Metrics for Migdal et al, Equation (51)

start0.0ms (0.0%)

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

analyze152.0ms (2.5%)

Memory

6.3MiB live, 196.2MiB allocated; 105ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0.0%	0.0%	99.9%	0.1%	0.0%	0.0%	0.0%	0
0.0%	0.0%	99.9%	0.1%	0.0%	0.0%	0.0%	1
0.0%	0.0%	50.0%	0.1%	0.0%	50.0%	0.0%	2
50.0%	25.0%	25.0%	0.1%	0.0%	50.0%	0.0%	3
50.0%	25.0%	25.0%	0.1%	0.0%	50.0%	0.0%	4
50.0%	25.0%	25.0%	0.1%	0.0%	50.0%	0.0%	5
50.0%	25.0%	25.0%	0.1%	0.0%	50.0%	0.0%	6
51.6%	25.0%	23.4%	0.1%	0.0%	51.5%	0.0%	7
52.5%	25.0%	22.6%	0.1%	0.0%	52.3%	0.0%	8
53.8%	25.0%	21.5%	0.1%	0.0%	53.5%	0.0%	9
54.5%	25.0%	20.9%	0.1%	0.0%	54.0%	0.0%	10
55.3%	25.0%	20.2%	0.1%	0.0%	54.7%	0.0%	11
55.7%	25.0%	19.9%	0.1%	0.0%	55.1%	0.0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample2.6s (42.1%)

Memory

49.7MiB live, 3 463.5MiB allocated; 704ms collecting garbage

Samples

1.2s	5 626×	1	invalid
729.0ms	8 254×	0	valid
125.0ms	475×	2	invalid
21.0ms	234×	0	exit
21.0ms	351×	0	invalid
0.0ms	2×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-pow: 482.0ms (33.0% of total)

adjust: 296.0ms (20.3% of total)

ival-div!: 232.0ms (15.9% of total)

ival-mult!: 206.0ms (14.1% of total)

ival-sqrt: 149.0ms (10.2% of total)

ival-sub!: 95.0ms (6.5% of total)

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

exact: 0.0ms (0.0% of total)

Bogosity

preprocess42.0ms (0.7%)

Memory

-34.2MiB live, 10.6MiB allocated; 8ms 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
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Symmetry

(abs k)

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample0.0ms (0.0%)

Memory

0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

Calls

Call 1

Inputs
1
(* 2 (PI))
2
(PI)

Outputs
#s(literal 1 binary64)
#s(literal 884279719003555/140737488355328 binary64)
#s(literal 2 binary64)
#s(literal 884279719003555/281474976710656 binary64)

Samples

0.0ms

1×

valid

Compiler

Compiled 8 to 6 computations (25.0% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total)

series73.0ms (1.2%)

Memory

5.7MiB live, 50.3MiB allocated; 6ms 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
26.0ms	n	0
20.0ms	n	-inf
7.0ms	n	inf
2.0ms	k	0
2.0ms	k	-inf

rewrite93.0ms (1.5%)

Memory

16.6MiB live, 62.6MiB allocated; 3ms 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	4159	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))
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(+.f64 (PI.f64) (PI.f64))
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#s(literal 2 binary64)
(PI.f64)
n
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(/.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))
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(/.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
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(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))
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(-.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))
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(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 k))) (neg.f64 k))
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(*.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))
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(/.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)))
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(/.f64 (-.f64 (.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (.f64 k k)) (+.f64 #s(literal 1 binary64) k))
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(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))

eval44.0ms (0.7%)

Memory: 4.0MiB live, 53.6MiB allocated; 15ms collecting garbage
Compiler: Compiled 7 466 to 1 284 computations (82.8% saved)

prune15.0ms (0.3%)

Memory

19.8MiB live, 19.8MiB allocated; 0ms collecting garbage

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	323	14	337
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	324	14	338

Accuracy

100.0%

Counts

338 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.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))
	99.6%	(/.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)))))
	99.6%	(.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))))
▶	99.2%	(.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))))
	54.3%	(.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))) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) k))))
	99.4%	(.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)))))
	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))))
▶	75.2%	(.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)))))
▶	95.5%	(.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)))))
	95.8%	(.f64 (/.f64 #s(literal 1 binary64) (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))))
	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))))
	54.9%	#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))))
▶	54.4%	#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)))

Compiler

Compiled 594 to 450 computations (24.2% saved)

sample0.0ms (0.0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Calls

Call 1

Inputs
(+ (PI) (PI))
(PI)
-1/2
1/2
2
1
(* 2 (PI))

