Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze269.0ms (4%)

Memory

-8.3MiB live, 224.8MiB allocated; 110ms collecting garbage

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
50%	25%	25%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
50%	25%	25%	0.1%	0%	50%	0%	6
51.6%	25%	23.4%	0.1%	0%	51.5%	0%	7
52.5%	25%	22.6%	0.1%	0%	52.3%	0%	8
53.8%	25%	21.5%	0.1%	0%	53.5%	0%	9
54.5%	25%	20.9%	0.1%	0%	54%	0%	10
55.3%	25%	20.2%	0.1%	0%	54.7%	0%	11
55.7%	25%	19.9%	0.1%	0%	55.1%	0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample4.2s (63.7%)

Memory

17.4MiB live, 4 897.5MiB allocated; 1.6s collecting garbage

Samples

1.4s	4 400×	1	invalid
1.2s	8 255×	0	valid
654.0ms	1 488×	2	invalid
35.0ms	379×	0	invalid
30.0ms	249×	0	exit
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 2.6s

ival-mult: 835.0ms (32.6% of total)

ival-pow: 701.0ms (27.3% of total)

ival-div: 350.0ms (13.6% of total)

ival-sqrt: 256.0ms (10% of total)

adjust: 159.0ms (6.2% of total)

ival-sub: 131.0ms (5.1% of total)

ival-pi: 102.0ms (4% of total)

exact: 24.0ms (0.9% of total)

ival-assert: 6.0ms (0.2% of total)

Bogosity

explain272.0ms (4.1%)

Memory

21.2MiB live, 265.8MiB allocated; 36ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
4	72	(1.0467540416284837e-271 5.921581158100909e-120)	1	(6.669075644278179e-5 3.131848763808647e-49)	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	0	-	`k`
0	0	-	0	-	`n`
0	0	-	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	0	-	`(sqrt.f64 k)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	0	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	0	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	75	26

Confusion

	Predicted +	Predicted -
+	3	1
-	72	180

Precision

0.04

Recall

0.75

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	1	0
-	72	25	155

Precision?

0.039603960396039604

Recall?

1.0

Freqs

test

number	freq
0	181
1	75

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

147.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-div: 55.0ms (64.3% of total)

ival-pow: 10.0ms (11.7% of total)

ival-mult: 9.0ms (10.5% of total)

ival-sqrt: 4.0ms (4.7% of total)

ival-sub: 3.0ms (3.5% of total)

ival-pi: 2.0ms (2.3% of total)

ival-true: 1.0ms (1.2% of total)

exact: 1.0ms (1.2% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess245.0ms (3.7%)

Memory

-34.9MiB live, 203.5MiB allocated; 145ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	104
1	76	90
2	162	88
3	382	88
4	1615	88
0	13	16
0	22	16
1	37	14
2	58	14
3	136	14
4	533	14
5	3201	14
0	8098	14

Stop Event

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

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Outputs

(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune10.0ms (0.2%)

Memory

-52.2MiB live, 0.7MiB allocated; 10ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 16 to 13 computations (18.8% saved)

series75.0ms (1.1%)

Memory

47.5MiB live, 91.1MiB allocated; 7ms collecting garbage

Counts

13 → 34

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))

Calls

6 calls:

Time	Variable		Point	Expression
30.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
22.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
15.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
3.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))

rewrite108.0ms (1.6%)

Memory

-37.8MiB live, 53.8MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	181	965
0	195	935
0	833	922

Stop Event

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

Counts

47 → 70

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))

Outputs
(.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
k
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ 1 (sqrt k)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt k) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* 2 (PI)) n) (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval17.0ms (0.3%)

Memory: 29.3MiB live, 29.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 740 to 286 computations (83.6% saved)

prune19.0ms (0.3%)

Memory

-6.4MiB live, 37.4MiB allocated; 6ms collecting garbage

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	57	15	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	15	73

Accuracy

99.9%

Counts

73 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	55.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
▶	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
	70.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
▶	96.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	64.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
	56.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
	48.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
	96.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k)))))
	47.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
	99.6%	(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
▶	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Compiler

Compiled 1 088 to 720 computations (33.8% saved)

series116.0ms (1.7%)

