Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze1.1s (23%)

Memory

-129.1MiB live, 197.1MiB allocated; 1.4s 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)

sample2.7s (56.6%)

Memory

127.3MiB live, 3 301.3MiB allocated; 811ms collecting garbage

Samples

1.0s	5 383×	1	invalid
969.0ms	8 256×	0	valid
102.0ms	454×	2	invalid
46.0ms	249×	0	exit
20.0ms	360×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-pow: 458.0ms (33.2% of total)

ival-mult!: 252.0ms (18.3% of total)

adjust: 208.0ms (15.1% of total)

ival-sqrt: 185.0ms (13.4% of total)

ival-div!: 177.0ms (12.8% of total)

ival-sub!: 101.0ms (7.3% of total)

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

exact: 0.0ms (0% of total)

Bogosity

preprocess49.0ms (1%)

Memory

-8.8MiB live, 37.3MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	101
1	128	87
2	466	87
3	2057	86

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.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))))

Symmetry

(abs k)

Compiler

Compiled 30 to 26 computations (13.3% saved)

series105.0ms (2.2%)

Memory

-24.2MiB live, 36.7MiB allocated; 71ms 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
71.0ms	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))
20.0ms	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))
7.0ms	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))
2.0ms	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))

rewrite22.0ms (0.5%)

Memory

11.1MiB live, 11.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	181	965
0	195	953

Stop Event

1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

47 → 47

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

eval4.0ms (0.1%)

Memory: 5.2MiB live, 5.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 612 to 222 computations (63.7% saved)

prune16.0ms (0.3%)

Memory

-32.9MiB live, 14.8MiB allocated; 11ms collecting garbage

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	22	12	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	12	35

Accuracy

99.9%

Counts

35 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.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) (.f64 #s(literal -1/2 binary64) k)))))
	53.8%	(.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))))
▶	48.0%	(.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) #s(literal 1/2 binary64))))
	63.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
	57.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
▶	48.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
	47.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
▶	99.4%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	53.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
	52.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
▶	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
	96.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))

Compiler

Compiled 756 to 630 computations (16.7% saved)

series97.0ms (2%)

Memory

36.5MiB live, 128.3MiB allocated; 6ms collecting garbage

Counts

42 → 66

Calls

Call 1

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

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 (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx (sqrt (/ (* n (PI)) k)) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (/ (* n (PI)) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) #s(hole binary64 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))))
#s(approx (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* k (* (log (* 2 (* n (PI)))) (sqrt 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 (* (* 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 (* 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 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#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 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))))
#s(approx (sqrt (/ (* n (PI)) k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) #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 (* (/ 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 (* n (PI)) #s(hole binary64 (* n (PI))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))))
#s(approx (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (sqrt (* n (PI))) #s(hole binary64 (sqrt (* n (PI)))))
#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 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) #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 (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (* n (PI))))))
#s(approx (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (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 (* (/ 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 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (/ (* n (PI)) k)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) #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)) (* (pow (sqrt -1) 2) (sqrt 2))))))))
#s(approx (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) #s(hole binary64 (* -1 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (* n (PI)))))))
#s(approx (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* k (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (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 (sqrt (* n (PI))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (* n (PI))) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))))

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	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) (+ 1/2 (* -1/2 k)) 1/2 (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (sqrt (* n (PI))) (* (sqrt (* n (PI))) (sqrt 2)))
24.0ms	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) (+ 1/2 (* -1/2 k)) 1/2 (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (sqrt (* n (PI))) (* (sqrt (* n (PI))) (sqrt 2)))
12.0ms	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) (+ 1/2 (* -1/2 k)) 1/2 (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (sqrt (* n (PI))) (* (sqrt (* n (PI))) (sqrt 2)))
12.0ms	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) (+ 1/2 (* -1/2 k)) 1/2 (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (sqrt (* n (PI))) (* (sqrt (* n (PI))) (sqrt 2)))
10.0ms	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) (+ 1/2 (* -1/2 k)) 1/2 (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (sqrt (* n (PI))) (* (sqrt (* n (PI))) (sqrt 2)))

rewrite35.0ms (0.7%)

Memory

-30.0MiB live, 18.8MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	285	2191
0	342	2175

Stop Event

1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

108 → 109

Calls

Call 1

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

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

eval7.0ms (0.1%)

Memory: 10.8MiB live, 10.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 288 to 444 computations (65.5% saved)

prune12.0ms (0.2%)