Outputs
#s(literal 884279719003555/140737488355328 binary64)
#s(literal 884279719003555/281474976710656 binary64)
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(literal 884279719003555/140737488355328 binary64)

Samples

0.0ms

1×

valid

Compiler

Compiled 13 to 9 computations (30.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total)

series1.0s (16.7%)

Memory

-193.2MiB live, 150.1MiB allocated; 1.5s 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))))
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#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)))))
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#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))))
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#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))))
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#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)))))
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#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 (/ 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))))))
#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) (.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))))))
#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 (log.f64 (.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k))))))
#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
867.0ms	n	-inf
58.0ms	n	0
22.0ms	n	inf
15.0ms	k	0
6.0ms	k	-inf

rewrite160.0ms (2.6%)

Memory

44.7MiB live, 137.1MiB allocated; 6ms 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)))))
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(*.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))))

eval140.0ms (2.3%)

Memory: -26.0MiB live, 202.0MiB allocated; 30ms collecting garbage
Compiler: Compiled 36 511 to 4 397 computations (88.0% saved)

prune38.0ms (0.6%)

Memory

6.6MiB live, 60.5MiB allocated; 9ms collecting garbage

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	1 267	19	1 286
Fresh	8	1	9
Picked	5	0	5
Done	0	0	0
Total	1 280	20	1 300

Accuracy

100.0%

Counts

1 300 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (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))
	95.5%	(/.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))
	75.3%	(.f64 (pow.f64 (.f64 (PI.f64) n) (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))) (sqrt.f64 k)))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) k))))
	54.1%	#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)))
	54.2%	#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)))
▶	54.3%	#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)))
	46.0%	#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))))
	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
	50.8%	#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)))
	54.4%	#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)))
	46.0%	#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))))))
	54.4%	#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))))))
▶	54.2%	#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)))))
	54.3%	#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)))))
	46.0%	#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)))))
▶	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) k)))
▶	54.3%	#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 1 052 to 792 computations (24.7% saved)

sample0.0ms (0.0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Calls

Call 1

Inputs
884279719003555/140737488355328
-1/2
1/2
(PI)
(sqrt 2)
2
1

Outputs
#s(literal 884279719003555/140737488355328 binary64)
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(literal 884279719003555/281474976710656 binary64)
#s(literal 6369051672525773/4503599627370496 binary64)
#s(literal 2 binary64)
#s(literal 1 binary64)

Samples

0.0ms

1×

valid

Compiler

Compiled 10 to 9 computations (10.0% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total)

series97.0ms (1.6%)

Memory

19.9MiB live, 111.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	341	2075

Stop Event

1×	iter-limit

Counts

41 → 87

Calls

Call 1

Inputs
(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 n #s(literal 884279719003555/140737488355328 binary64))
n
#s(literal 884279719003555/140737488355328 binary64)
(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))) (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)
(PI.f64)
#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)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(sqrt.f64 #s(literal 2 binary64))
#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 (/ (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)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(*.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))) (.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)))))
(.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))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))
(neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(neg.f64 (sqrt.f64 (sqrt.f64 k)))
(sqrt.f64 (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))