Memory

-2.5MiB live, 141.2MiB allocated; 23ms collecting garbage

Counts

35 → 134

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(literal 1 binary64)
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))

Outputs
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
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#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))

Calls

6 calls:

Time	Variable		Point	Expression
38.0ms	n	@	-inf	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
36.0ms	n	@	0	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
12.0ms	n	@	inf	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
9.0ms	k	@	0	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
9.0ms	k	@	inf	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))

rewrite84.0ms (1.3%)

Memory

-1.7MiB live, 131.4MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	411	5105
0	464	4445
0	1713	4381

Stop Event

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

Counts

169 → 303

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(literal 1 binary64)
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ (* (PI) n) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
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#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
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#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
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#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
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#s(approx n #s(hole binary64 n))
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#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
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#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
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Outputs
(.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
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(pow.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
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(+.f64 (cosh.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sinh.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(/.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal -2 binary64))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ (* (PI) n) k) 2) (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
#s(approx (/ (* (PI) n) k) (/.f64 (*.f64 (PI.f64) n) k))
#s(approx (/ 1 (sqrt k)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (+ (* -1/2 k) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* -1/2 k) 1/2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
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#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (neg.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval46.0ms (0.7%)

Memory: 23.8MiB live, 125.6MiB allocated; 11ms collecting garbage
Compiler: Compiled 10 863 to 1 047 computations (90.4% saved)

prune29.0ms (0.4%)

Memory

-24.8MiB live, 66.8MiB allocated; 5ms collecting garbage

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	340	16	356
Fresh	7	3	10
Picked	3	2	5
Done	0	0	0
Total	350	21	371

Accuracy

99.9%

Counts

371 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
	79.7%	(/.f64 (pow.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k))
	55.9%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 k))
	56.7%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
	47.6%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
	47.0%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))
✓	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	98.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64))))))
	96.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
	70.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	96.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))))
▶	96.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
▶	47.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
▶	99.6%	(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
▶	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
▶	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))

Compiler

Compiled 1 406 to 927 computations (34.1% saved)

series205.0ms (3.1%)

Memory

3.4MiB live, 248.4MiB allocated; 46ms collecting garbage

Counts

50 → 126

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal -1 binary64))
k
#s(literal -1 binary64)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
(/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k)
(fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))
(.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))
(.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))
(*.f64 (pow.f64 k #s(literal 3 binary64)) n)
(pow.f64 k #s(literal 3 binary64))
#s(literal 3 binary64)
(sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)

Outputs
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (pow k -1)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow k -1) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* n (/ (PI) k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* n (/ (PI) k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ (PI) k) #s(hole binary64 (/ (PI) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (log (* 2 (* n (PI)))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (log (* 2 (* n (PI)))))) (* 1/2 (log (* 2 (* n (PI))))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (sqrt (* (pow k 3) (* n (PI))))))
#s(approx (* (* (pow k 3) n) (PI)) #s(hole binary64 (* (pow k 3) (* n (PI)))))
#s(approx (* (pow k 3) n) #s(hole binary64 (* (pow k 3) n)))
#s(approx (pow k 3) #s(hole binary64 (pow k 3)))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* (* (* (PI) n) k) 2) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* (* (PI) n) k) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* -1/2 (* k (log (* 2 (* n (PI))))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/2 (/ (log (* 2 (* n (PI)))) k))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (pow k -1)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* -1 (* k (+ (* -1/2 (/ (log (* 2 (* n (PI)))) k)) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1 (* k (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -2) (sqrt -1))))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -2) (sqrt -1)))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2))))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
#s(approx (log (* (* 2 n) (PI))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (* 2 n) (PI)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* 2 n) #s(hole binary64 (* 2 n)))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (log (* (* 2 n) (PI))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (log (* (* 2 n) (PI))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))) k))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2)))))

Calls

6 calls:

Time	Variable		Point	Expression
60.0ms	n	@	0	((* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) k -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (log (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n))
41.0ms	k	@	-inf	((* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) k -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (log (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n))
39.0ms	n	@	-inf	((* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) k -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (log (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n))
27.0ms	k	@	inf	((* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) k -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (log (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n))
18.0ms	k	@	0	((* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) k -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (log (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n))

rewrite104.0ms (1.6%)

