 2)))
(+.f64 (log.f64 n) (+.f64 (log.f64 2) (log.f64 (PI.f64))))
(+.f64 (log.f64 2) (+.f64 (log.f64 n) (log.f64 (PI.f64))))
(+.f64 (log.f64 (*.f64 2 n)) (log.f64 (PI.f64)))
(+.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 2 n)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (.f64 2 n)) 2)) (+.f64 (log.f64 (cbrt.f64 (.f64 2 n))) (log.f64 (PI.f64))))
(+.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))) (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))))
(+.f64 0 (log.f64 (.f64 (PI.f64) (.f64 2 n))))
(+.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n)))) (log.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2)))
(+.f64 (log.f64 (sqrt.f64 (.f64 2 n))) (+.f64 (log.f64 (sqrt.f64 (.f64 2 n))) (log.f64 (PI.f64))))
(+.f64 (log.f64 (sqrt.f64 (PI.f64))) (+.f64 (log.f64 (sqrt.f64 (PI.f64))) (log.f64 (*.f64 2 n))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (+.f64 (log.f64 (cbrt.f64 (PI.f64))) (log.f64 (*.f64 2 n))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2)) (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n)))))
(+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))
(+.f64 (.f64 (log.f64 (PI.f64)) 1) (.f64 (log.f64 (*.f64 2 n)) 1))
(+.f64 (.f64 (log.f64 (.f64 2 n)) 1) (*.f64 (log.f64 (PI.f64)) 1))
(+.f64 (+.f64 (log.f64 (*.f64 2 n)) (log.f64 (sqrt.f64 (PI.f64)))) (log.f64 (sqrt.f64 (PI.f64))))
(+.f64 (+.f64 (log.f64 (*.f64 2 n)) (log.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2))) (log.f64 (cbrt.f64 (PI.f64))))
(+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 n)) (log.f64 2))
(+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 2)) (log.f64 n))
(+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 (pow.f64 (cbrt.f64 (.f64 2 n)) 2))) (log.f64 (cbrt.f64 (.f64 2 n))))
(+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 (sqrt.f64 (.f64 2 n)))) (log.f64 (sqrt.f64 (.f64 2 n))))
(+.f64 (+.f64 0 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))))) (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))))
(+.f64 (+.f64 0 (log.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2))) (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n)))))
(+.f64 (+.f64 0 (log.f64 (*.f64 (PI.f64) 2))) (log.f64 n))
(+.f64 (+.f64 0 (.f64 (log.f64 (PI.f64)) 1)) (.f64 (log.f64 (*.f64 2 n)) 1))
(+.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 (pow.f64 (cbrt.f64 n) 2))) (log.f64 (cbrt.f64 n)))
(+.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) 0) (log.f64 n))
(+.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 (sqrt.f64 n))) (log.f64 (sqrt.f64 n)))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))))) 1)
(-.f64 (+.f64 0 (exp.f64 (log1p.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) 1)
(.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 1)
(.f64 1 (log.f64 (.f64 (PI.f64) (*.f64 2 n))))
(.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n)))))
(.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (cbrt.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 2)))
(.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n)))))
(/.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 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3)) (-.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 1 (-.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 1 (+.f64 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3))) (-.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 (.f64 (log.f64 (PI.f64)) (log.f64 (PI.f64))) (.f64 (log.f64 (.f64 2 n)) (log.f64 (.f64 2 n)))) 1) (-.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)) 1) (-.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)))))
(pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 1)
(pow.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) 2)
(pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) 3)
(pow.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 3) 1/3)
(sqrt.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2))
(cbrt.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 3))
(expm1.f64 (log1p.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))
(exp.f64 (log.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))
(exp.f64 (.f64 (log.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 1))
(log1p.f64 (-.f64 (.f64 (PI.f64) (.f64 2 n)) 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 n (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 (sqrt.f64 2) 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 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (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 (sqrt.f64 2)) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 (sqrt.f64 2) (.f64 k k)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 3))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 -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 (sqrt.f64 2)) (.f64 (.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 n (.f64 2 (PI.f64)))) (.f64 (sqrt.f64 2) k))))) (.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 -1/48 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (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 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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(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 (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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(+.f64 (+.f64 0 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))))) (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))))
(.f64 2 (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 2 (log.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
