Metrics for Migdal et al, Equation (51)

start0.0ms (0.0%)

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

analyze92.0ms (1.6%)

Memory

19.0MiB live, 110.8MiB allocated; 10ms 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)

sample2.3s (41.0%)

Memory

90.1MiB live, 2 831.9MiB allocated; 572ms collecting garbage

Samples

1.0s	5 492×	1	invalid
646.0ms	8 256×	0	valid
102.0ms	455×	2	invalid
23.0ms	372×	0	invalid
23.0ms	250×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-pow: 468.0ms (36.0% of total)

ival-div!: 228.0ms (17.5% of total)

adjust: 204.0ms (15.7% of total)

ival-mult!: 187.0ms (14.4% of total)

ival-sqrt: 146.0ms (11.2% of total)

ival-sub!: 68.0ms (5.2% of total)

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

exact: 0.0ms (0.0% of total)

Bogosity

preprocess66.0ms (1.2%)

Memory

-48.6MiB live, 59.7MiB allocated; 54ms 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

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

Calls

Call 1

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

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

series95.0ms (1.7%)

Memory

39.3MiB live, 274.1MiB allocated; 32ms 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
#s(literal 1 binary64)
k
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 2 binary64)
(PI.f64)
(*.f64 #s(literal 2 binary64) (PI.f64))
n
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(-.f64 #s(literal 1 binary64) k)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

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

Calls

6 calls:

Time	Variable	Point
35.0ms	n	-inf
32.0ms	n	0
8.0ms	n	inf
2.0ms	k	0
2.0ms	k	-inf

rewrite115.0ms (2.1%)

Memory

-9.1MiB live, 173.5MiB allocated; 34ms 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
#s(literal 1 binary64)
k
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 2 binary64)
(PI.f64)
(*.f64 #s(literal 2 binary64) (PI.f64))
n
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(-.f64 #s(literal 1 binary64) k)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

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

eval42.0ms (0.7%)

Memory: -3.5MiB live, 85.8MiB allocated; 16ms collecting garbage
Compiler: Compiled 7 451 to 1 285 computations (82.8% saved)

prune24.0ms (0.4%)

Memory

-12.4MiB live, 41.5MiB allocated; 12ms collecting garbage

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	319	17	336
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	320	17	337

Accuracy

100.0%

Counts

337 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
▶	99.5%	(/.f64 #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))))
▶	99.4%	(.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))))
	47.3%	(.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))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 k #s(literal -1/2 binary64))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal -1/2 binary64))))
	99.5%	(.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)))))
	72.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
▶	98.9%	(.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))))
	72.1%	(.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)))))
	96.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	99.5%	(.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))))
	99.3%	(.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.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))))
	96.4%	(.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	47.9%	#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))))
▶	47.3%	#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 702 to 532 computations (24.2% saved)

sample0.0ms (0.0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Calls

Call 1

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

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

series164.0ms (2.9%)

Memory

28.0MiB live, 270.5MiB allocated; 47ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	471	4091

Stop Event

1×	iter-limit

Counts

36 → 116

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
48.0ms	n	0
31.0ms	n	-inf
18.0ms	n	inf
17.0ms	k	0
15.0ms	k	inf

rewrite237.0ms (4.2%)

Memory

-4.9MiB live, 652.4MiB allocated; 53ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	258
0	75	225
1	279	207
2	889	207
0	4202	207

Stop Event

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

Counts

36 → 2 972

Calls

Call 1

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

Outputs
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 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 #s(literal -2 binary64) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 #s(literal -2 binary64) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 k)))) (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 2 binary64) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 k)))) (/.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(.f64 (pow.f64 (sqrt.f64 (.f64 k (sqrt.f64 k))) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)))
(*.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 (neg.f64 (sqrt.f64 (.f64 k (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 (neg.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (.f64 k (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 (.f64 k (sqrt.f64 k))) #s(literal -1/2 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 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))))
(.f64 (/.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 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))))
(*.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 #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 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 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 k)))
(pow.f64 (*.f64 k k) #s(literal -1/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal -2 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -2 binary64))
(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 (sqrt.f64 k))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal 2 binary64)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k)))) (.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))) (.f64 #s(literal 2 binary64) (sqrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
(/.f64 #s(literal -2 binary64) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 0 binary64)))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) #s(literal 2 binary64) (/.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 0 binary64)))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 0 binary64)))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
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n
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(+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))))
(+.f64 (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))))
(+.f64 (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 #s(literal 0 binary64) (.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))))

eval206.0ms (3.7%)