Outputs
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (sqrt k)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #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 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #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 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))
#s(approx (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (fma.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))))
#s(approx (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))))
#s(approx (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))))))) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #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 (* (/ 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 (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 (/ (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt k)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (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 (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))
#s(approx (/ 1 k) (/.f64 #s(literal 1 binary64) k))
#s(approx (* (/ (sqrt (* (+ n n) (PI))) (neg (neg (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt k)))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))))
#s(approx (/ (sqrt (* (+ n n) (PI))) (neg (neg (sqrt (sqrt k))))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
#s(approx (neg (neg (sqrt (sqrt k)))) (sqrt.f64 (sqrt.f64 k)))
#s(approx (neg (sqrt (sqrt k))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))))
#s(approx (/ 1 (sqrt (sqrt k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (-.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 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (-.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 (sqrt (/ (* (+ n n) (PI)) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))))
#s(approx (/ (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt k)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (*.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 (sqrt (/ 1 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (* (/ (sqrt (* (+ n n) (PI))) (neg (neg (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt k)))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.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 (* (+ n n) (PI))) (neg (neg (sqrt (sqrt k))))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#s(approx (neg (neg (sqrt (sqrt k)))) (*.f64 k (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))
#s(approx (neg (sqrt (sqrt k))) (.f64 #s(literal -1 binary64) (.f64 k (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) 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 (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (+.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 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (+.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 (/ (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (.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 (* (/ (sqrt (* (+ n n) (PI))) (neg (neg (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt k)))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.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 (* (+ n n) (PI))) (neg (neg (sqrt (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) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))))
#s(approx (neg (neg (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 (neg (sqrt (sqrt k))) (.f64 k (sqrt.f64 (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) 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 (/ (pow (* n 884279719003555/140737488355328) (+ (* 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 #s(literal 884279719003555/140737488355328 binary64)) (log.f64 n)))) (sqrt.f64 k)))
#s(approx (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (log.f64 n)))))
#s(approx (* n 884279719003555/140737488355328) (*.f64 #s(literal 884279719003555/140737488355328 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 (* (+ n n) (PI)) (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))
#s(approx (+ n n) (*.f64 #s(literal 2 binary64) n))
#s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))))
#s(approx (sqrt (* (PI) n)) (sqrt.f64 (*.f64 n (PI.f64))))
#s(approx (* (PI) n) (*.f64 n (PI.f64)))
#s(approx (sqrt (* 2 (* n (PI)))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* 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 #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (*.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 (/ (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt k)) (/.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (sqrt.f64 k)))
#s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))))
#s(approx (sqrt (* (PI) n)) (*.f64 n (sqrt.f64 (/.f64 (PI.f64) n))))
#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 (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt (* 2 (* n (PI)))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (* (/ (sqrt (* (+ n n) (PI))) (neg (neg (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt k)))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))))
#s(approx (/ (sqrt (* (+ n n) (PI))) (neg (neg (sqrt (sqrt k))))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 (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 (.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 (/ (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (.f64 #s(literal -1 binary64) (.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))))
#s(approx (sqrt (* (PI) n)) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (/.f64 (PI.f64) n)))))
#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 (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (sqrt (* 2 (* 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))) (neg (neg (sqrt (sqrt k))))) (/ 1 (sqrt (sqrt k)))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64)))))
#s(approx (/ (sqrt (* (+ n n) (PI))) (neg (neg (sqrt (sqrt k))))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 (sqrt.f64 k)))))

Calls

6 calls:

Time	Variable	Point
26.0ms	n	0
21.0ms	n	-inf
18.0ms	n	inf
6.0ms	k	-inf
6.0ms	k	0

rewrite143.0ms (2.4%)

Memory

-27.9MiB live, 113.1MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	330
0	86	299
1	332	283
2	1045	279
0	4048	279

Stop Event

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

Counts

41 → 1 484

Calls

Call 1

Inputs
(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 n #s(literal 884279719003555/140737488355328 binary64))
n
#s(literal 884279719003555/140737488355328 binary64)
(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))) (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)
(PI.f64)
#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)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(sqrt.f64 #s(literal 2 binary64))
#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 (/ (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)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(*.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))) (.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)))))
(.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))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))
(neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(neg.f64 (sqrt.f64 (sqrt.f64 k)))
(sqrt.f64 (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))

Outputs
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (neg.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #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 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 k)))))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
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(exp.f64 (*.f64 (log.f64 k) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 k) (/.f64 #s(literal -1/2 binary64) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) (/.f64 #s(literal -1/2 binary64) #s(literal 2 binary64))))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))))
(pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64))
(pow.f64 k #s(literal -1/4 binary64))
(/.f64 #s(literal -2 binary64) (*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 0 binary64) (sqrt.f64 (sqrt.f64 k))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (sqrt.f64 (sqrt.f64 k))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 0 binary64) (sqrt.f64 (sqrt.f64 k))))
(fabs.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (sqrt.f64 k))))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 0 binary64) (sqrt.f64 (sqrt.f64 k))))

eval152.0ms (2.5%)

Memory: 16.8MiB live, 203.6MiB allocated; 40ms collecting garbage
Compiler: Compiled 45 452 to 5 097 computations (88.8% saved)

prune93.0ms (1.5%)

Memory

-9.4MiB live, 136.6MiB allocated; 17ms collecting garbage

Pruning

59 alts after pruning (57 fresh and 2 done)

	Pruned	Kept	Total
New	1 191	47	1 238
Fresh	5	10	15
Picked	3	2	5
Done	0	0	0
Total	1 199	59	1 258