Memory

21.9MiB live, 108.1MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	415	4656
0	486	4354
0	1695	4316

Stop Event

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

Counts

176 → 329

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal -1 binary64))
k
#s(literal -1 binary64)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
(/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k)
(fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))
(.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))
(.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))
(*.f64 (pow.f64 k #s(literal 3 binary64)) n)
(pow.f64 k #s(literal 3 binary64))
#s(literal 3 binary64)
(sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (pow k -1)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow k -1) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* n (/ (PI) k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* n (/ (PI) k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ (PI) k) #s(hole binary64 (/ (PI) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (log (* 2 (* n (PI)))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (log (* 2 (* n (PI)))))) (* 1/2 (log (* 2 (* n (PI))))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (sqrt (* (pow k 3) (* n (PI))))))
#s(approx (* (* (pow k 3) n) (PI)) #s(hole binary64 (* (pow k 3) (* n (PI)))))
#s(approx (* (pow k 3) n) #s(hole binary64 (* (pow k 3) n)))
#s(approx (pow k 3) #s(hole binary64 (pow k 3)))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* (* (* (PI) n) k) 2) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* (* (PI) n) k) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* -1/2 (* k (log (* 2 (* n (PI))))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/2 (/ (log (* 2 (* n (PI)))) k))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (pow k -1)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* -1 (* k (+ (* -1/2 (/ (log (* 2 (* n (PI)))) k)) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1 (* k (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -2) (sqrt -1))))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -2) (sqrt -1)))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2))))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
#s(approx (log (* (* 2 n) (PI))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (* 2 n) (PI)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* 2 n) #s(hole binary64 (* 2 n)))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (log (* (* 2 n) (PI))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (log (* (* 2 n) (PI))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))) k))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2)))))

Outputs
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) k)
(/.f64 #s(literal -1 binary64) (neg.f64 k))
(exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))
k
#s(literal -1 binary64)
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(+.f64 (cosh.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sinh.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k)) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
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(pow.f64 k #s(literal 3 binary64))
(exp.f64 (*.f64 (log.f64 k) #s(literal 3 binary64)))
#s(literal 3 binary64)
(.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)))
(pow.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))
(.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) n) (*.f64 k #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 (PI.f64) n) k))
(fma.f64 (.f64 k n) (PI.f64) (.f64 (*.f64 (PI.f64) n) k))
(fma.f64 (.f64 (PI.f64) n) k (.f64 (*.f64 (PI.f64) n) k))
(fma.f64 (PI.f64) (.f64 n k) (.f64 (*.f64 (PI.f64) n) k))
(fma.f64 k (.f64 (PI.f64) n) (.f64 (*.f64 (PI.f64) n) k))
(+.f64 (.f64 (.f64 (PI.f64) n) k) (.f64 (.f64 (PI.f64) n) k))
(.f64 (.f64 k n) (PI.f64))
(.f64 (.f64 (PI.f64) n) k)
(.f64 (PI.f64) (.f64 n k))
(.f64 k (.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (sqrt (pow k -1)) (pow.f64 k #s(literal -1/2 binary64)))
#s(approx (pow k -1) (pow.f64 k #s(literal -1 binary64)))
#s(approx k k)
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (fma.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (+ (* -1/2 k) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* -1/2 k) 1/2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (* n (/ (PI) k)) 2) (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
#s(approx (* n (/ (PI) k)) (/.f64 (*.f64 (PI.f64) n) k))
#s(approx (/ (PI) k) (/.f64 (PI.f64) k))
#s(approx (sqrt (pow k -1)) (pow.f64 k #s(literal -1/2 binary64)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (fma.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (log.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))
#s(approx (* (* (pow k 3) n) (PI)) (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))
#s(approx (* (pow k 3) n) (*.f64 (pow.f64 k #s(literal 3 binary64)) n))
#s(approx (pow k 3) (pow.f64 k #s(literal 3 binary64)))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (* (* (PI) n) k) 2) (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
#s(approx (* (* (PI) n) k) (.f64 (.f64 (PI.f64) n) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (.f64 (fma.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) k)) k))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64)))) k))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (.f64 (.f64 k k) (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal -1 binary64)))
#s(approx (sqrt (pow k -1)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64)))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (sqrt k) (neg.f64 (*.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (.f64 (neg.f64 k) (fma.f64 (/.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) k) #s(literal -1/2 binary64) (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (.f64 (neg.f64 k) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 (.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64))))) (.f64 k k)))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 (.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (.f64 (sqrt.f64 (.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) #s(literal -1 binary64)))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) (neg.f64 (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* (PI) 2) n) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))
#s(approx n n)
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (sqrt (* (* (PI) 2) n)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))
#s(approx (* (* (PI) 2) n) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (log (* (* (PI) 2) n)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))
#s(approx (* (* (PI) 2) n) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))
#s(approx (* 2 n) (*.f64 n #s(literal 2 binary64)))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* (PI) 2) n)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))
#s(approx (* (PI) n) (*.f64 (PI.f64) n))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (.f64 n (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64)))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64)))) n))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (neg.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (sqrt (* (* (PI) 2) n)) (neg.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (exp (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (* (* 2 n) (PI))) (/ (- 1 k) 2)) (.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) k) n) #s(literal 2 binary64)))) n)) k))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (neg.f64 (.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) k) n) #s(literal 2 binary64)))) n)))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (neg.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) #s(literal -1 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (neg.f64 (.f64 (sqrt.f64 (.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) #s(literal -1 binary64))))

