Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze116.0ms (2.1%)

Memory

-45.0MiB live, 103.7MiB allocated; 41ms 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)

sample2.8s (50.2%)

Memory

83.3MiB live, 3 856.2MiB allocated; 880ms collecting garbage

Samples

1.3s	5 528×	1	invalid
656.0ms	8 255×	0	valid
145.0ms	504×	2	invalid
23.0ms	367×	0	invalid
23.0ms	248×	0	exit
0.0ms	1×	1	valid

Precisions

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

ival-pow: 499.0ms (35.8% of total)

ival-mult!: 256.0ms (18.3% of total)

adjust: 219.0ms (15.7% of total)

ival-div!: 215.0ms (15.4% of total)

ival-sqrt: 138.0ms (9.9% of total)

ival-sub!: 67.0ms (4.8% of total)

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

exact: 0.0ms (0% of total)

Bogosity

preprocess41.0ms (0.7%)

Memory

-11.8MiB live, 32.7MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	101
1	128	87
2	462	87
3	2175	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 32 to 26 computations (18.8% saved)

series100.0ms (1.8%)

Memory

14.1MiB live, 242.9MiB allocated; 57ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	158	937

Stop Event

1×	iter-limit

Counts

13 → 37

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

Calls

6 calls:

Time	Variable	Point
43.0ms	n	0
25.0ms	n	-inf
12.0ms	n	inf
2.0ms	k	0
2.0ms	k	-inf

rewrite103.0ms (1.9%)

Memory

1.5MiB live, 192.8MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	97	51
2	351	51
3	1690	51
0	4163	48