(+.f64 (+.f64 0 (log.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n))) 2))) (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 n)))))
(+.f64 (log.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 2 (log.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 3 (log.f64 (cbrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
(+.f64 (+.f64 0 (log.f64 (*.f64 (PI.f64) 2))) (log.f64 n))
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(+.f64 (+.f64 0 (.f64 (log.f64 (PI.f64)) 1)) (.f64 (log.f64 (*.f64 2 n)) 1))
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(+.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 (pow.f64 (cbrt.f64 n) 2))) (log.f64 (cbrt.f64 n)))
(+.f64 (log.f64 (.f64 2 (PI.f64))) (+.f64 (.f64 2 (log.f64 (cbrt.f64 n))) (log.f64 (cbrt.f64 n))))
(+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 3 (log.f64 (cbrt.f64 n))))
(+.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) 0) (log.f64 n))
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(+.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 (sqrt.f64 n))) (log.f64 (sqrt.f64 n)))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (+.f64 (log.f64 (sqrt.f64 n)) (log.f64 (sqrt.f64 n))))
(+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 2 (log.f64 (sqrt.f64 n))))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))))) 1)
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(-.f64 (+.f64 0 (exp.f64 (log1p.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) 1)
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 1)
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 1 (log.f64 (.f64 (PI.f64) (*.f64 2 n))))
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n)))))
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) (cbrt.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n))) 2)))
(.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (cbrt.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)) (cbrt.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n)))))
(.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (cbrt.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)) (cbrt.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(/.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 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 2 n))))
(/.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n))) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n)))))
(.f64 (/.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 2 n))))
(/.f64 (+.f64 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3)) (-.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 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3)) (-.f64 (fma.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 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3)) (fma.f64 (log.f64 (PI.f64)) (log.f64 (PI.f64)) (.f64 (log.f64 (.f64 2 n)) (-.f64 (log.f64 (.f64 2 n)) (log.f64 (PI.f64))))))
(/.f64 (.f64 1 (-.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 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 2 n))))
(/.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n))) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n)))))
(.f64 (/.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 2 n))))
(/.f64 (.f64 1 (+.f64 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3))) (-.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 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3)) (-.f64 (fma.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 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3)) (fma.f64 (log.f64 (PI.f64)) (log.f64 (PI.f64)) (.f64 (log.f64 (.f64 2 n)) (-.f64 (log.f64 (.f64 2 n)) (log.f64 (PI.f64))))))
(/.f64 (.f64 (-.f64 (.f64 (log.f64 (PI.f64)) (log.f64 (PI.f64))) (.f64 (log.f64 (.f64 2 n)) (log.f64 (.f64 2 n)))) 1) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n))))
(/.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 2 n))))
(/.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n))) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n)))))
(.f64 (/.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 (log.f64 (PI.f64)) (log.f64 (.f64 2 n)))) (-.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)) 1) (-.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 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3)) (-.f64 (fma.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 (pow.f64 (log.f64 (PI.f64)) 3) (pow.f64 (log.f64 (.f64 2 n)) 3)) (fma.f64 (log.f64 (PI.f64)) (log.f64 (PI.f64)) (.f64 (log.f64 (.f64 2 n)) (-.f64 (log.f64 (.f64 2 n)) (log.f64 (PI.f64))))))
(pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 1)
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(pow.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) 2)
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))) 3)
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(pow.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 3) 1/3)
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2))
(sqrt.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))
(fabs.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(cbrt.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 3))
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(expm1.f64 (log1p.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(exp.f64 (log.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(exp.f64 (.f64 (log.f64 (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 1))
(log.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (.f64 n (.f64 2 (PI.f64))))
(log1p.f64 (-.f64 (.f64 (PI.f64) (.f64 2 n)) 1))
(log1p.f64 (fma.f64 (PI.f64) (*.f64 2 n) -1))
(log1p.f64 (fma.f64 2 (*.f64 n (PI.f64)) -1))