eval37.0ms (0.6%)

Memory: 16.7MiB live, 61.4MiB allocated; 3ms collecting garbage
Compiler: Compiled 11 786 to 1 178 computations (90% saved)

prune57.0ms (0.8%)

Memory

-9.2MiB live, 46.8MiB allocated; 9ms collecting garbage

Pruning

24 alts after pruning (20 fresh and 4 done)

	Pruned	Kept	Total
New	301	10	311
Fresh	4	10	14
Picked	3	2	5
Done	0	2	2
Total	308	24	332

Accuracy

99.9%

Counts

332 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
	55.9%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 k))
	56.7%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
▶	47.6%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
	47.0%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))
	47.0%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (exp ( (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
✓	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	98.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
	96.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
	96.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	96.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))))
	46.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
▶	46.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
✓	47.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
	56.7%	(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (exp ( (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))))
▶	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	96.3%	(.f64 (sqrt.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	54.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
▶	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64)))) k))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
▶	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
✓	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))

Compiler

Compiled 1 506 to 1 067 computations (29.2% saved)

series189.0ms (2.8%)

Memory

-19.1MiB live, 216.6MiB allocated; 21ms collecting garbage

Counts

57 → 143

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))
(.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 n k)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(sqrt.f64 n)
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
(fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
(.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64)))) k))
(/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64)))) k)
(fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))
(.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))
(.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))
(*.f64 (pow.f64 k #s(literal 3 binary64)) n)
(pow.f64 k #s(literal 3 binary64))
#s(literal 3 binary64)
(sqrt.f64 (.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64))
(.f64 (.f64 k n) (PI.f64))
(*.f64 k n)