Stop Event

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

Counts

13 → 308

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
(.f64 (neg.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64))
(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(neg.f64 (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 k (/.f64 #s(literal -1/2 binary64) #s(literal 2 binary64))) (pow.f64 k (/.f64 #s(literal -1/2 binary64) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal -1 binary64))
(*.f64 (pow.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 k) #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 k #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 #s(literal -2 binary64) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
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(neg.f64 (.f64 #s(literal -2 binary64) (.f64 n (PI.f64))))
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(fma.f64 (.f64 (cbrt.f64 (PI.f64)) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 n (PI.f64)))
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(fma.f64 (.f64 n (PI.f64)) #s(literal 1 binary64) (.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64)))
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(fma.f64 (cbrt.f64 (PI.f64)) (.f64 (cbrt.f64 (PI.f64)) (.f64 (cbrt.f64 (PI.f64)) n)) (*.f64 n (PI.f64)))
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(fma.f64 n (PI.f64) (*.f64 n (PI.f64)))
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(fma.f64 #s(literal 1 binary64) (.f64 n (PI.f64)) (.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
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(-.f64 (.f64 n (PI.f64)) (.f64 (neg.f64 n) (PI.f64)))
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(-.f64 (.f64 n (PI.f64)) (neg.f64 (.f64 n (PI.f64))))
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(+.f64 (.f64 #s(literal 1 binary64) (.f64 n (PI.f64))) (.f64 #s(literal 1 binary64) (.f64 n (PI.f64))))
(+.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))
(log.f64 (pow.f64 (exp.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64)))
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(.f64 (.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (PI.f64)) (PI.f64))) (PI.f64))
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(.f64 (.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(.f64 (.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
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(.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)))))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)))
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(/.f64 (-.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (neg.f64 (PI.f64))))
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(neg.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))
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(neg.f64 (-.f64 (neg.f64 (PI.f64)) (PI.f64)))
(-.f64 (PI.f64) (*.f64 (neg.f64 (PI.f64)) #s(literal 1 binary64)))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (log.f64 (neg.f64 (exp.f64 (PI.f64)))) (log.f64 (neg.f64 (exp.f64 (PI.f64)))))
(+.f64 (log.f64 (exp.f64 (PI.f64))) (log.f64 (exp.f64 (PI.f64))))
(+.f64 (PI.f64) (PI.f64))
(log.f64 (exp.f64 (+.f64 (PI.f64) (PI.f64))))
#s(literal 2 binary64)
(PI.f64)
n
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) #s(literal 1/2 binary64))
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(*.f64 (-.f64 #s(literal 2 binary64) (+.f64 k k)) #s(literal 1/4 binary64))
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(*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (/.f64 (-.f64 #s(literal 2 binary64) (+.f64 k k)) #s(literal 2 binary64)) #s(literal 2 binary64))
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(/.f64 (+.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3 binary64)) (pow.f64 (.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 k #s(literal -1/2 binary64)) (.f64 k #s(literal -1/2 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (+.f64 #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) (neg.f64 k))) #s(literal -4 binary64))
(/.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 k))) #s(literal 4 binary64))
(/.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (neg.f64 k))) #s(literal 4 binary64))
(/.f64 (-.f64 #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) k)) #s(literal -4 binary64))
(/.f64 (-.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 k))) #s(literal -4 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (+.f64 k k))) #s(literal -4 binary64))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) k) (.f64 #s(literal 1/2 binary64) k))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (-.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal 3 binary64))) (fma.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (.f64 #s(literal 1/2 binary64) k) (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (-.f64 #s(literal 2 binary64) (+.f64 k k)) #s(literal 4 binary64))
(/.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -2 binary64))
(/.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (+.f64 k k))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))
(neg.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(fma.f64 (neg.f64 k) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 k) #s(literal 1/2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal -1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 k k) #s(literal 4 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(+.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 k)) #s(literal 1/2 binary64))
(+.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (neg.f64 k)))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 k))) (neg.f64 k))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 k #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (neg.f64 k) #s(literal 2 binary64) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (neg.f64 k) (neg.f64 k)) (.f64 #s(literal 1 binary64) #s(literal 1 binary64))) (-.f64 (neg.f64 k) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 (neg.f64 k) #s(literal 3 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (fma.f64 (neg.f64 k) (neg.f64 k) (-.f64 (.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (.f64 (neg.f64 k) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (.f64 (neg.f64 k) (neg.f64 k))) (-.f64 #s(literal 1 binary64) (neg.f64 k)))
(/.f64 (+.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (pow.f64 (neg.f64 k) #s(literal 3 binary64))) (fma.f64 #s(literal 1 binary64) #s(literal 1 binary64) (-.f64 (.f64 (neg.f64 k) (neg.f64 k)) (.f64 #s(literal 1 binary64) (neg.f64 k)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (.f64 k k)) (+.f64 #s(literal 1 binary64) k))
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(neg.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)))
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)))
(neg.f64 (-.f64 k #s(literal 1 binary64)))
(fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 0 binary64)))
(fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
(fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 0 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
(fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) k) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) k) #s(literal 0 binary64))
(-.f64 (neg.f64 k) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (neg.f64 k) #s(literal 1 binary64))
(+.f64 (-.f64 #s(literal 1 binary64) k) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 0 binary64)))
(+.f64 (-.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
(+.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 0 binary64))
(+.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (neg.f64 k)))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) k))
(+.f64 #s(literal 1 binary64) (neg.f64 k))

eval49.0ms (0.9%)

Memory: -11.0MiB live, 96.9MiB allocated; 30ms collecting garbage
Compiler: Compiled 7 436 to 1 275 computations (82.9% saved)

prune17.0ms (0.3%)

Memory

0.4MiB live, 46.9MiB allocated; 2ms collecting garbage

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	319	16	335
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	320	16	336

Accuracy

100.0%

Counts

336 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	99.4%	(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	99.5%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (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))))
	49.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 k #s(literal -1/2 binary64))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal -1/2 binary64))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
	73.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
▶	73.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
▶	95.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 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))))
	96.2%	(.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
	95.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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)))) (sqrt.f64 k)))

Compiler

Compiled 632 to 502 computations (20.6% saved)

series210.0ms (3.8%)