localize41.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.4b	(/.f64 1 (cbrt.f64 (pow.f64 k 3/2)))
	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	20.1b	(cbrt.f64 (pow.f64 k 3/2))

Compiler

Compiled 66 to 49 computations (25.8% saved)

series1.0ms (0%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(cbrt.f64 (pow.f64 k 3/2))
0.0ms	k	@	-inf	(cbrt.f64 (pow.f64 k 3/2))
0.0ms	k	@	inf	(cbrt.f64 (pow.f64 k 3/2))
0.0ms	k	@	-inf	(/.f64 1 (cbrt.f64 (pow.f64 k 3/2)))
0.0ms	k	@	0	(/.f64 1 (cbrt.f64 (pow.f64 k 3/2)))

rewrite56.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1478×	`add-sqr-sqrt`
1438×	`*-un-lft-identity`
1360×	`add-cube-cbrt`
1346×	`add-cbrt-cube`
1334×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	180	16
2	2045	16

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 k 3/2))
(/.f64 1 (cbrt.f64 (pow.f64 k 3/2)))

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

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

simplify49.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1492×	`associate-*r/`
1330×	`associate-/r/`
1040×	`associate-*l/`
880×	`*-commutative`
512×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1040
1	216	798
2	723	568
3	3249	568

Stop Event

1×	node limit

Counts

50 → 64

Calls

Call 1

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

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

eval428.0ms (3.9%)

Compiler: Compiled 24398 to 16074 computations (34.1% saved)

prune289.0ms (2.6%)

Pruning

37 alts after pruning (31 fresh and 6 done)

	Pruned	Kept	Total
New	1102	20	1122
Fresh	7	11	18
Picked	1	0	1
Done	3	6	9
Total	1113	37	1150

Error

Counts

1150 → 37

Alt Table

Click to see full alt table

Status	Error	Program
▶	41.2b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)
	34.5b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 1/4) 2)
✓	0.7b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	21.6b	(/.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))))
	21.4b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 (+.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (*.f64 (+.f64 1 k) 1/2))))
	0.7b	(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
	3.6b	(/.f64 (pow.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 1/2)) (+.f64 1 (.f64 k -1))) (sqrt.f64 k))
✓	3.6b	(/.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 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 k))) (sqrt.f64 k))
	20.8b	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) 1) (sqrt.f64 k))
	20.9b	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
	3.6b	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
✓	3.6b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
▶	21.5b	(/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 -1 k)))))
	33.9b	(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 n 2) (PI.f64)))))
	16.0b	(.f64 (pow.f64 (pow.f64 k 3/2) -1/3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.7b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 (.f64 k -1/2) 1/2)) (pow.f64 k -1/2))
	20.9b	(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 2))
	41.8b	(.f64 (/.f64 1 (-.f64 (+.f64 1 (sqrt.f64 k)) 1)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	4.2b	(.f64 (/.f64 1 (exp.f64 (.f64 (.f64 3/2 (log.f64 k)) 1/3))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	34.5b	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 2))
	34.5b	(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
▶	34.5b	(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 2 (/.f64 k n))))
	3.7b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	14.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	34.6b	(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))
	34.4b	(sqrt.f64 (*.f64 (PI.f64) (/.f64 2 (/.f64 k n))))
	34.4b	(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) (/.f64 1 n)) k)))
	34.4b	(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
	34.3b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	34.4b	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
✓	34.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
▶	34.4b	(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))
	36.2b	(exp.f64 (.f64 (log.f64 (.f64 (/.f64 n k) (*.f64 (PI.f64) 2))) 1/2))
	39.7b	(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2))

Compiler

Compiled 1031 to 850 computations (17.6% saved)

localize28.0ms (0.2%)

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 (.f64 k -1/2) 1/2)) (pow.f64 k -1/2))
	0.2b	(.f64 (PI.f64) (.f64 2 n))
✓	0.5b	(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 (*.f64 k -1/2) 1/2))

Compiler

Compiled 53 to 38 computations (28.3% saved)

series49.0ms (0.4%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
26.0ms	k	@	0	(pow.f64 k -1/2)
10.0ms	k	@	-inf	(pow.f64 k -1/2)
10.0ms	k	@	inf	(pow.f64 k -1/2)
1.0ms	n	@	0	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 (.f64 k -1/2) 1/2)) (pow.f64 k -1/2))
1.0ms	k	@	-inf	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 (.f64 k -1/2) 1/2)) (pow.f64 k -1/2))

rewrite82.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1112×	`swap-sqr`
550×	`associate-*r/`
546×	`distribute-rgt-in`
500×	`distribute-lft-in`
358×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	77
1	348	77
2	4347	77

Stop Event

1×	node limit

Counts

3 → 59

Calls

Call 1

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

simplify100.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1194×	`unswap-sqr`
1028×	`distribute-lft-in`
986×	`distribute-rgt-in`
916×	`*-commutative`
812×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	4609
1	564	3871
2	1822	3601
3	6774	3601