Accuracy

100.0%

Counts

1 258 → 59

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	48.7%	(/.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #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))
	95.5%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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))) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) k))))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
	54.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	54.1%	#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)))
	54.2%	#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)))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
	54.1%	#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))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
	54.3%	#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))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	54.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
	28.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 k)))
	54.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 #s(approx (sqrt ( (PI) n)) (*.f64 n (sqrt.f64 (/.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	46.0%	#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))))
	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))))
	50.8%	#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)))
	54.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
	54.4%	#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))))))
	54.2%	#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)))))
	54.3%	#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)))))
▶	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))))
	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n))))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))))
	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
	53.9%	#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))))
	39.7%	#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)))))
	27.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 (.f64 (PI.f64) n) k)) (.f64 k k))))
✓	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) k)))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))) k)))
	4.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)))
	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fabs.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))
	39.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))
	39.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
▶	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k))))
	27.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) k)) #s(literal 1/2 binary64))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
	54.3%	#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 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))
	54.3%	#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 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k))))))
	50.7%	#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 (exp.f64 (.f64 (log.f64 k) #s(literal -1 binary64))))))))
	54.3%	#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 #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))))
	42.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 k (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 #s(literal 1 binary64) k)))))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) k))))))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))))
	54.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
▶	54.3%	#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 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
▶	42.8%	#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)))
	52.2%	#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 3 604 to 2 671 computations (25.9% saved)

sample0.0ms (0.0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Calls

Call 1

Inputs
(PI)
1/2
2
(sqrt 2)
1
(* (sqrt 2) 1)

Outputs
#s(literal 884279719003555/281474976710656 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
#s(literal 6369051672525773/4503599627370496 binary64)
#s(literal 1 binary64)
#s(literal 6369051672525773/4503599627370496 binary64)

Samples

0.0ms

1×

valid

Compiler

Compiled 12 to 8 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total)

series88.0ms (1.4%)

Memory

13.9MiB live, 105.9MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	397	2807

Stop Event

1×	iter-limit

Counts

42 → 96

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
17.0ms	n	0
15.0ms	n	-inf
14.0ms	n	inf
9.0ms	k	-inf
8.0ms	k	0

rewrite126.0ms (2.1%)

Memory

13.1MiB live, 109.1MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	59	391
0	92	381
1	341	354
2	1197	349
0	4153	349

Stop Event

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

Counts

42 → 1 032

Calls

Call 1

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

Outputs
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k #s(literal 1/2 binary64)))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k #s(literal 1/2 binary64)))))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 n n) k) (PI.f64)))) (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 k #s(literal -2 binary64)))))
(.f64 (.f64 #s(literal -1 binary64) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) #s(literal -1 binary64)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 k)))
(.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k)))))
(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 n n) k) (PI.f64))) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 k #s(literal -2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 k)))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))))))
(/.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (sqrt.f64 k) (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 n n) k) (PI.f64))))) (.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -1 binary64) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) #s(literal -1 binary64))) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) #s(literal 1 binary64))) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))))
(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (.f64 #s(literal 2 binary64) (neg.f64 (neg.f64 (sqrt.f64 k)))))
(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 (.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 (/.f64 (+.f64 n n) k) (PI.f64)))) (.f64 #s(literal 2 binary64) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k)))))
(/.f64 (.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))))
(/.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 #s(literal -1 binary64) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 n n) k) (PI.f64)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64)))))
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(fabs.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))))))
(fabs.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)))))
(fabs.f64 (sqrt.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))) #s(literal 1/2 binary64)))
(.f64 (.f64 (*.f64 (PI.f64) n) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (neg.f64 (.f64 (neg.f64 (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)))) (neg.f64 (sqrt.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)))))
(*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))
(.f64 (.f64 (neg.f64 (PI.f64)) n) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (/.f64 n (sqrt.f64 k))))
(.f64 (sqrt.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))) (sqrt.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))))
(.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (PI.f64) n))
(*.f64 (PI.f64) (/.f64 n (sqrt.f64 k)))
(*.f64 n (/.f64 (PI.f64) (sqrt.f64 k)))
(pow.f64 (.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)) (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)) #s(literal 1 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 (neg.f64 (PI.f64)) n))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 k)))))
(/.f64 (.f64 (.f64 (PI.f64) n) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (.f64 (PI.f64) n) #s(literal 1 binary64)) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 (.f64 (PI.f64) n) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (neg.f64 (*.f64 (neg.f64 (PI.f64)) n)) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (PI.f64)) n)) (sqrt.f64 k))
(/.f64 (*.f64 (neg.f64 (PI.f64)) n) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (PI.f64) n) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (PI.f64) n) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (.f64 (PI.f64) n) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (.f64 (.f64 (PI.f64) n) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (neg.f64 (*.f64 (neg.f64 (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (*.f64 (neg.f64 (PI.f64)) n)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (PI.f64) n)))
(neg.f64 (.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (.f64 (.f64 (PI.f64) n) #s(literal -1 binary64)) (sqrt.f64 k)))
(neg.f64 (/.f64 (*.f64 (neg.f64 (PI.f64)) n) (sqrt.f64 k)))
(sqrt.f64 (.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)) (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))))
(fabs.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)))) (sqrt.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)))))
(fabs.f64 (.f64 (sqrt.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))) (neg.f64 (sqrt.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64))))))
(fabs.f64 (*.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n (sqrt.f64 k))))
(log.f64 (pow.f64 (exp.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k))))
(pow.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(/.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))))
(/.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (sqrt.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k))))))
(neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))))
(sqrt.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(fabs.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))))
(fabs.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(cosh.f64 (asinh.f64 #s(literal 1 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(fabs.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(fabs.f64 (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k (/.f64 #s(literal 1/4 binary64) #s(literal 2 binary64))) (pow.f64 k (/.f64 #s(literal 1/4 binary64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 (sqrt.f64 k) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))))
(pow.f64 (sqrt.f64 k) #s(literal 1/2 binary64))
(pow.f64 k #s(literal 1/4 binary64))
(sqrt.f64 (sqrt.f64 k))
(fabs.f64 (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(fabs.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(fabs.f64 (sqrt.f64 (sqrt.f64 k)))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal 1/2 binary64)))