Memory

16.6MiB live, 385.1MiB allocated; 63ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	501	4040

Stop Event

1×	iter-limit

Counts

36 → 118

Calls

Call 1

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

Outputs
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (.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)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (.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)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (fma.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* k -1/2) 1/2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (* (log (* n (+ (PI) (PI)))) (+ (* k -1/2) 1/2)) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))
#s(approx (* (log (* n (+ (PI) (PI)))) (+ (* k -1/2) 1/2)) (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 (* (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt k)))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt k)))) (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)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt k)))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #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)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt k)))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #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)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))))))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64)))))
#s(approx (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt k)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))))
#s(approx (* (sqrt (sqrt k)) (sqrt (sqrt k))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64)))
#s(approx (sqrt (sqrt k)) (sqrt.f64 (sqrt.f64 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 (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2)))) (/.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2)))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2)))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (.f64 k (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))) (sqrt.f64 k)))))))) (/.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2)))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (.f64 k (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))) (sqrt.f64 k)) (.f64 k (fma.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))) (sqrt.f64 k)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))) (sqrt.f64 k)) (fma.f64 #s(literal -1/48 binary64) (/.f64 (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (.f64 #s(literal -1/48 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 3 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (sqrt.f64 k))))))))))))) (/.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (sqrt.f64 k))))
#s(approx (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))
#s(approx (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (.f64 k (fma.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))))))))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (.f64 k (fma.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))) (.f64 k (fma.f64 #s(literal -1/16 binary64) (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/16 binary64) (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 3 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))))))))))))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))
#s(approx (pow (* n (PI)) (+ (* k -1/2) 1/2)) (fma.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (log.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))))
#s(approx (pow (* n (PI)) (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))))
#s(approx (pow (* n (PI)) (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 3 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))))))) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))))
#s(approx (pow 2 (+ (* k -1/2) 1/2)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
#s(approx (pow 2 (+ (* k -1/2) 1/2)) (fma.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (log.f64 #s(literal 2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
#s(approx (pow 2 (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 #s(literal 2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 k (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
#s(approx (pow 2 (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 #s(literal 2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 k (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k)))))
#s(approx (+ (* k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ (* k -1/2) 1/2) (.f64 k (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.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) k)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (log (* n (+ (PI) (PI)))) (+ (* k -1/2) 1/2)) (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))
#s(approx (* (log (* n (+ (PI) (PI)))) (+ (* k -1/2) 1/2)) (.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 (* (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt k)))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.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) k)))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64)))))
#s(approx (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt k)))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 k #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64)))))
#s(approx (* (sqrt (sqrt k)) (sqrt (sqrt k))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64))))
#s(approx (sqrt (sqrt k)) (*.f64 k (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) 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) (*.f64 #s(literal -1 binary64) k))
#s(approx (- 1 k) (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))))
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#s(approx (pow (* n (PI)) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (log.f64 (.f64 n (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
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#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
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#s(approx (sqrt k) (.f64 #s(literal -1 binary64) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(literal -1 binary64) (/.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))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal -1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (log (* n (+ (PI) (PI)))) (+ (* k -1/2) 1/2)) (.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)))))))))
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#s(approx (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt k)))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 k #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))) #s(literal 2 binary64)))))
#s(approx (* (sqrt (sqrt k)) (sqrt (sqrt k))) (.f64 (pow.f64 k #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))) #s(literal 2 binary64))))
#s(approx (sqrt (sqrt k)) (.f64 #s(literal -1 binary64) (.f64 k (sqrt.f64 (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))))
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#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 (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2)))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (.f64 (log.f64 (.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k))))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
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#s(approx (pow (* n (PI)) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (log.f64 (.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
#s(approx (pow 2 (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
#s(approx (* n (+ (PI) (PI))) (.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 (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)))) (sqrt.f64 k)))
#s(approx (pow (* 2 (* n (PI))) 1/2) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))
#s(approx (* n (PI)) (*.f64 n (PI.f64)))
#s(approx (* (log (* n (+ (PI) (PI)))) (+ (* k -1/2) 1/2)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
#s(approx (log (* n (+ (PI) (PI)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
#s(approx (* (/ 1 (* (sqrt (sqrt k)) (sqrt (sqrt k)))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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)))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))))
#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 (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2)))) (/.f64 (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (PI.f64)))))))
#s(approx (pow (* n (PI)) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (PI.f64))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.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 k)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.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 (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)))) (sqrt.f64 k)))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k)))
#s(approx (pow (* 2 (* n (PI))) 1/2) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (* (log (* n (+ (PI) (PI)))) (+ (* k -1/2) 1/2)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.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 (* n (+ (PI) (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 (sqrt k)) (sqrt (sqrt k)))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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)))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))))
#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 (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2)))) (/.f64 (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (PI.f64)) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 k)))
#s(approx (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (PI.f64)) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (pow (* n (PI)) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (PI.f64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.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 k)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.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 (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)))) (sqrt.f64 k)))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (pow (* 2 (* n (PI))) 1/2) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (* (log (* n (+ (PI) (PI)))) (+ (* k -1/2) 1/2)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.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 (* n (+ (PI) (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 (sqrt k)) (sqrt (sqrt k)))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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)))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))))
#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 (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2)))) (/.f64 (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal -1 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (sqrt.f64 k)))
#s(approx (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal -1 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (pow (* n (PI)) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal -1 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))