Memory

13.3MiB live, 13.3MiB allocated; 0ms collecting garbage

Pruning

15 alts after pruning (10 fresh and 5 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	7	7
Picked	0	5	5
Done	0	0	0
Total	68	15	83

Accuracy

99.9%

Counts

83 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(.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) (.f64 #s(literal -1/2 binary64) k)))))
	53.8%	(.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))))
✓	48.0%	(.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) #s(literal 1/2 binary64))))
	63.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
▶	57.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
✓	48.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
▶	47.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
	53.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (.f64 n (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (sqrt.f64 (/.f64 (PI.f64) n))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))))
	43.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (.f64 n (PI.f64)))))))))
✓	99.4%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	48.0%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(approx (- 1 k) #s(literal 1 binary64)) #s(literal 2 binary64))))
	53.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
▶	52.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
✓	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
▶	96.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))

Compiler

Compiled 911 to 741 computations (18.7% saved)

series98.0ms (2%)

Memory

21.9MiB live, 113.9MiB allocated; 5ms collecting garbage

Counts

55 → 128

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (sqrt (/ 1 k)) (/ 1 k) 1 k (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (* n (PI)) n (PI) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (sqrt 2) (* (/ 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 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* (pow k 3) (* n (PI)))) (* (pow k 3) (* n (PI))) (pow k 3) 3 (* (log (* 2 (* n (PI)))) (sqrt 2)) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* 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))) (+ (* -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))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (pow (log (* 2 (* n (PI)))) 2))
17.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (sqrt (/ 1 k)) (/ 1 k) 1 k (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (* n (PI)) n (PI) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (sqrt 2) (* (/ 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 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* (pow k 3) (* n (PI)))) (* (pow k 3) (* n (PI))) (pow k 3) 3 (* (log (* 2 (* n (PI)))) (sqrt 2)) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* 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))) (+ (* -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))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (pow (log (* 2 (* n (PI)))) 2))
17.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (sqrt (/ 1 k)) (/ 1 k) 1 k (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (* n (PI)) n (PI) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (sqrt 2) (* (/ 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 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* (pow k 3) (* n (PI)))) (* (pow k 3) (* n (PI))) (pow k 3) 3 (* (log (* 2 (* n (PI)))) (sqrt 2)) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* 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))) (+ (* -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))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (pow (log (* 2 (* n (PI)))) 2))
15.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (sqrt (/ 1 k)) (/ 1 k) 1 k (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (* n (PI)) n (PI) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (sqrt 2) (* (/ 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 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* (pow k 3) (* n (PI)))) (* (pow k 3) (* n (PI))) (pow k 3) 3 (* (log (* 2 (* n (PI)))) (sqrt 2)) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* 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))) (+ (* -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))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (pow (log (* 2 (* n (PI)))) 2))
15.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (sqrt (/ 1 k)) (/ 1 k) 1 k (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (* n (PI)) n (PI) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (sqrt 2) (* (/ 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 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* (pow k 3) (* n (PI)))) (* (pow k 3) (* n (PI))) (pow k 3) 3 (* (log (* 2 (* n (PI)))) (sqrt 2)) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* 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))) (+ (* -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))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (pow (log (* 2 (* n (PI)))) 2))

rewrite43.0ms (0.9%)

Memory

-9.8MiB live, 36.5MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	482	5608
0	579	5569

Stop Event

1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

183 → 186

Calls

Call 1

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

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

eval23.0ms (0.5%)

Memory: -26.5MiB live, 24.3MiB allocated; 4ms collecting garbage
Compiler: Compiled 4 227 to 1 043 computations (75.3% saved)

prune17.0ms (0.4%)

Memory

22.3MiB live, 22.3MiB allocated; 0ms collecting garbage

Pruning

22 alts after pruning (15 fresh and 7 done)

	Pruned	Kept	Total
New	145	11	156
Fresh	1	4	5
Picked	1	4	5
Done	2	3	5
Total	149	22	171