Outputs
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* (PI) (/ n k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (PI) (/ n k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* (sqrt (pow k 3)) (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* k (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) #s(hole binary64 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (sqrt (* (pow k 3) (* n (PI))))))
#s(approx (* (* (pow k 3) n) (PI)) #s(hole binary64 (* (pow k 3) (* n (PI)))))
#s(approx (* (pow k 3) n) #s(hole binary64 (* (pow k 3) n)))
#s(approx (pow k 3) #s(hole binary64 (pow k 3)))
#s(approx (sqrt (* (* (* k n) (PI)) 2)) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* (* (* k n) (PI)) 2) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* (* k n) (PI)) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* k n) #s(hole binary64 (* k n)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2)))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2)))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) #s(hole binary64 (* -1 (* k (+ (* -1 (* (/ (sqrt 2) k) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) #s(hole binary64 (* -1 (* k (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -2) (sqrt -1))))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -2) (sqrt -1)))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2))))
#s(approx (sqrt (* (* (* k n) (PI)) 2)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (sqrt (* (PI) 2)) (sqrt n)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (sqrt n) #s(hole binary64 (sqrt n)))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))))
#s(approx (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) #s(hole binary64 (* (sqrt (* n (PI))) (+ (log n) (log (* 2 (PI)))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (log (* (* 2 n) (PI))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (* 2 n) (PI)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* 2 n) #s(hole binary64 (* 2 n)))
#s(approx (sqrt (* (* 2 n) (PI))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) #s(hole binary64 (* n (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (sqrt 2))))))
#s(approx (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (* n (PI))))))
#s(approx (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) #s(hole binary64 (* (sqrt (* n (PI))) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* 2 n) (PI))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) #s(hole binary64 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (sqrt (* (PI) 2)) (sqrt n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt n) #s(hole binary64 (* -1 (* (sqrt n) (pow (sqrt -1) 2)))))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) #s(hole binary64 (* -1 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (* n (PI)))))))
#s(approx (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (log (* (* 2 n) (PI))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (* 2 n) (PI))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))) k))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2)))))

Calls

6 calls:

Time	Variable		Point	Expression
51.0ms	n	@	0	((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) 2)) (sqrt n)) (sqrt (* (PI) 2)) (* (PI) 2) (sqrt n) (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2)) (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt (* (PI) n)) (* (PI) n) (log (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* 2 n) (sqrt 2) (sqrt (* (* 2 n) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* k n) (PI)) 2)) (* (* (* k n) (PI)) 2) (* (* k n) (PI)) (* k n))
42.0ms	k	@	0	((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) 2)) (sqrt n)) (sqrt (* (PI) 2)) (* (PI) 2) (sqrt n) (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2)) (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt (* (PI) n)) (* (PI) n) (log (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* 2 n) (sqrt 2) (sqrt (* (* 2 n) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* k n) (PI)) 2)) (* (* (* k n) (PI)) 2) (* (* k n) (PI)) (* k n))
32.0ms	n	@	inf	((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) 2)) (sqrt n)) (sqrt (* (PI) 2)) (* (PI) 2) (sqrt n) (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2)) (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt (* (PI) n)) (* (PI) n) (log (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* 2 n) (sqrt 2) (sqrt (* (* 2 n) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* k n) (PI)) 2)) (* (* (* k n) (PI)) 2) (* (* k n) (PI)) (* k n))
23.0ms	n	@	-inf	((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) 2)) (sqrt n)) (sqrt (* (PI) 2)) (* (PI) 2) (sqrt n) (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2)) (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt (* (PI) n)) (* (PI) n) (log (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* 2 n) (sqrt 2) (sqrt (* (* 2 n) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* k n) (PI)) 2)) (* (* (* k n) (PI)) 2) (* (* k n) (PI)) (* k n))
19.0ms	k	@	inf	((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) 2)) (sqrt n)) (sqrt (* (PI) 2)) (* (PI) 2) (sqrt n) (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2)) (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt (* (PI) n)) (* (PI) n) (log (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* 2 n) (sqrt 2) (sqrt (* (* 2 n) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* k n) (PI)) 2)) (* (* (* k n) (PI)) 2) (* (* k n) (PI)) (* k n))

rewrite123.0ms (1.8%)

Memory

13.5MiB live, 103.0MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	523	5694
0	612	5047
0	2287	5010

Stop Event

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

Counts

200 → 385

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))
(.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 n k)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(sqrt.f64 n)
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
(fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
(.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64)))) k))
(/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64)))) k)
(fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))
(.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))
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(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))
(.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))
(*.f64 (pow.f64 k #s(literal 3 binary64)) n)
(pow.f64 k #s(literal 3 binary64))
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(sqrt.f64 (.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64))
(.f64 (.f64 k n) (PI.f64))
(*.f64 k n)
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
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#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
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#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
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#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* (PI) (/ n k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (PI) (/ n k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
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#s(approx (sqrt (* (* 2 n) (PI))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))) k))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2)))))