Calls

6 calls:

Time	Variable	Point
61.0ms	n	0
51.0ms	n	inf
51.0ms	n	-inf
10.0ms	k	0
8.0ms	k	inf

rewrite147.0ms (2.7%)

Memory

6.8MiB live, 152.6MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	262
0	75	221
1	284	214
2	1019	214
0	4080	214

Stop Event

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

Counts

36 → 1 566

Calls

Call 1

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

Outputs
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (cosh.f64 (.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(.f64 (/.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(.f64 (/.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(.f64 (/.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))))
(.f64 (/.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(.f64 (/.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))) (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))))
(.f64 (/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(.f64 (/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (fabs.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))) (/.f64 (fabs.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))))
(.f64 (/.f64 (fabs.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))) (/.f64 (fabs.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))))
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(/.f64 (-.f64 (.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (.f64 (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) (exp.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)) (log.f64 (.f64 (+.f64 n n) (PI.f64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (-.f64 (.f64 (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))))
(/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal -1/2 binary64) k)) (exp.f64 (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))))
(/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal -1/2 binary64) k)) (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64))) (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(neg.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fma.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal 1/2 binary64) (cosh.f64 (.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fma.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal 1/2 binary64) (sinh.f64 (.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fma.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 1 binary64) (.f64 (sinh.f64 (.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (.f64 #s(literal 1 binary64) (sinh.f64 (.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(sqrt.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(-.f64 (.f64 #s(literal 1 binary64) (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (.f64 #s(literal -1 binary64) (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(-.f64 (.f64 #s(literal 1 binary64) (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (.f64 #s(literal 1 binary64) (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))))
(-.f64 (.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (.f64 (sinh.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)) (log.f64 (.f64 (+.f64 n n) (PI.f64))))) #s(literal 1 binary64)))
(-.f64 (.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (neg.f64 (.f64 (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(-.f64 (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(-.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)) (log.f64 (.f64 (+.f64 n n) (PI.f64))))))
(fabs.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fabs.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)))) (log.f64 (.f64 (+.f64 n n) (PI.f64)))))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 1 binary64) (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (.f64 #s(literal 1 binary64) (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(+.f64 (.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (.f64 (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(+.f64 (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(+.f64 (cosh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 #s(literal -1/2 binary64) k)) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (.f64 (PI.f64) n) (.f64 #s(literal -1/2 binary64) k)))
(*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 #s(literal -1/2 binary64) k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (.f64 (PI.f64) n) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) k)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))

eval159.0ms (2.9%)