Stop Event

1×	node limit

Counts

107 → 116

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

localize9.0ms (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)
✓	13.3b	(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	k	@	-inf	(/.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))))

rewrite79.0ms (0.7%)

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 (0.8%)

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))

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 2 (/.f64 k n))
✓	0.3b	(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 2 (/.f64 k n))))
✓	1.0b	(sqrt.f64 (PI.f64))
✓	13.3b	(sqrt.f64 (/.f64 2 (/.f64 k n)))

Compiler

Compiled 31 to 15 computations (51.6% saved)

series7.0ms (0.1%)

Counts

4 → 24

Calls

18 calls:

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

rewrite82.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1768×	`associate-*r/`
1394×	`associate-*l/`
1278×	`associate-/r*`
748×	`associate-/l*`
270×	`add-sqr-sqrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	270	62
2	3371	62

Stop Event

1×	node limit

Counts

4 → 160

Calls

Call 1

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

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

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1304×	`associate-*r/`
1090×	`distribute-rgt-in`
1084×	`distribute-lft-in`
962×	`associate-*l/`
870×	`associate-/r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	343	4524
1	679	4468
2	2961	4468

Stop Event

1×	node limit

Counts

184 → 218

Calls

Call 1

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

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

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2)
✓	0.3b	(.f64 (/.f64 n k) (.f64 (PI.f64) 2))
✓	25.6b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)

Compiler

Compiled 41 to 24 computations (41.5% saved)

series136.0ms (1.2%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
59.0ms	k	@	0	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)
22.0ms	k	@	-inf	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)
20.0ms	n	@	-inf	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)
16.0ms	n	@	0	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)
9.0ms	k	@	inf	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)

rewrite93.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1152×	`associate-*r/`
990×	`associate-*l/`
910×	`associate-/r*`
694×	`associate-/l*`
300×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	306	73
2	3702	73

Stop Event

1×	node limit

Counts

3 → 235

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)
(.f64 (/.f64 n k) (.f64 (PI.f64) 2))
(pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2)

Outputs

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

simplify142.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1554×	`distribute-lft-in`
1008×	`times-frac`
814×	`associate-/l/`
776×	`associate-r`
754×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	604	4294977995
1	1493	9915
2	6597	9915

Stop Event

1×	node limit

Counts

307 → 372

Calls

Call 1

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

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

localize40.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 -1 k)))))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 -1 k))))
✓	0.6b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 -1 k))

Compiler

Compiled 68 to 45 computations (33.8% saved)

series15.0ms (0.1%)

Counts

3 → 48

Calls

18 calls:

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

rewrite96.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1356×	`associate-*r/`
1054×	`associate-*l/`
872×	`associate-/r*`
372×	`add-sqr-sqrt`
360×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	107
1	376	103
2	4595	103

Stop Event

1×	node limit

Counts

3 → 132

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify117.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1716×	`distribute-lft-in`
1646×	`associate-*l/`
1422×	`associate-/r/`
484×	`associate-/l*`
370×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	380	10364
1	948	9078
2	3895	9078

Stop Event

1×	node limit

Counts

180 → 250

Calls

Call 1

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

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

eval663.0ms (6%)

Compiler: Compiled 22776 to 14230 computations (37.5% saved)

prune314.0ms (2.8%)

Pruning

42 alts after pruning (32 fresh and 10 done)

	Pruned	Kept	Total
New	1255	16	1271
Fresh	10	16	26
Picked	1	0	1
Done	0	10	10
Total	1266	42	1308