Accuracy

99.9%

Counts

171 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(.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) (.f64 #s(literal -1/2 binary64) k)))))
	53.8%	(.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))))
✓	48.0%	(.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) #s(literal 1/2 binary64))))
	63.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
✓	57.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
✓	47.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
	43.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (.f64 n (PI.f64)))))))))
▶	99.4%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))))
	48.0%	(.f64 #s(approx (/ 1 (sqrt k)) (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(literal 1/2 binary64))))
	53.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
✓	52.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
▶	37.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (.f64 (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
	56.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (.f64 n (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (.f64 (sqrt.f64 (/.f64 (.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
✓	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	96.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
▶	96.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(approx (- 1 k) (.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))))))))
	45.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) #s(approx (* (log (* 2 (* n (PI)))) (- 1 k)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
	57.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (exp ( 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))))
	48.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (exp ( 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))))
	47.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (exp ( 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
▶	16.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 k #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))))
▶	2.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))

Compiler

Compiled 1 516 to 1 271 computations (16.2% saved)

series89.0ms (1.8%)

Memory

-25.4MiB live, 114.2MiB allocated; 7ms collecting garbage

Counts

52 → 116

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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 (* -1/2 k)) 1/2 (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) (* (log (* 2 (* n (PI)))) (- 1 k)) (- 1 k) (* k (- (/ 1 k) 1)) (- (/ 1 k) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))) (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2)) (sqrt (/ (* n (PI)) (pow k 3))) (/ (* n (PI)) (pow k 3)) (pow k 3) 3)
14.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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 (* -1/2 k)) 1/2 (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) (* (log (* 2 (* n (PI)))) (- 1 k)) (- 1 k) (* k (- (/ 1 k) 1)) (- (/ 1 k) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))) (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2)) (sqrt (/ (* n (PI)) (pow k 3))) (/ (* n (PI)) (pow k 3)) (pow k 3) 3)
14.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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 (* -1/2 k)) 1/2 (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) (* (log (* 2 (* n (PI)))) (- 1 k)) (- 1 k) (* k (- (/ 1 k) 1)) (- (/ 1 k) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))) (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2)) (sqrt (/ (* n (PI)) (pow k 3))) (/ (* n (PI)) (pow k 3)) (pow k 3) 3)
14.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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 (* -1/2 k)) 1/2 (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) (* (log (* 2 (* n (PI)))) (- 1 k)) (- 1 k) (* k (- (/ 1 k) 1)) (- (/ 1 k) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))) (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2)) (sqrt (/ (* n (PI)) (pow k 3))) (/ (* n (PI)) (pow k 3)) (pow k 3) 3)
13.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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 (* -1/2 k)) 1/2 (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) (* (log (* 2 (* n (PI)))) (- 1 k)) (- 1 k) (* k (- (/ 1 k) 1)) (- (/ 1 k) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))) (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2)) (sqrt (/ (* n (PI)) (pow k 3))) (/ (* n (PI)) (pow k 3)) (pow k 3) 3)

rewrite38.0ms (0.8%)

Memory

10.9MiB live, 10.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	421	4943
0	492	4888

Stop Event

1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

168 → 169

Calls

Call 1

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

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

eval13.0ms (0.3%)

Memory: 10.4MiB live, 10.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 3 238 to 861 computations (73.4% saved)

prune21.0ms (0.4%)

Memory

15.3MiB live, 15.3MiB allocated; 0ms collecting garbage

Pruning

22 alts after pruning (11 fresh and 11 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	3	7	10
Picked	1	4	5
Done	0	7	7
Total	130	22	152

Accuracy

99.9%

Counts

152 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(.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) (.f64 #s(literal -1/2 binary64) k)))))
	53.8%	(.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))))
✓	48.0%	(.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) #s(literal 1/2 binary64))))
	63.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
✓	57.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
✓	47.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
	43.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (.f64 n (PI.f64)))))))))
✓	99.4%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))))
	48.0%	(.f64 #s(approx (/ 1 (sqrt k)) (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(literal 1/2 binary64))))
	48.9%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
	47.9%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
	53.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
✓	52.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
✓	37.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (.f64 (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
	56.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (.f64 n (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (.f64 (sqrt.f64 (/.f64 (.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
✓	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	96.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
✓	96.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(approx (- 1 k) (.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))))))))
	45.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) #s(approx (* (log (* 2 (* n (PI)))) (- 1 k)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
	33.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (.f64 k #s(approx (+ ( -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 k #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))))
	27.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (.f64 k #s(approx (+ ( -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))) (.f64 n (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 (PI.f64) (.f64 k n))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (.f64 (sqrt.f64 (/.f64 (PI.f64) (.f64 (pow.f64 k #s(literal 3 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)))))))))
✓	2.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))