Memory: -2.0MiB live, 186.3MiB allocated; 58ms collecting garbage
Compiler: Compiled 36 353 to 4 366 computations (88% saved)

prune38.0ms (0.7%)

Memory

-4.0MiB live, 89.8MiB allocated; 6ms collecting garbage

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	1 257	21	1 278
Fresh	10	1	11
Picked	4	1	5
Done	0	0	0
Total	1 271	23	1 294

Accuracy

100.0%

Counts

1 294 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
▶	99.5%	(/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
	52.1%	(/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ ( k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	99.3%	(/.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64))) (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))
	99.3%	(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 k))
	95.7%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	99.4%	(.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
▶	88.6%	(sqrt.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) k))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k)))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
	46.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) (sqrt.f64 k))))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
▶	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))))
▶	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 n n) (PI.f64)) (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
▶	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) k)))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))

Compiler

Compiled 1 143 to 873 computations (23.6% saved)

series78.0ms (1.4%)

Memory

16.5MiB live, 159.3MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	396	2874

Stop Event

1×	iter-limit

Counts

37 → 102

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
13.0ms	n	inf
12.0ms	n	-inf
12.0ms	n	0
10.0ms	k	-inf
6.0ms	k	0

rewrite127.0ms (2.3%)

Memory

11.7MiB live, 194.8MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	293
0	76	283
1	320	266
2	1083	265
0	4062	261

Stop Event

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

Counts

37 → 1 018

Calls

Call 1

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

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

eval135.0ms (2.5%)

Memory: 15.4MiB live, 241.8MiB allocated; 43ms collecting garbage
Compiler: Compiled 28 825 to 4 253 computations (85.2% saved)

prune112.0ms (2%)

Memory

-6.6MiB live, 102.1MiB allocated; 110ms collecting garbage

Pruning

45 alts after pruning (43 fresh and 2 done)

	Pruned	Kept	Total
New	962	32	994
Fresh	6	11	17
Picked	4	1	5
Done	0	1	1
Total	972	45	1 017

Accuracy

100.0%

Counts

1 017 → 45

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.3%	(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 k))
	99.3%	(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
▶	99.4%	(.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	88.6%	(sqrt.f64 (/.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (fma.f64 k #s(literal -1 binary64) #s(literal 1 binary64))) k))
	52.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) #s(approx ( 2 (+ (* -1/2 k) 1/2)) (*.f64 #s(literal -1 binary64) k))) k))
	88.8%	(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal -1 binary64) k)) (.f64 (+.f64 n n) (PI.f64))) k))
	86.0%	(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) k))
	39.4%	(sqrt.f64 (/.f64 #s(approx (pow (* (+ n n) (PI)) (* 2 (+ (* -1/2 k) 1/2))) (fma.f64 #s(literal -2 binary64) (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))))) (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
	88.6%	(sqrt.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) k)))
▶	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k)))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
	46.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) (sqrt.f64 k))))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	49.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
	49.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	49.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k))) (sqrt.f64 (+.f64 n n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	44.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	44.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (sqrt.f64 k))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))))
▶	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) (sqrt.f64 k))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	39.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
	46.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
✓	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) k)))
	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))
▶	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k))))
	30.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (+.f64 n n) (PI.f64)) k) (/.f64 (*.f64 (+.f64 n n) (PI.f64)) k)))))
	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (fabs.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) k))))
▶	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 (+.f64 n n) (PI.f64)) k)) #s(literal 1/2 binary64))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (/ (* (+ n n) (PI)) (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 k)))))
	38.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k)))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))

Compiler

Compiled 2 498 to 1 870 computations (25.1% saved)

series223.0ms (4.1%)

Memory

-0.1MiB live, 269.9MiB allocated; 49ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	332	2109