Error

Counts

1308 → 42

Alt Table

Click to see full alt table

Status	Error	Program
	41.2b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
✓	41.2b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2) 1/3)
	34.5b	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 1/4) 2)
✓	0.7b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
	3.6b	(/.f64 (pow.f64 (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 1/2)) (+.f64 1 (.f64 k -1))) (sqrt.f64 k))
✓	3.6b	(/.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 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 1/2 k))) (sqrt.f64 k))
	20.8b	(/.f64 (sqrt.f64 (*.f64 (/.f64 n 1/2) (PI.f64))) (sqrt.f64 k))
	33.9b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
	20.8b	(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
	20.8b	(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
	33.9b	(/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k (/.f64 n 1/2))))
	3.6b	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
✓	3.6b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 k -1/2)) (log.f64 (.f64 (PI.f64) (.f64 2 n))))) (sqrt.f64 k))
	20.6b	(/.f64 1 (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 1/2 n) (PI.f64)))))
	33.9b	(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 n 2) (PI.f64)))))
	16.0b	(.f64 (pow.f64 (pow.f64 k 3/2) -1/3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.7b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 (.f64 k -1/2) 1/2)) (pow.f64 k -1/2))
	3.7b	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 (.f64 k -1/2) 1/2)) (exp.f64 (*.f64 -1/2 (log.f64 k))))
	41.8b	(.f64 (/.f64 1 (-.f64 (+.f64 1 (sqrt.f64 k)) 1)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	4.2b	(.f64 (/.f64 1 (exp.f64 (.f64 (.f64 3/2 (log.f64 k)) 1/3))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	20.7b	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2)))
	34.6b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) 2)))
	34.4b	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
	34.5b	(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
✓	34.5b	(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 2 (/.f64 k n))))
	14.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	34.6b	(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))
	34.3b	(sqrt.f64 (/.f64 (PI.f64) (/.f64 (/.f64 k 2) n)))
	34.4b	(sqrt.f64 (*.f64 (PI.f64) (/.f64 2 (/.f64 k n))))
	34.4b	(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
	34.4b	(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) (/.f64 1 n)) k)))
	34.4b	(sqrt.f64 (*.f64 2 (/.f64 (/.f64 n k) (/.f64 1 (PI.f64)))))
	34.4b	(sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
✓	34.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
✓	34.4b	(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))
	34.4b	(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
	36.2b	(exp.f64 (.f64 (log.f64 (.f64 (/.f64 n k) (*.f64 (PI.f64) 2))) 1/2))
	39.7b	(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)) 3/2))
	39.7b	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2))

Compiler

Compiled 590 to 486 computations (17.6% saved)

regimes144.0ms (1.3%)

Counts

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

Outputs
(/.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))

Calls

4 calls:

34.0ms	(.f64 (.f64 2 (PI.f64)) n)
34.0ms	n
33.0ms	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
0.5b	1	`k`
0.5b	1	`n`
0.5b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1037 to 688 computations (33.7% saved)

regimes134.0ms (1.2%)

Counts

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

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

Calls

4 calls:

32.0ms	(.f64 (.f64 2 (PI.f64)) n)
31.0ms	n
31.0ms	k
17.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.7b	1	`k`
0.7b	1	`n`
0.7b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.7b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 954 to 635 computations (33.4% saved)

regimes43.0ms (0.4%)

Counts

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

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

Calls

2 calls:

17.0ms	n
17.0ms	k

Results

Error	Segments	Branch
0.7b	1	`k`
0.7b	1	`n`

Compiler

Compiled 353 to 218 computations (38.2% saved)

regimes160.0ms (1.4%)

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

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

Calls

2 calls:

120.0ms	n
31.0ms	k

Results

Error	Segments	Branch
0.5b	2	`k`
8.5b	8	`n`

Compiler

Compiled 339 to 209 computations (38.3% saved)

bsearch22.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
21.0ms	2.7076752261115734e-45	5.600329018504739e-42

Results

19.0ms

128×

body

256

valid

Compiler

Compiled 255 to 211 computations (17.3% saved)

regimes52.0ms (0.5%)

Counts

31 → 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 (PI.f64) (/.f64 (/.f64 k 2) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 n k) (/.f64 1 (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) (/.f64 1 n)) k)))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 n 2) (PI.f64)))))
(*.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 n (/.f64 (PI.f64) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) 2)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2)))
(/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k (/.f64 n 1/2))))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (*.f64 (/.f64 n 1/2) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 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))
(/.f64 1 (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 1/2 n) (PI.f64)))))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) 1) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) 1) (sqrt.f64 k))
(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)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)

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

Calls

2 calls:

29.0ms	k
16.0ms	n

Results

Error	Segments	Branch
19.2b	2	`k`
20.6b	1	`n`

Compiler

Compiled 299 to 181 computations (39.5% saved)

bsearch4.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
4.0ms	2.469879173479378e+97	1.494271318041616e+102

Results

2.0ms	16×	body	256	valid
1.0ms	8×	body	256	infinite

Compiler

Compiled 50 to 42 computations (16% saved)

regimes45.0ms (0.4%)