Outputs
(.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k)) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))
(.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64)))
(/.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k)
(fma.f64 (/.f64 n k) (PI.f64) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (PI.f64) (/.f64 n k) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 n (/.f64 (PI.f64) k) (*.f64 (/.f64 n k) (PI.f64)))
(+.f64 (.f64 (/.f64 n k) (PI.f64)) (.f64 (/.f64 n k) (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 k))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 (neg.f64 n) (neg.f64 k))
(/.f64 n k)
(.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) #s(approx ( (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
(.f64 #s(approx ( (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) #s(approx ( (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))
(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
(pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
(pow.f64 n #s(literal 1/2 binary64))
(sqrt.f64 n)
(/.f64 (neg.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64))) (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))) (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)) (-.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))
(fma.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)))
(fma.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)))
(fma.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))
(fma.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))
(-.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)) (.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(+.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)))
(.f64 (.f64 k (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k)
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
(.f64 k (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
(.f64 (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(.f64 (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 (*.f64 (PI.f64) n))))
(.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))
(fma.f64 (log.f64 n) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 n) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (.f64 (log.f64 n) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))
(+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 n)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(log.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
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#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64))) k (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (+ (* -1/2 k) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* -1/2 k) 1/2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (* (PI) (/ n k)) 2) (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))
#s(approx (* (PI) (/ n k)) (*.f64 (/.f64 n k) (PI.f64)))
#s(approx (/ n k) (/.f64 n k))
#s(approx (/ 1 (sqrt k)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/48 binary64)) (pow.f64 k #s(literal 3/2 binary64)) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64))) k (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/48 binary64)) k (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64))) k (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))
#s(approx (* (* (pow k 3) n) (PI)) (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))
#s(approx (* (pow k 3) n) (*.f64 (pow.f64 k #s(literal 3 binary64)) n))
#s(approx (pow k 3) (pow.f64 k #s(literal 3 binary64)))
#s(approx (sqrt (* (* (* k n) (PI)) 2)) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (* (* k n) (PI)) 2) (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
#s(approx (* (* k n) (PI)) (.f64 (.f64 (PI.f64) n) k))
#s(approx (* k n) (*.f64 n k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64)))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (.f64 (fma.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64)))) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64)))) k))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) (.f64 (.f64 k k) (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64)))) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))) #s(literal -1 binary64)))
#s(approx (/ 1 (sqrt k)) (*.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (sqrt k) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k))))
#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) #s(literal 2 binary64)))
#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (.f64 (neg.f64 k) (fma.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal 1/2 binary64) (neg.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) k)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))))
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#s(approx n n)
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#s(approx (sqrt n) (sqrt.f64 n))
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#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
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#s(approx (/ (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
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#s(approx (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) (.f64 k (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))
#s(approx (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2)) (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) k) (.f64 n (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64)))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* k n) (PI)) 2))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64)))) n))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
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#s(approx (sqrt (* (* (PI) (/ n k)) 2)) (neg.f64 (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))))
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#s(approx (sqrt n) (neg.f64 (*.f64 (sqrt.f64 n) #s(literal -1 binary64))))
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#s(approx (+ (* (* k (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2))) -1/2) (sqrt (* (* 2 n) (PI)))) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (neg.f64 k) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 (.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))
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#s(approx (* (* (sqrt (* (PI) n)) (log (* (* 2 n) (PI)))) (sqrt 2)) (neg.f64 (.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
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#s(approx (sqrt (* (PI) n)) (neg.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n)))))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (* (sqrt (* (PI) 2)) (sqrt n)) (neg.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))))
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#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (neg.f64 (.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (neg.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))))

eval81.0ms (1.2%)

Memory: 20.1MiB live, 116.2MiB allocated; 30ms collecting garbage
Compiler: Compiled 17 550 to 1 518 computations (91.4% saved)

prune51.0ms (0.8%)

Memory

-40.1MiB live, 105.9MiB allocated; 17ms collecting garbage

Pruning

26 alts after pruning (21 fresh and 5 done)

	Pruned	Kept	Total
New	365	9	374
Fresh	3	12	15
Picked	4	1	5
Done	0	4	4
Total	372	26	398