Memory: 39.8MiB live, 503.0MiB allocated; 122ms collecting garbage
Compiler: Compiled 50 547 to 4 703 computations (90.7% saved)

prune60.0ms (1.1%)

Memory

-23.9MiB live, 118.7MiB allocated; 32ms collecting garbage

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	1 750	22	1 772
Fresh	10	2	12
Picked	5	0	5
Done	0	0	0
Total	1 765	24	1 789

Accuracy

100.0%

Counts

1 789 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	73.6%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	98.9%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
▶	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
	47.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
	74.4%	(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	47.4%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	96.1%	(.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)))))
	47.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
▶	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (sqrt.f64 k))))
	47.2%	#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)))
	47.2%	#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)))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	41.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
	44.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
	47.3%	#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)))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	47.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
▶	47.3%	#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 (PI.f64) (PI.f64)) n))))
	41.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
▶	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	47.3%	#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 1 226 to 938 computations (23.5% saved)

sample0.0ms (0.0%)

Memory

0.8MiB live, 0.7MiB allocated; 0ms collecting garbage

Calls

Call 1

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

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

Samples

0.0ms

1×

valid

Compiler

Compiled 9 to 7 computations (22.2% saved)

Precisions

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

adjust: 0.0ms (0.0% of total)

series89.0ms (1.6%)

Memory

30.5MiB live, 166.9MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	426	3333

Stop Event

1×	iter-limit

Counts

31 → 109

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
15.0ms	n	inf
13.0ms	n	-inf
12.0ms	n	0
11.0ms	k	-inf
10.0ms	k	0

rewrite225.0ms (4.0%)

Memory

-56.5MiB live, 374.1MiB allocated; 119ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	271
0	66	245
1	278	227
2	1091	226
0	4194	226

Stop Event

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

Counts

31 → 1 428

Calls

Call 1

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

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

eval258.0ms (4.6%)

Memory: 40.8MiB live, 836.3MiB allocated; 102ms collecting garbage
Compiler: Compiled 57 086 to 6 425 computations (88.7% saved)

prune108.0ms (1.9%)

Memory

-22.5MiB live, 507.2MiB allocated; 54ms collecting garbage

Pruning

48 alts after pruning (48 fresh and 0 done)

	Pruned	Kept	Total
New	1 776	38	1 814
Fresh	9	10	19
Picked	5	0	5
Done	0	0	0
Total	1 790	48	1 838

Accuracy

100.0%

Counts

1 838 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	73.6%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
▶	99.5%	(/.f64 #s(literal 1 binary64) (.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)))
	74.4%	(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
	96.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 (sqrt.f64 k))))
	47.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
	47.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 (sqrt.f64 k))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 k))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))) (sqrt.f64 (sqrt.f64 k))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 (sqrt.f64 k))))
	47.2%	#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)))
	47.2%	#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)))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	41.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 k)) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k)))))))
	44.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (/ 1 (sqrt (sqrt k))) (sqrt (* (+ (PI) (PI)) n))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 k))))
	47.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	47.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))))
▶	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
▶	47.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	36.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
	47.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))
	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
	47.4%	#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))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))))
	44.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	21.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 n (PI.f64)) k (.f64 (.f64 n (PI.f64)) k)) (.f64 k k))))
▶	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fabs.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
	34.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (.f64 n (+.f64 (PI.f64) (PI.f64))))))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
	26.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
	34.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
▶	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k)))
	49.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))

Compiler

Compiled 2 742 to 2 036 computations (25.7% saved)

sample0.0ms (0.0%)

Memory

1.3MiB live, 1.3MiB allocated; 0ms collecting garbage

Calls

Call 1

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

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

Samples

0.0ms

1×

valid

Compiler

Compiled 11 to 9 computations (18.2% saved)

