Metrics for Migdal et al, Equation (51)

start0.0ms (0.0%)

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

analyze131.0ms (2.0%)

Memory

-14.3MiB live, 145.9MiB allocated; 68ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample2.6s (39.9%)

Memory

39.0MiB live, 3 917.1MiB allocated; 727ms collecting garbage

Samples

1.1s	5 406×	1	invalid
677.0ms	8 255×	0	valid
127.0ms	497×	2	invalid
44.0ms	247×	0	exit
19.0ms	347×	0	invalid
0.0ms	1×	1	valid

Precisions

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

ival-pow: 468.0ms (34.9% of total)

adjust: 247.0ms (18.4% of total)

ival-mult!: 227.0ms (16.9% of total)

ival-div!: 195.0ms (14.5% of total)

ival-sqrt: 148.0ms (11.0% of total)

ival-sub!: 57.0ms (4.2% of total)

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

exact: 0.0ms (0.0% of total)

Bogosity

preprocess50.0ms (0.8%)

Memory

1.9MiB live, 51.2MiB allocated; 23ms 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

0.7MiB live, 0.7MiB 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)

series120.0ms (1.8%)

Memory

22.4MiB live, 202.6MiB allocated; 45ms 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
50.0ms	n	0
28.0ms	n	-inf
8.0ms	n	inf
2.0ms	k	0
2.0ms	k	-inf

rewrite130.0ms (2.0%)

Memory

17.4MiB live, 243.1MiB allocated; 46ms 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))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (+.f64 k k))))
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(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))
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(.f64 (pow.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 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))))
(.f64 (pow.f64 (.f64 (cbrt.f64 (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
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(.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) (+.f64 n n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (cbrt.f64 (PI.f64)) n (.f64 (cbrt.f64 (PI.f64)) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
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(.f64 (pow.f64 (cbrt.f64 (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (+.f64 n n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) (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 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 n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (+.f64 n n) (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))))
(.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
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(.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 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)))

eval55.0ms (0.9%)

Memory: 3.8MiB live, 93.4MiB allocated; 12ms collecting garbage
Compiler: Compiled 7 451 to 1 285 computations (82.8% saved)

prune77.0ms (1.2%)

Memory

-12.6MiB live, 42.8MiB allocated; 61ms collecting garbage

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	320	16	336
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	321	16	337

Accuracy

100.0%

Counts

337 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	99.6%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	99.4%	(.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))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	52.2%	(.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)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
	73.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
▶	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
	74.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	95.8%	(.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))))
	99.4%	(.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))))
▶	52.3%	#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)))
	95.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
	95.8%	#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)))))

Compiler

Compiled 682 to 540 computations (20.8% saved)

sample0.0ms (0.0%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Calls

Call 1

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

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

Samples

0.0ms

1×

valid

Compiler

Compiled 13 to 9 computations (30.8% saved)

Precisions

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

adjust: 0.0ms (0.0% of total)

series130.0ms (2.0%)

Memory

52.5MiB live, 662.0MiB allocated; 57ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	528	4505