Compiler

Compiled 1 636 to 969 computations (40.8% saved)

regimes83.0ms (1.7%)

Memory

-32.8MiB live, 18.5MiB allocated; 3ms collecting garbage

Counts

31 → 1

Calls

Call 1

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

Calls

4 calls:

57.0ms	k
8.0ms	n
8.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms	(.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
99.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.4%	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))))`
99.4%	1	`k`
99.4%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes16.0ms (0.3%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Counts

13 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

4.0ms	n
4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	k
3.0ms	(.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
99.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.4%	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))))`
99.4%	1	`k`
99.4%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes15.0ms (0.3%)

Memory

10.4MiB live, 10.4MiB allocated; 0ms collecting garbage

Counts

12 → 2

Calls

Call 1

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

Calls

4 calls:

4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	n
4.0ms	k
3.0ms	(.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
63.8%	4	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
97.0%	3	`(.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))))`
97.0%	2	`k`
63.8%	4	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes6.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated; 0ms collecting garbage

Counts

9 → 2

Calls

Call 1

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

Outputs

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

Calls

2 calls:

3.0ms	k
3.0ms	(.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
65.4%	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))))`
65.3%	2	`k`

Compiler

Compiled 16 to 15 computations (6.3% saved)

regimes12.0ms (0.2%)

Memory

8.5MiB live, 8.5MiB allocated; 0ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

Calls

4 calls:

3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	n
3.0ms	k
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
48.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
48.0%	1	`n`
48.0%	1	`k`
48.0%	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))))`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes13.0ms (0.3%)

Memory

-39.5MiB live, 8.2MiB allocated; 1ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

Outputs
(.f64 #s(approx (/ 1 (sqrt k)) (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(literal 1/2 binary64))))

Calls

4 calls:

6.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	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
48.0%	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))))`
48.0%	1	`k`
48.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
48.0%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes8.0ms (0.2%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
2.0ms	k
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
47.9%	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))))`
47.9%	1	`k`
47.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
47.9%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes5.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs

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

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

Outputs

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

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

Calls

4 calls:

1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	k
1.0ms	n
1.0ms	(.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
48.1%	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))))`
38.8%	2	`k`
47.8%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
47.8%	2	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes4.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	n
1.0ms	k
1.0ms	(.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
37.1%	1	`k`
37.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
37.1%	1	`n`
37.1%	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 23 computations (-4.5% saved)

bsearch13.0ms (0.3%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.8298369388293177	41.1886902323454

Samples

7.0ms

112×

valid

Compiler

Compiled 264 to 277 computations (-4.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-pow: 2.0ms (40.7% of total)

ival-sqrt: 1.0ms (20.3% of total)

ival-div!: 1.0ms (20.3% of total)

ival-mult!: 1.0ms (20.3% of total)

ival-sub!: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.6647690773439945e-70	2.0038776467832353e-69

Compiler

Compiled 18 to 18 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.6725222937764953e+151	1.3254862145491741e+154

Compiler

Compiled 18 to 18 computations (0% saved)

derivations17.0ms (0.4%)

Memory

6.0MiB live, 6.0MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 200 to 105 computations (47.5% saved)

preprocess93.0ms (1.9%)

Memory: -10.4MiB live, 83.3MiB allocated; 6ms collecting garbage
Remove: (abs k)
Compiler: Compiled 871 to 676 computations (22.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.1s (23%)

sample2.7s (56.6%)

preprocess49.0ms (1%)

series105.0ms (2.2%)

rewrite22.0ms (0.5%)

eval4.0ms (0.1%)

prune16.0ms (0.3%)

series97.0ms (2%)

rewrite35.0ms (0.7%)

eval7.0ms (0.1%)

prune12.0ms (0.2%)

series98.0ms (2%)

rewrite43.0ms (0.9%)

eval23.0ms (0.5%)

prune17.0ms (0.4%)

series89.0ms (1.8%)

rewrite38.0ms (0.8%)

eval13.0ms (0.3%)

prune21.0ms (0.4%)

regimes83.0ms (1.7%)

regimes16.0ms (0.3%)

regimes15.0ms (0.3%)

regimes6.0ms (0.1%)

regimes12.0ms (0.2%)

regimes13.0ms (0.3%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch13.0ms (0.3%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

derivations17.0ms (0.4%)

preprocess93.0ms (1.9%)

end0.0ms (0%)

Profiling