Precisions

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

adjust: 0.0ms (0.0% of total)

series127.0ms (2.3%)

Memory

29.3MiB live, 255.4MiB allocated; 64ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	385	2428

Stop Event

1×	iter-limit

Counts

39 → 93

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
29.0ms	n	0
24.0ms	n	-inf
23.0ms	n	inf
13.0ms	k	-inf
6.0ms	k	0

rewrite162.0ms (2.9%)

Memory

19.7MiB live, 348.2MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	343
0	81	331
1	297	303
2	1036	300
0	4125	295

Stop Event

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

Counts

39 → 999

Calls

Call 1

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

Outputs
#s(literal 1 binary64)
#s(literal 884279719003555/140737488355328 binary64)
n
(*.f64 (neg.f64 (neg.f64 n)) #s(literal 884279719003555/140737488355328 binary64))
(*.f64 #s(literal -884279719003555/140737488355328 binary64) (neg.f64 n))
(*.f64 (neg.f64 n) #s(literal -884279719003555/140737488355328 binary64))
(.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 1 binary64))
(*.f64 n #s(literal 884279719003555/140737488355328 binary64))
(*.f64 #s(literal 884279719003555/140737488355328 binary64) (neg.f64 (neg.f64 n)))
(*.f64 #s(literal 884279719003555/140737488355328 binary64) n)
(neg.f64 (*.f64 #s(literal -884279719003555/140737488355328 binary64) n))
(fma.f64 (neg.f64 (neg.f64 n)) #s(literal 884279719003555/140737488355328 binary64) (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal -884279719003555/140737488355328 binary64) (neg.f64 n) (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 0 binary64)))
(fma.f64 (neg.f64 n) #s(literal -884279719003555/140737488355328 binary64) (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))
(fma.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 1/2 binary64) (.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 1 binary64) (.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 0 binary64)))
(fma.f64 n #s(literal 884279719003555/140737488355328 binary64) (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 884279719003555/140737488355328 binary64) (neg.f64 (neg.f64 n)) (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 884279719003555/140737488355328 binary64) n (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 #s(literal 0 binary64) (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))
(+.f64 (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 n #s(literal 884279719003555/140737488355328 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 n #s(literal 884279719003555/140737488355328 binary64))))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 n #s(literal 884279719003555/140737488355328 binary64))) (.f64 #s(literal 0 binary64) (.f64 n #s(literal 884279719003555/140737488355328 binary64))))
(+.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 0 binary64)))
#s(literal 1/2 binary64)
k
#s(literal -1/2 binary64)
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (*.f64 k #s(literal 1/2 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 1/2 binary64) (-.f64 k #s(literal 1 binary64)))
(/.f64 (/.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal -2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))
(/.f64 (-.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -2 binary64))
(/.f64 (+.f64 #s(literal 2 binary64) (*.f64 k #s(literal -2 binary64))) #s(literal -4 binary64))
(/.f64 (+.f64 #s(literal -2 binary64) (*.f64 (neg.f64 k) #s(literal -2 binary64))) #s(literal 4 binary64))
(/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(/.f64 (-.f64 (pow.f64 #s(literal -1/2 binary64) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(/.f64 (fma.f64 (neg.f64 k) #s(literal 2 binary64) #s(literal 2 binary64)) #s(literal -4 binary64))
(/.f64 (fma.f64 (neg.f64 k) #s(literal -2 binary64) #s(literal -2 binary64)) #s(literal 4 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) k #s(literal -2 binary64)) #s(literal 4 binary64))
(/.f64 (fma.f64 k #s(literal -2 binary64) #s(literal 2 binary64)) #s(literal -4 binary64))
(/.f64 (+.f64 #s(literal -2 binary64) (+.f64 k k)) #s(literal 4 binary64))
(/.f64 (+.f64 #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) (neg.f64 k))) #s(literal 4 binary64))
(/.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 k))) #s(literal -4 binary64))
(/.f64 (-.f64 (*.f64 (neg.f64 k) #s(literal -2 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64))
(/.f64 (-.f64 (*.f64 (neg.f64 k) #s(literal 2 binary64)) #s(literal -2 binary64)) #s(literal -4 binary64))
(/.f64 (-.f64 (*.f64 k #s(literal -2 binary64)) #s(literal -2 binary64)) #s(literal -4 binary64))
(/.f64 (-.f64 (+.f64 k k) #s(literal 2 binary64)) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (+.f64 k k))) #s(literal 4 binary64))
(/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 k #s(literal 1/2 binary64)))) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 k #s(literal 1/2 binary64))) (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (+.f64 (pow.f64 #s(literal -1/2 binary64) #s(literal 3 binary64)) (pow.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 k #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 k #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 3 binary64))) (fma.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 k #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64) (.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 2 binary64) (+.f64 k k)) #s(literal -4 binary64))
(/.f64 (-.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 k #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (-.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 #s(literal -1/2 binary64) #s(literal 3 binary64))) (fma.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 k #s(literal 1/2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))
(/.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 k #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (-.f64 #s(literal 1 binary64) k)))
(neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 (/.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(fma.f64 (neg.f64 k) #s(literal -1/2 binary64) #s(literal -1/2 binary64))
(fma.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))
(fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 1 binary64)) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 k #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
(-.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(-.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(+.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 k #s(literal 1/2 binary64))))
(.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 k #s(literal 1/2 binary64))) (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 #s(literal 884279719003555/140737488355328 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 #s(literal 884279719003555/140737488355328 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -1/2 binary64) k)))
(/.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 k #s(literal 1/2 binary64))) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 #s(literal 2 binary64) #s(literal 2 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 (pow.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal 1 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 (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))
(*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))
(*.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 k) #s(literal 0 binary64)))
(pow.f64 (*.f64 k k) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal 1 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(/.f64 (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(neg.f64 (neg.f64 (sqrt.f64 k)))
(sqrt.f64 k)
(fabs.f64 (neg.f64 (sqrt.f64 k)))
(fabs.f64 (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sqrt.f64 k))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
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(.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) k)) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k)) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
(.f64 (sqrt.f64 (.f64 #s(literal -2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal -1 binary64) k)))
(*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k))))
(.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))
(.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) k))))
(pow.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k)) #s(literal 1/2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
(/.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (sqrt.f64 k))))
(/.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1 binary64)) (sqrt.f64 k))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k)))) (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 (neg.f64 k)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k)) #s(literal -1/2 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))))
(neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k)))))
(neg.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) k)))))
(neg.f64 (.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
(neg.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k)))))
(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k)))
(fabs.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k))))))
(fabs.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (neg.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(fabs.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(fabs.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(fabs.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 (sqrt.f64 k))))
(fabs.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k)))))
(fabs.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) k))) #s(literal 1/2 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k))))