Stop Event

1×	iter-limit

Counts

37 → 128

Calls

Call 1

Inputs
n
(PI.f64)
(+.f64 (PI.f64) (PI.f64))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
k
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(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)))
(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))
#s(literal 2 binary64)
(*.f64 n (PI.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 (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)))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(/.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 (/.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)))))
(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 #s(literal 2 binary64) (PI.f64))
(.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) (.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 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 (+ (* 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 (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (fma.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (+ (* 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 (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal -1/2 binary64)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)) (fma.f64 #s(literal 1/2 binary64) (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal -1/2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal -1/2 binary64))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* 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 (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)) (fma.f64 k (fma.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal -1/2 binary64))) (.f64 k (fma.f64 #s(literal 1/48 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal -1/2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal -1/2 binary64))))))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal -1/2 binary64))))
#s(approx (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2))) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal -1/2 binary64))))
#s(approx (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 k (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 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal -1/2 binary64)))))
#s(approx (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2))) (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)) (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))))))) (.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 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal -1/2 binary64)))))
#s(approx (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2))) (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)) (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)))))) (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)) (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)) (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)) (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))))))) (.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 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal -1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (/.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 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (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 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (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 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (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 (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 k) #s(literal 1 binary64))
#s(approx (- 1 k) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
#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 (* 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 (+ (* 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 (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) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (pow (* 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 (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (+ (* 1/2 k) -1/2) (*.f64 #s(literal 1/2 binary64) k))
#s(approx (+ (* 1/2 k) -1/2) (.f64 k (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* 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 (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2))) (/.f64 #s(literal 1 binary64) (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 (* (/ 1 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (/.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 (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 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 (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 (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 (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 (+ (* 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 (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) (.f64 #s(literal -1 binary64) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (pow (* 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 (/ 1 (sqrt k)) (/.f64 #s(literal -1 binary64) (*.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 (* n (+ (PI) (PI))) (+ (* 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 (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2))) (/.f64 #s(literal 1 binary64) (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 (* (/ 1 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (/.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 (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 k) (.f64 #s(literal -1 binary64) (.f64 k (-.f64 #s(literal 1 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 (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)) (* (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 (* n (+ (PI) (PI))) (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))
#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 (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* 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))) (+ (* 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 (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2))) (/.f64 #s(literal 1 binary64) (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 (* (/ 1 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (/.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 (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 (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 (* 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 (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (pow (* 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))) (+ (* 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 (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2))) (/.f64 #s(literal 1 binary64) (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 (* (/ 1 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (/.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 (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 (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 (* 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 (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (sqrt k)) (/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (pow (* 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))) (+ (* 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 (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2))) (/.f64 #s(literal 1 binary64) (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 (* (/ 1 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (/.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 (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 (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
24.0ms	n	-inf
24.0ms	n	0
21.0ms	n	inf
11.0ms	k	inf
9.0ms	k	-inf

rewrite265.0ms (4.1%)

Memory

-12.6MiB live, 1 013.0MiB allocated; 174ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	268
0	78	222
1	311	215
2	1024	215
0	4129	215

Stop Event

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

Counts

37 → 2 102

Calls

Call 1

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

eval175.0ms (2.7%)

Memory: 51.1MiB live, 458.2MiB allocated; 103ms collecting garbage
Compiler: Compiled 43 205 to 5 031 computations (88.4% saved)

prune48.0ms (0.7%)

Memory

-18.6MiB live, 118.4MiB allocated; 13ms collecting garbage

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	1 533	22	1 555
Fresh	10	1	11
Picked	5	0	5
Done	0	0	0
Total	1 548	23	1 571

Accuracy

100.0%

Counts

1 571 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.6%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
	99.3%	(/.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	74.2%	(.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)))
	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))))
	52.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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))))))))))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal -1/2 binary64))) (sqrt.f64 k)))
	52.0%	#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))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k)))
	52.1%	#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)))
	52.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	42.8%	#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))))
	52.3%	#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)))
	48.9%	#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)))
	52.2%	#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)))
	42.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	51.9%	#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)))))
▶	52.2%	#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))))
▶	42.8%	#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)))))
▶	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	52.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
▶	52.2%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (/.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)))))

Compiler

Compiled 1 282 to 960 computations (25.1% saved)

sample0.0ms (0.0%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Calls

Call 1

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

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

series296.0ms (4.6%)

Memory

7.5MiB live, 366.9MiB allocated; 212ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	412	2731

Stop Event

1×	iter-limit

Counts

34 → 96

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
176.0ms	k	0
28.0ms	n	0
26.0ms	n	inf
22.0ms	n	-inf
14.0ms	k	-inf

rewrite168.0ms (2.6%)

Memory

10.5MiB live, 436.8MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	273
0	76	243
1	324	229
2	1088	228
0	4336	228

Stop Event

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

Counts

34 → 1 601

Calls

Call 1

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

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

eval166.0ms (2.6%)