eval136.0ms (2.2%)

Memory: 16.1MiB live, 198.9MiB allocated; 25ms collecting garbage
Compiler: Compiled 40 766 to 5 278 computations (87.1% saved)

prune69.0ms (1.1%)

Memory

11.7MiB live, 104.3MiB allocated; 8ms collecting garbage

Pruning

60 alts after pruning (57 fresh and 3 done)

	Pruned	Kept	Total
New	1 103	23	1 126
Fresh	18	34	52
Picked	4	1	5
Done	0	2	2
Total	1 125	60	1 185

Accuracy

100.0%

Counts

1 185 → 60

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	48.7%	(/.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(approx (+ ( k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	57.2%	(/.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64))) #s(approx (pow ( (+ n n) (PI)) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))))))) (sqrt.f64 k))
	72.0%	(/.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 n n) k) (PI.f64))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 binary64))))
	95.5%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	71.9%	(.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 n n) k) (PI.f64))) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 k #s(literal -2 binary64))))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
	54.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	54.1%	#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)))
	54.2%	#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)))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
	54.1%	#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))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
	54.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 k)))
	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
	50.8%	#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)))
	54.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
	54.4%	#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))))))
	54.3%	#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)))))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))))
	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n))))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))))
	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
	53.9%	#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))))
	39.7%	#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)))))
✓	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 n n) (PI.f64)) k)))
	39.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 k))))
	27.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 k (.f64 (PI.f64) (+.f64 n n))) (*.f64 k k))))
	4.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)))
	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fabs.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))
	39.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))
	39.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
✓	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k))))
	28.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (+.f64 (/.f64 (.f64 k n) (.f64 k k)) (/.f64 (.f64 k n) (*.f64 k k))))))
	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)))))
	27.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
	15.2%	#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))))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) k)) #s(literal 1/2 binary64))))
	50.7%	#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 (exp.f64 (.f64 (log.f64 k) #s(literal -1 binary64))))))))
	54.3%	#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 #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
	42.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 k (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 #s(literal 1 binary64) k)))))))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))))
	54.2%	#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 (PI.f64) n)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	54.2%	#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 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k)) k)))))
	54.3%	#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 (PI.f64) n)) #s(approx (/ (sqrt 2) (* (sqrt (/ 1 k)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))))
	54.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 #s(approx (sqrt ( (PI) n)) (.f64 n (sqrt.f64 (/.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
	54.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (/ (* (PI) n) (sqrt k))) (/ (* (sqrt 2) 1) (sqrt (sqrt k)))) (/.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)))
	54.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) k)))
	42.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) k)))
	42.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n)) k)))
	54.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
	39.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 k (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))) k)))
	42.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (.f64 k (*.f64 (PI.f64) (+.f64 n n)))))))
	52.2%	#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 1 893 to 1 400 computations (26.0% saved)

regimes528.0ms (8.7%)

Memory

-61.3MiB live, 536.2MiB allocated; 106ms collecting garbage

Counts

6 → 1

9 → 1

11 → 1

17 → 1

29 → 2

32 → 3

51 → 3

74 → 3

77 → 3

80 → 2

104 → 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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n 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))))