Stop Event

1×	iter-limit

Counts

35 → 89

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
100.0ms	n	0
34.0ms	n	-inf
24.0ms	k	-inf
22.0ms	k	0
19.0ms	n	inf

rewrite118.0ms (2.1%)

Memory

17.6MiB live, 164.7MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	289
0	72	262
1	282	247
2	989	246
0	4192	246

Stop Event

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

Counts

35 → 1 255

Calls

Call 1

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

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

eval153.0ms (2.8%)

Memory: -42.3MiB live, 256.1MiB allocated; 53ms collecting garbage
Compiler: Compiled 34 718 to 4 641 computations (86.6% saved)

prune61.0ms (1.1%)

Memory

38.4MiB live, 131.3MiB allocated; 6ms collecting garbage

Pruning

59 alts after pruning (52 fresh and 7 done)

	Pruned	Kept	Total
New	1 064	25	1 089
Fresh	11	27	38
Picked	0	5	5
Done	0	2	2
Total	1 075	59	1 134

Accuracy

100.0%

Counts

1 134 → 59

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.3%	(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 k))
	99.3%	(/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
✓	99.4%	(.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	88.6%	(sqrt.f64 (/.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (fma.f64 k #s(literal -1 binary64) #s(literal 1 binary64))) k))
	52.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) #s(approx ( 2 (+ (* -1/2 k) 1/2)) (*.f64 #s(literal -1 binary64) k))) k))
	88.8%	(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (.f64 #s(literal -1 binary64) k)) (.f64 (+.f64 n n) (PI.f64))) k))
	86.0%	(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 (+.f64 n n) (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) k))
	39.4%	(sqrt.f64 (/.f64 #s(approx (pow (* (+ n n) (PI)) (* 2 (+ (* -1/2 k) 1/2))) (fma.f64 #s(literal -2 binary64) (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))))) (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
	88.6%	(sqrt.f64 (.f64 (pow.f64 (.f64 (+.f64 n n) (PI.f64)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) k)))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
	49.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (sqrt.f64 n)))) (sqrt.f64 k)))
	49.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
✓	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k)))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	47.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (exp.f64 (.f64 (log.f64 n) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
	46.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
	49.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (+.f64 (PI.f64) (PI.f64)))))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (.f64 (/.f64 n (sqrt.f64 k)) (+.f64 (PI.f64) (PI.f64))))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	49.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))))))
	44.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 n n) (sqrt.f64 k))) (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k))) (sqrt.f64 (+.f64 n n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	44.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (sqrt.f64 k))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	39.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
	40.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 k) (+.f64 n n)) (PI.f64)) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n))))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (+.f64 n n) (PI.f64)))))
	44.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 (sqrt.f64 k)))))))
✓	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) (sqrt.f64 k))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64)))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (neg.f64 (sqrt.f64 k)))))
	46.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
✓	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) k)))
	24.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 k (+.f64 n n)) (PI.f64)) (*.f64 k k))))
	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fabs.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))
	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
✓	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k))))
	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
	30.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (+.f64 n n) (PI.f64)) k) (/.f64 (*.f64 (+.f64 n n) (PI.f64)) k)))))
	13.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
✓	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 (+.f64 n n) (PI.f64)) k)) #s(literal 1/2 binary64))))
	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	38.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k)))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))

Compiler

Compiled 1 658 to 1 252 computations (24.5% saved)

regimes433.0ms (7.9%)

Memory

9.2MiB live, 931.8MiB allocated; 121ms collecting garbage

Accuracy

Total -0.1b remaining (-0.1%)

Threshold costs -0.1b (-0.1%)

Counts

7 → 1

15 → 1

56 → 2

63 → 3

67 → 2

68 → 2

95 → 1

Calls

Call 1

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

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

Call 2

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

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

Call 3

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

Outputs

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

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

Call 4

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

Outputs

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

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

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

Call 5

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

Outputs

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

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

Call 6

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

Outputs

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

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

Call 7

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

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

Calls

24 calls:

33.0ms	k
28.0ms	n
26.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	k
24.0ms	(.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
39.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
39.5%	1	`k`
39.5%	1	`n`
39.5%	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))))`
50.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
50.1%	1	`n`
50.1%	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))))`
50.1%	1	`k`
61.5%	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))))`
61.5%	2	`k`
61.4%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
61.4%	2	`n`
61.5%	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))))`
63.2%	3	`k`
97.3%	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))))`
97.3%	2	`k`
93.4%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.2%	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))))`
99.2%	2	`k`
93.4%	2	`n`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.5%	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))))`
99.5%	1	`k`
99.5%	1	`n`

Compiler

Compiled 2 699 to 577 computations (78.6% saved)

bsearch12.0ms (0.2%)

Memory

39.4MiB live, 39.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	2.1816952119613078e-51	3.4404451507140954e-50

Samples

7.0ms	96×	0	valid
0.0ms	1×	1	invalid

Compiler

Compiled 253 to 216 computations (14.6% saved)

Precisions

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

ival-pow: 2.0ms (44.4% of total)

ival-div!: 1.0ms (22.2% of total)

ival-sqrt: 1.0ms (22.2% of total)

ival-mult!: 1.0ms (22.2% of total)

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

adjust: 0.0ms (0% of total)

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

bsearch53.0ms (1%)

Memory

-31.2MiB live, 68.7MiB allocated; 49ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
51.0ms	0.4631650673657468	1777561.7441802544

Samples

45.0ms

144×

valid

Compiler

Compiled 433 to 369 computations (14.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-sqrt: 25.0ms (59.9% of total)

ival-pow: 14.0ms (33.5% of total)

ival-div!: 1.0ms (2.4% of total)

ival-mult!: 1.0ms (2.4% of total)

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

adjust: 0.0ms (0% of total)

bsearch32.0ms (0.6%)

Memory

-8.6MiB live, 36.6MiB allocated; 12ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
23.0ms	3.638411158092561e+175	8.7285795414526e+176
7.0ms	4.906945727268852e-8	7.404935105867272e-8

Samples

23.0ms

176×

valid

Compiler

Compiled 708 to 553 computations (21.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult!: 13.0ms (67.9% of total)

ival-pow: 3.0ms (15.7% of total)

ival-div!: 2.0ms (10.5% of total)

ival-sqrt: 1.0ms (5.2% of total)

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

adjust: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	4.906945727268852e-8	7.404935105867272e-8

Compiler

Compiled 267 to 210 computations (21.3% saved)

derivations117.0ms (2.1%)

Memory

18.2MiB live, 106.7MiB allocated; 18ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 320 to 78 computations (75.6% saved)

preprocess97.0ms (1.8%)

Memory: -5.8MiB live, 131.0MiB allocated; 40ms collecting garbage
Remove: (abs k)
Compiler: Compiled 976 to 485 computations (50.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze116.0ms (2.1%)

sample2.8s (50.2%)

preprocess41.0ms (0.7%)

series100.0ms (1.8%)

rewrite103.0ms (1.9%)

eval49.0ms (0.9%)

prune17.0ms (0.3%)

series210.0ms (3.8%)

rewrite147.0ms (2.7%)

eval159.0ms (2.9%)

prune38.0ms (0.7%)

series78.0ms (1.4%)

rewrite127.0ms (2.3%)

eval135.0ms (2.5%)

prune112.0ms (2%)

series223.0ms (4.1%)

rewrite118.0ms (2.1%)

eval153.0ms (2.8%)

prune61.0ms (1.1%)

regimes433.0ms (7.9%)

bsearch12.0ms (0.2%)

bsearch53.0ms (1%)

bsearch32.0ms (0.6%)

bsearch1.0ms (0%)

derivations117.0ms (2.1%)

preprocess97.0ms (1.8%)

end0.0ms (0%)

Profiling