eval165.0ms (2.9%)

Memory: -30.8MiB live, 407.1MiB allocated; 74ms collecting garbage
Compiler: Compiled 45 867 to 5 149 computations (88.8% saved)

prune74.0ms (1.3%)

Memory

33.8MiB live, 169.7MiB allocated; 14ms collecting garbage

Pruning

48 alts after pruning (45 fresh and 3 done)

	Pruned	Kept	Total
New	1 243	30	1 273
Fresh	28	15	43
Picked	5	0	5
Done	-3	3	0
Total	1 273	48	1 321

Accuracy

100.0%

Counts

1 321 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
	73.6%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	99.5%	(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
✓	99.5%	(/.f64 #s(literal 1 binary64) (.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)))
	96.1%	(/.f64 #s(literal 1 binary64) (.f64 (exp.f64 (.f64 (log.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (sqrt.f64 k)))
	74.4%	(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	47.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
	47.2%	#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)))
	47.2%	#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)))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	41.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (sqrt.f64 k)))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))))
	47.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
✓	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 k #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	36.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
	47.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))))
	44.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	21.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 n (PI.f64)) k (.f64 (.f64 n (PI.f64)) k)) (.f64 k k))))
✓	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
	34.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
	26.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) k) (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
	36.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (fabs.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))))
	34.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) #s(literal 1/2 binary64))))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 k k) (PI.f64))) (sqrt.f64 n)) k)))
	36.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 k k) n)) (sqrt.f64 (PI.f64))) k)))
	37.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))) k)))
	36.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (.f64 (sqrt.f64 (.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) k)))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n)) k)))
	25.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n) (.f64 (*.f64 (+.f64 k k) (PI.f64)) n)))) k)))
	51.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) 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)))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 #s(literal 1 binary64) (/.f64 k (sqrt.f64 (.f64 (.f64 (+.f64 k k) (PI.f64)) n))))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (.f64 (*.f64 (+.f64 k k) (PI.f64)) n)))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))) k)))
	49.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))))))