Memory: 8.9MiB live, 385.6MiB allocated; 63ms collecting garbage
Compiler: Compiled 51 448 to 5 814 computations (88.7% saved)

prune94.0ms (1.5%)

Memory

8.0MiB live, 199.2MiB allocated; 17ms collecting garbage

Pruning

48 alts after pruning (45 fresh and 3 done)

	Pruned	Kept	Total
New	1 459	35	1 494
Fresh	8	10	18
Picked	5	0	5
Done	-3	3	0
Total	1 469	48	1 517

Accuracy

100.0%

Counts

1 517 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (pow.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 #s(literal 1 binary64) (sqrt.f64 k))))
✓	99.6%	(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	51.6%	(/.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(approx (+ ( k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	99.3%	(/.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	74.2%	(.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)))
	52.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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))))))))))
	52.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k)))
	52.1%	#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)))
	52.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	52.3%	#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)))
	48.9%	#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)))
	52.2%	#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)))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	52.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
▶	52.1%	#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))))
	52.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
▶	52.1%	#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 n n)) (sqrt.f64 (PI.f64)))))
	52.1%	#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) n)) (sqrt.f64 #s(literal 2 binary64)))))
✓	52.2%	#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))))
	52.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (fabs.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	52.2%	#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))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 n (sqrt.f64 k))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n (sqrt.f64 k))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	39.0%	#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)))))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
	42.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	42.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n (sqrt.f64 k))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
▶	39.1%	#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)))))
	23.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 (.f64 (PI.f64) n) k)) (.f64 k k))))
✓	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	24.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
	4.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fabs.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k))))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
▶	39.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
	42.3%	#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)))
	52.0%	#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 2 670 to 2 011 computations (24.7% saved)

sample3.0ms (0.0%)

Memory

-49.7MiB live, 1.1MiB allocated; 5ms collecting garbage

Calls

Call 1

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

Outputs
#s(literal 884279719003555/140737488355328 binary64)
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 884279719003555/281474976710656 binary64)
#s(literal 884279719003555/140737488355328 binary64)
#s(literal 2 binary64)
#s(literal 6369051672525773/4503599627370496 binary64)
#s(literal 7982422502469483/4503599627370496 binary64)

Samples

2.0ms

1×

valid

Compiler

Compiled 15 to 11 computations (26.7% saved)

Precisions

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

adjust: 0.0ms (0.0% of total)

series99.0ms (1.5%)

Memory

8.8MiB live, 256.6MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	346	2001

Stop Event

1×	iter-limit

Counts

39 → 85

Calls

Call 1

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

Outputs
#s(approx k k)
#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 (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))
#s(approx (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (fma.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))))
#s(approx (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))))
#s(approx (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))))))) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (/ 1 (/ 1 (sqrt k)))) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (/ 1 (/ 1 (sqrt k)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (/ 1 (/ 1 (sqrt k)))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (/ 1 (/ 1 (sqrt k)))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (sqrt.f64 k)) (.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (+ (PI) (PI)) k) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
#s(approx (* n (/ (+ (PI) (PI)) k)) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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 (/ n k) (/.f64 n k))
#s(approx (* (PI) (/ n k)) (/.f64 (*.f64 n (PI.f64)) k))
#s(approx (sqrt (* (PI) (/ n k))) (/.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) k))
#s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64))))) k))
#s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)))
#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)))) (sqrt (* (+ (PI) (PI)) n))) (/.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) (*.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 (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
#s(approx (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 (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (/ 1 (/ 1 (sqrt k)))) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k)))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) 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 (sqrt (* (PI) (/ n k))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
#s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (*.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)))) (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 (+ (* 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 (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
#s(approx (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 (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (/ 1 (/ 1 (sqrt k)))) (.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (.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)))) (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 (* n 884279719003555/140737488355328) (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))
#s(approx (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (log.f64 n)))))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (/ 1 (/ 1 (sqrt k)))) (/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (log.f64 n)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (+ n n) (*.f64 #s(literal 2 binary64) n))
#s(approx (sqrt (+ n n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
#s(approx (* (sqrt (+ n n)) (sqrt (PI))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))))
#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 (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
#s(approx (/ (pow (* n 884279719003555/140737488355328) (+ (* k -1/2) 1/2)) (/ 1 (/ 1 (sqrt k)))) (/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (* (PI) (/ n k))) (.f64 n (sqrt.f64 (/.f64 (PI.f64) (.f64 k n)))))
#s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (sqrt (+ n n)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 2 binary64) n))))
#s(approx (* (sqrt (+ n n)) (sqrt (PI))) (.f64 n (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))))
#s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 n (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))) (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 (sqrt k)) (sqrt (sqrt k)))) (sqrt (* (+ (PI) (PI)) n))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (* (PI) (/ n k))) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (.f64 #s(literal -1 binary64) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (.f64 k n)))))))
#s(approx (sqrt (+ n n)) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))))
#s(approx (* (sqrt (+ n n)) (sqrt (PI))) (.f64 #s(literal -1 binary64) (.f64 n (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) n))))))
#s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))) (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 (sqrt k)) (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
27.0ms	n	-inf
22.0ms	n	0
19.0ms	n	inf
5.0ms	k	-inf
5.0ms	k	0