Accuracy

99.9%

Counts

398 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
	47.6%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
	47.0%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))
	47.0%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (exp ( (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
✓	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	98.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
	96.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
	96.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	96.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))))
	46.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))))
	46.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
✓	46.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
	46.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))))
✓	47.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	47.0%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(approx (+ ( -1/2 k) 1/2) #s(literal 1/2 binary64)))))
	70.9%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	56.7%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx ( (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64))) k (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))))
	96.3%	(.f64 (sqrt.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	54.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
✓	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))))

Compiler

Compiled 2 541 to 914 computations (64% saved)

regimes57.0ms (0.9%)

Memory

32.4MiB live, 124.2MiB allocated; 6ms collecting garbage

Counts

51 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (exp ( (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(approx (+ ( -1/2 k) 1/2) #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k))
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) k) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 k n) (PI.f64)) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx ( (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64))) k (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))))
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (exp ( (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))

Outputs
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))

Calls

4 calls:

15.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
15.0ms	k
13.0ms	n
11.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.6%	1	`k`
99.6%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes27.0ms (0.4%)

Memory

13.9MiB live, 58.9MiB allocated; 5ms collecting garbage

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (exp ( (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(approx (+ ( -1/2 k) 1/2) #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Outputs
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))

Calls

4 calls:

9.0ms	k
6.0ms	n
6.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
5.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.6%	1	`k`
99.6%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes26.0ms (0.4%)

Memory

-40.3MiB live, 56.5MiB allocated; 9ms collecting garbage

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (exp ( (log (* (* 2 n) (PI))) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(approx (+ ( -1/2 k) 1/2) #s(literal 1/2 binary64)))))

Outputs
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))

Calls

4 calls:

9.0ms	n
5.0ms	k
5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
47.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
47.0%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
47.0%	1	`k`
47.0%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes11.0ms (0.2%)

Memory

21.5MiB live, 21.5MiB allocated; 0ms collecting garbage

Counts

7 → 2

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))

Outputs

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))

Calls

4 calls:

3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	k
2.0ms	n
2.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
46.9%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
47.1%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
46.9%	2	`n`
37.7%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes6.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms collecting garbage

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))))

Calls

3 calls:

2.0ms

(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)

2.0ms

(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
37.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
37.7%	1	`n`
37.7%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 22 to 21 computations (4.5% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	9.257831882868097e+139	1.1473328003444379e+149

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify88.0ms (1.3%)

Memory

-31.8MiB live, 62.2MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	186
1	125	180
2	258	180
3	757	176
4	4157	176

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 100000000000000005928380124081487003706362488767045328864850074482999577828473980652023296508018124569151792237293382948229697163514582401024 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))))

Outputs
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 100000000000000005928380124081487003706362488767045328864850074482999577828473980652023296508018124569151792237293382948229697163514582401024 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))))

derivations42.0ms (0.6%)

Memory

17.6MiB live, 64.5MiB allocated; 8ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 198 to 79 computations (60.1% saved)

preprocess31.0ms (0.5%)

Memory: 24.6MiB live, 70.0MiB allocated; 3ms collecting garbage
Compiler: Compiled 428 to 184 computations (57% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze269.0ms (4%)

sample4.2s (63.7%)

explain272.0ms (4.1%)

preprocess245.0ms (3.7%)

eval0.0ms (0%)

prune10.0ms (0.2%)

series75.0ms (1.1%)

rewrite108.0ms (1.6%)

eval17.0ms (0.3%)

prune19.0ms (0.3%)

series116.0ms (1.7%)

rewrite84.0ms (1.3%)

eval46.0ms (0.7%)

prune29.0ms (0.4%)

series205.0ms (3.1%)

rewrite104.0ms (1.6%)

eval37.0ms (0.6%)

prune57.0ms (0.8%)

series189.0ms (2.8%)

rewrite123.0ms (1.8%)

eval81.0ms (1.2%)

prune51.0ms (0.8%)

regimes57.0ms (0.9%)

regimes27.0ms (0.4%)

regimes26.0ms (0.4%)

regimes11.0ms (0.2%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

simplify88.0ms (1.3%)

derivations42.0ms (0.6%)

preprocess31.0ms (0.5%)

end0.0ms (0%)

Profiling