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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#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))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n 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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)))))

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

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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(approx (/ (sqrt 2) (* (sqrt (/ 1 k)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 k n)) (sqrt.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 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) k)))
#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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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)))

Outputs

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

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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(approx (/ (sqrt 2) (* (sqrt (/ 1 k)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 k n)) (sqrt.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 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) k)))
#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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (sqrt.f64 (/.f64 (.f64 k (.f64 (PI.f64) (+.f64 n n))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (.f64 k (*.f64 (PI.f64) (+.f64 n n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 k (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))) k)))

Outputs

#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))) (sqrt.f64 (/.f64 (*.f64 k (*.f64 (PI.f64) (+.f64 n n))) (*.f64 k 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 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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(approx (/ (sqrt 2) (* (sqrt (/ 1 k)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 k n)) (sqrt.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 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) k)))
#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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (sqrt.f64 (/.f64 (.f64 k (.f64 (PI.f64) (+.f64 n n))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (.f64 k (*.f64 (PI.f64) (+.f64 n n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 k (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 #s(approx (sqrt ( (PI) n)) (*.f64 n (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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))
#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 #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 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 (+.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 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))))
#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 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#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 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (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))) #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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 k (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 #s(literal 1 binary64) k)))))))
#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 (PI.f64) n)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) 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 (PI.f64) n) (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))

Outputs

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

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 k (*.f64 (PI.f64) (+.f64 n n))) (*.f64 k 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 8

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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(approx (/ (sqrt 2) (* (sqrt (/ 1 k)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 k n)) (sqrt.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 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) k)))
#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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (sqrt.f64 (/.f64 (.f64 k (.f64 (PI.f64) (+.f64 n n))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (.f64 k (*.f64 (PI.f64) (+.f64 n n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 k (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 #s(approx (sqrt ( (PI) n)) (*.f64 n (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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))
#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 #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 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 (+.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 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))))
#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 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#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 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (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))) #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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 k (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 #s(literal 1 binary64) k)))))))
#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 (PI.f64) n)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) 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 (PI.f64) n) (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 (.f64 (PI.f64) n) k)) (.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.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 (.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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (neg.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) n)) (sqrt.f64 #s(literal 2 binary64))) (*.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) n)) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (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 (+.f64 n n) (PI.f64)) (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))) 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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 #s(approx (sqrt ( (PI) n)) (.f64 n (sqrt.f64 (/.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #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 (PI.f64) n) (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (/ (* (PI) n) (sqrt k))) (/ (* (sqrt 2) 1) (sqrt (sqrt k)))) (/.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.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))) (sqrt.f64 (.f64 (PI.f64) (+.f64 (/.f64 (.f64 k n) (.f64 k k)) (/.f64 (.f64 k n) (*.f64 k 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))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #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 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 k)))

Outputs

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

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 k 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 9

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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(approx (/ (sqrt 2) (* (sqrt (/ 1 k)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 k n)) (sqrt.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 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) k)))
#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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (sqrt.f64 (/.f64 (.f64 k (.f64 (PI.f64) (+.f64 n n))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (.f64 k (*.f64 (PI.f64) (+.f64 n n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 k (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 #s(approx (sqrt ( (PI) n)) (*.f64 n (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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))
#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 #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 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 (+.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 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))))
#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 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#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 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (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))) #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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 k (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 #s(literal 1 binary64) k)))))))
#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 (PI.f64) n)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) 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 (PI.f64) n) (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 (.f64 (PI.f64) n) k)) (.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.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 (.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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (neg.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) n)) (sqrt.f64 #s(literal 2 binary64))) (*.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) n)) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (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 (+.f64 n n) (PI.f64)) (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))) 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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 #s(approx (sqrt ( (PI) n)) (.f64 n (sqrt.f64 (/.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #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 (PI.f64) n) (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (/ (* (PI) n) (sqrt k))) (/ (* (sqrt 2) 1) (sqrt (sqrt k)))) (/.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.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))) (sqrt.f64 (.f64 (PI.f64) (+.f64 (/.f64 (.f64 k n) (.f64 k k)) (/.f64 (.f64 k n) (*.f64 k 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))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #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 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 k)))
#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))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 (PI.f64) (+.f64 n n)))) 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)))