Compiler

Compiled 1 407 to 1 033 computations (26.6% saved)

regimes671.0ms (12.0%)

Memory

-0.7MiB live, 1 721.6MiB allocated; 210ms collecting garbage

Counts

1 → 1

2 → 1

3 → 1

4 → 1

10 → 1

42 → 2

77 → 2

84 → 1

100 → 1

108 → 1

Calls

Call 1

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

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

Call 2

Inputs

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

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

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

Call 3

Inputs

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

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

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

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

Call 4

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

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

Call 5

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

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

Call 6

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

Outputs

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

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

Call 7

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

Outputs

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

Call 8

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

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

Call 9

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

Outputs
(/.f64 #s(literal 1 binary64) (.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)))

Call 10

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

Calls

40 calls:

47.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
45.0ms	n
42.0ms	k
39.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
35.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
36.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
36.5%	1	`k`
36.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
36.5%	1	`n`
36.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
36.5%	1	`k`
36.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
36.5%	1	`n`
36.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
36.5%	1	`k`
36.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
36.5%	1	`n`
36.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
36.5%	1	`k`
36.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
36.5%	1	`n`
47.4%	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))))`
47.4%	1	`k`
47.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
47.4%	1	`n`
60.3%	2	`k`
60.3%	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))))`
60.3%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
60.3%	2	`n`
75.2%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
75.2%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
62.3%	2	`k`
75.2%	2	`n`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.5%	1	`k`
99.5%	1	`n`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.5%	1	`k`
99.5%	1	`n`
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 3 232 to 698 computations (78.4% saved)

bsearch5.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
4.0ms	6.204729800082503e-9	3.717604291570212e-8

Samples

2.0ms

32×

valid

Compiler

Compiled 177 to 134 computations (24.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-pow: 1.0ms (68.0% 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)

bsearch16.0ms (0.3%)

Memory

-44.3MiB live, 11.9MiB allocated; 21ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
15.0ms	5960394577955215000.0	21698296220642173000.0

Samples

2.0ms

32×

valid

Compiler

Compiled 131 to 108 computations (17.6% saved)

Precisions

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

ival-pow: 1.0ms (66.2% 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)

derivations186.0ms (3.3%)

Memory

29.9MiB live, 340.3MiB allocated; 66ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 299 to 88 computations (70.6% saved)

preprocess118.0ms (2.1%)

Memory: 15.5MiB live, 306.2MiB allocated; 40ms collecting garbage
Compiler: Compiled 913 to 511 computations (44.0% saved)

end0.0ms (0.0%)

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

start0.0ms (0.0%)

analyze92.0ms (1.6%)

sample2.3s (41.0%)

preprocess66.0ms (1.2%)

sample0.0ms (0.0%)

series95.0ms (1.7%)

rewrite115.0ms (2.1%)

eval42.0ms (0.7%)

prune24.0ms (0.4%)

sample0.0ms (0.0%)

series164.0ms (2.9%)

rewrite237.0ms (4.2%)

eval206.0ms (3.7%)

prune60.0ms (1.1%)

sample0.0ms (0.0%)

series89.0ms (1.6%)

rewrite225.0ms (4.0%)

eval258.0ms (4.6%)

prune108.0ms (1.9%)

sample0.0ms (0.0%)

series127.0ms (2.3%)

rewrite162.0ms (2.9%)

eval165.0ms (2.9%)

prune74.0ms (1.3%)

regimes671.0ms (12.0%)

bsearch5.0ms (0.1%)

bsearch16.0ms (0.3%)

derivations186.0ms (3.3%)

preprocess118.0ms (2.1%)

end0.0ms (0.0%)

Profiling