Counts

25 → 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 (PI.f64) (/.f64 (/.f64 k 2) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 n k) (/.f64 1 (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) (/.f64 1 n)) k)))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 n 2) (PI.f64)))))
(*.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 n (/.f64 (PI.f64) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) 2)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2)))
(/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k (/.f64 n 1/2))))
(/.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (*.f64 (/.f64 n 1/2) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 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))

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

Calls

2 calls:

26.0ms	k
13.0ms	n

Results

Error	Segments	Branch
19.3b	2	`k`
20.7b	1	`n`

Compiler

Compiled 233 to 139 computations (40.3% saved)

bsearch4.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
4.0ms	1.9826920605991678e+118	2.281905986811808e+126

Results

2.0ms	16×	body	256	valid
1.0ms	6×	body	256	infinite

Compiler

Compiled 48 to 40 computations (16.7% saved)

regimes29.0ms (0.3%)

Counts

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

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

Calls

2 calls:

12.0ms	n
11.0ms	k

Results

Error	Segments	Branch
20.7b	1	`k`
20.7b	1	`n`

Compiler

Compiled 202 to 120 computations (40.6% saved)

regimes23.0ms (0.2%)

Counts

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

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

Calls

2 calls:

9.0ms	n
9.0ms	k

Results

Error	Segments	Branch
33.9b	1	`k`
33.9b	1	`n`

Compiler

Compiled 157 to 94 computations (40.1% saved)

regimes16.0ms (0.1%)

Counts

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

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

Calls

2 calls:

7.0ms	k
6.0ms	n

Results

Error	Segments	Branch
34.3b	1	`k`
34.3b	1	`n`

Compiler

Compiled 102 to 65 computations (36.3% saved)

regimes8.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

3 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 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)))))

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

Calls

2 calls:

4.0ms	n
3.0ms	k

Results

Error	Segments	Branch
34.4b	1	`k`
34.4b	1	`n`

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	509
1	99	509
2	107	509
3	111	509
4	113	509

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.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 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 3163659274634887/25108406941546723055343157692830665664409421777856138051584) (/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 1/2 n) (PI.f64))))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 40000000000000002943034953908449993590304248608709827196983431605407036575208760808202718624612352) (/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 1/2 n) (PI.f64))))) (cbrt.f64 (pow.f64 (.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2)))
(if (<=.f64 k 19999999999999999331299997886547518366483030189726856989175506568457504104549882393640764156980535349390222311028686848) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2))) (cbrt.f64 (pow.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2)))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 n 2) (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))

Outputs
(/.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 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 (.f64 k -1/2) 1/2)) (pow.f64 k -1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 3163659274634887/25108406941546723055343157692830665664409421777856138051584) (/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 1/2 n) (PI.f64))))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 3163659274634887/25108406941546723055343157692830665664409421777856138051584) (/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 1/2 n) (PI.f64))))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (-.f64 1 k)) k)))
(if (<=.f64 k 40000000000000002943034953908449993590304248608709827196983431605407036575208760808202718624612352) (/.f64 1 (.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 1/2 n) (PI.f64))))) (cbrt.f64 (pow.f64 (.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2)))
(if (<=.f64 k 19999999999999999331299997886547518366483030189726856989175506568457504104549882393640764156980535349390222311028686848) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2))) (cbrt.f64 (pow.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2)))
(if (<=.f64 k 19999999999999999331299997886547518366483030189726856989175506568457504104549882393640764156980535349390222311028686848) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 2 n))) (cbrt.f64 (pow.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))) 3/2)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n 2)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 2 n)))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 n 2) (PI.f64)))))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 2 n)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))

Compiler

Compiled 188 to 148 computations (21.3% saved)

soundness651.0ms (5.9%)

Algorithm

8×	egg-herbie

Rules

1758×	`distribute-lft-in`
1758×	`distribute-lft-in`
1716×	`distribute-lft-in`
1646×	`associate-*l/`
1466×	`distribute-lft-in`

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
0	301	6798
1	725	5792
2	2872	5788
0	423	9967
1	1036	9313
2	4383	9177
0	368	10290
1	833	9482
2	2823	9468
0	380	10364
1	948	9078
2	3895	9078
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
0	301	6798
1	725	5792
2	2872	5788
0	423	9967
1	1036	9313
2	4383	9177

Stop Event

1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 874 to 647 computations (26% saved)

end90.0ms (0.8%)

Compiler: Compiled 168 to 111 computations (33.9% saved)