Outputs

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

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

Call 10

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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(approx (/ (sqrt 2) (* (sqrt (/ 1 k)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 k n)) (sqrt.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 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) k)))
#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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (sqrt.f64 (/.f64 (.f64 k (.f64 (PI.f64) (+.f64 n n))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (.f64 k (*.f64 (PI.f64) (+.f64 n n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 k (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 #s(approx (sqrt ( (PI) n)) (*.f64 n (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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))
#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 #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 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 (+.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 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))))
#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 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#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 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (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))) #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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 k (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 #s(literal 1 binary64) k)))))))
#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 (PI.f64) n)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) 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 (PI.f64) n) (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 (.f64 (PI.f64) n) k)) (.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.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 (.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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (neg.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) n)) (sqrt.f64 #s(literal 2 binary64))) (*.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) n)) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (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 (+.f64 n n) (PI.f64)) (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))) 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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 #s(approx (sqrt ( (PI) n)) (.f64 n (sqrt.f64 (/.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #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 (PI.f64) n) (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (/ (* (PI) n) (sqrt k))) (/ (* (sqrt 2) 1) (sqrt (sqrt k)))) (/.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.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))) (sqrt.f64 (.f64 (PI.f64) (+.f64 (/.f64 (.f64 k n) (.f64 k k)) (/.f64 (.f64 k n) (*.f64 k 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))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #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 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 k)))
#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))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 (PI.f64) (+.f64 n n)))) 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 n #s(literal 884279719003555/140737488355328 binary64)) #s(approx (+ ( k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) 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)))

Outputs

#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)))

(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(approx (+ (* k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))

Call 11

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 (PI.f64) (PI.f64)) (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#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 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(approx (/ (sqrt 2) (* (sqrt (/ 1 k)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 k n)) (sqrt.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 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) k)))
#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))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (sqrt.f64 (/.f64 (.f64 k (.f64 (PI.f64) (+.f64 n n))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (.f64 k (*.f64 (PI.f64) (+.f64 n n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 k (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ n n) (PI)) k)) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (/.f64 n (sqrt.f64 k)) (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 #s(approx (sqrt ( (PI) n)) (*.f64 n (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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))
#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 #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
#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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 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 (+.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 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))))
#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 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#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 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (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))) #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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 k (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 #s(literal 1 binary64) k)))))))
#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 (PI.f64) n)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) 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 (PI.f64) n) (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 (.f64 (PI.f64) n) k)) (.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.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 (.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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (neg.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) n)) (sqrt.f64 #s(literal 2 binary64))) (*.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) n)) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (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 (+.f64 n n) (PI.f64)) (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))) 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))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 #s(approx (sqrt ( (PI) n)) (.f64 n (sqrt.f64 (/.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #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 (PI.f64) n) (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (/ (* (PI) n) (sqrt k))) (/ (* (sqrt 2) 1) (sqrt (sqrt k)))) (/.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.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))) (sqrt.f64 (.f64 (PI.f64) (+.f64 (/.f64 (.f64 k n) (.f64 k k)) (/.f64 (.f64 k n) (*.f64 k 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))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #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 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 k)))
#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))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 (PI.f64) (+.f64 n n)))) 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 n #s(literal 884279719003555/140737488355328 binary64)) #s(approx (+ ( k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) 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)))
(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (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))))
(/.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 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
#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 (exp.f64 (.f64 (log.f64 k) #s(literal -1 binary64))))))))
(/.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))))
(/.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 n n) (PI.f64))) #s(approx (pow ( (+ n n) (PI)) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))))))) (sqrt.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 (sqrt.f64 (.f64 (/.f64 (+.f64 n n) k) (PI.f64))) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 k #s(literal -2 binary64))))
(/.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 n n) k) (PI.f64))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k #s(literal 1/2 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)))) (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))
(.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 (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 (pow.f64 (.f64 (PI.f64) n) (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))) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (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 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))) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) 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))))

Outputs
(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))

Calls

38 calls:

66.0ms	n
29.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	k
22.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
39.9%	1	`k`
39.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
39.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
39.9%	1	`n`
53.9%	1	`k`
53.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
53.9%	1	`n`
53.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
54.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
54.4%	1	`n`
54.4%	1	`k`
54.4%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
54.4%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
54.4%	1	`k`
54.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
54.4%	1	`n`
65.0%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
65.0%	2	`n`
65.0%	2	`k`
65.0%	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))))`
66.9%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
66.9%	3	`n`
81.0%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
81.0%	3	`n`
81.0%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
81.0%	3	`n`
81.4%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
81.4%	3	`n`
79.8%	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))))`
72.0%	4	`k`
98.1%	2	`k`
81.8%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
98.1%	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))))`
81.8%	3	`n`
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.6%	1	`k`
99.6%	1	`n`

Compiler

Compiled 3 366 to 731 computations (78.3% saved)

bsearch17.0ms (0.3%)

Memory

15.2MiB live, 15.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	8.790478322933411e-5	109.34379033569591

Samples

9.0ms

144×

valid

Compiler

Compiled 487 to 405 computations (16.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-pow: 2.0ms (31.7% of total)

ival-sqrt: 1.0ms (15.8% of total)

ival-div!: 1.0ms (15.8% of total)

ival-mult!: 1.0ms (15.8% of total)

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

adjust: 0.0ms (0.0% of total)

bsearch31.0ms (0.5%)

Memory

21.3MiB live, 21.3MiB allocated; 0ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	5.715285593097121e+24	2.0839458160057157e+26
16.0ms	13043571.923180325	3496889976245.448

Samples

18.0ms

256×

valid

Compiler

Compiled 1 126 to 856 computations (24.0% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow: 5.0ms (41.2% of total)

ival-sqrt: 2.0ms (16.5% of total)

ival-div!: 2.0ms (16.5% of total)

ival-mult!: 2.0ms (16.5% of total)

ival-sub!: 1.0ms (8.2% of total)

adjust: 0.0ms (0.0% of total)

bsearch15.0ms (0.2%)

Memory

-33.5MiB live, 12.6MiB allocated; 2ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	9.897900148190111e+28	3.626212972271315e+29
5.0ms	13043571.923180325	3496889976245.448

Samples

6.0ms

96×

valid

Compiler

Compiled 1 070 to 758 computations (29.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-pow: 2.0ms (45.9% of total)

ival-sqrt: 1.0ms (22.9% of total)

ival-div!: 1.0ms (22.9% of total)

ival-mult!: 1.0ms (22.9% of total)

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

adjust: 0.0ms (0.0% of total)

bsearch3.0ms (0.0%)

Memory

1.9MiB live, 1.9MiB allocated; 0ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	9.897900148190111e+28	3.626212972271315e+29
1.0ms	13043571.923180325	3496889976245.448

Compiler

Compiled 1 028 to 758 computations (26.3% saved)

bsearch2.0ms (0.0%)

Memory

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

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	9.897900148190111e+28	3.626212972271315e+29
1.0ms	13043571.923180325	3496889976245.448

Compiler

Compiled 839 to 650 computations (22.5% saved)

bsearch6.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
5.0ms	9.158721242396077e-21	6.518650934219745e-20

Samples

3.0ms

48×

valid

Compiler

Compiled 205 to 162 computations (21.0% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-pow: 1.0ms (45.3% of total)

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

adjust: 0.0ms (0.0% of total)

ival-sqrt: 0.0ms (0.0% of total)

ival-div!: 0.0ms (0.0% of total)

ival-mult!: 0.0ms (0.0% of total)

derivations140.0ms (2.3%)

Memory

20.9MiB live, 71.9MiB allocated; 2ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 696 to 126 computations (81.9% saved)

preprocess104.0ms (1.7%)

Memory: -25.2MiB live, 166.5MiB allocated; 17ms collecting garbage
Compiler: Compiled 2 104 to 865 computations (58.9% saved)

end0.0ms (0.0%)

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

start0.0ms (0.0%)

analyze152.0ms (2.5%)

sample2.6s (42.1%)

preprocess42.0ms (0.7%)

sample0.0ms (0.0%)

series73.0ms (1.2%)

rewrite93.0ms (1.5%)

eval44.0ms (0.7%)

prune15.0ms (0.3%)

sample0.0ms (0.0%)

series1.0s (16.7%)

rewrite160.0ms (2.6%)

eval140.0ms (2.3%)

prune38.0ms (0.6%)

sample0.0ms (0.0%)

series97.0ms (1.6%)

rewrite143.0ms (2.4%)

eval152.0ms (2.5%)

prune93.0ms (1.5%)

sample0.0ms (0.0%)

series88.0ms (1.4%)

rewrite126.0ms (2.1%)

eval136.0ms (2.2%)

prune69.0ms (1.1%)

regimes528.0ms (8.7%)

bsearch17.0ms (0.3%)

bsearch31.0ms (0.5%)

bsearch15.0ms (0.2%)

bsearch3.0ms (0.0%)

bsearch2.0ms (0.0%)

bsearch6.0ms (0.1%)

derivations140.0ms (2.3%)

preprocess104.0ms (1.7%)

end0.0ms (0.0%)

Profiling