rewrite217.0ms (3.3%)

Memory

37.0MiB live, 1 278.6MiB allocated; 48ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	285
0	77	240
1	299	226
2	1152	226
0	4068	226

Stop Event

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

Counts

39 → 1 946

Calls

Call 1

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

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

eval197.0ms (3.0%)

Memory: -20.4MiB live, 459.4MiB allocated; 114ms collecting garbage
Compiler: Compiled 56 731 to 6 518 computations (88.5% saved)

prune129.0ms (2.0%)

Memory

16.6MiB live, 213.0MiB allocated; 13ms collecting garbage

Pruning

58 alts after pruning (52 fresh and 6 done)

	Pruned	Kept	Total
New	1 651	21	1 672
Fresh	9	31	40
Picked	5	0	5
Done	-3	6	3
Total	1 662	58	1 720

Accuracy

100.0%

Counts

1 720 → 58

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 (pow.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 #s(literal 1 binary64) (sqrt.f64 k))))
✓	99.6%	(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	51.6%	(/.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(approx (+ ( k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	99.3%	(/.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	74.2%	(.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)))
	52.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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))))))))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k)))
	52.1%	#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)))
	52.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	52.3%	#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)))
	48.9%	#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)))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 k)))))
	52.0%	#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)))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))))
✓	52.1%	#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))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))))
✓	52.1%	#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 n n)) (sqrt.f64 (PI.f64)))))
	52.1%	#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 n n)) #s(literal 7982422502469483/4503599627370496 binary64))))
	52.1%	#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) n)) (sqrt.f64 #s(literal 2 binary64)))))
	27.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 n n) (+.f64 n n)))) (sqrt.f64 (PI.f64)))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (fabs.f64 (+.f64 n n))) (sqrt.f64 (PI.f64)))))
	52.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (sqrt (+ n n)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 (PI.f64)))))
	52.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (fabs.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	52.2%	#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))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) (sqrt.f64 (+.f64 n n))))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 n (sqrt.f64 k))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n (sqrt.f64 k))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
	39.0%	#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)))))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
	42.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	42.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n (sqrt.f64 k))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
	52.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
	39.1%	#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 (/.f64 #s(literal 1 binary64) k) n)))))
	39.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(literal 6369051672525773/4503599627370496 binary64) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))))
✓	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	24.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
	4.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fabs.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k))))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (fma.f64 (PI.f64) k (.f64 (PI.f64) k)) (*.f64 k k)))))
✓	39.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
	39.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 n (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 k))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
	42.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64))))) k)))
	51.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
	42.3%	#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)))
	52.0%	#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 1 707 to 1 289 computations (24.5% saved)

regimes1.1s (17.1%)

Memory

-147.2MiB live, 976.7MiB allocated; 1.4s collecting garbage

Counts

9 → 1

17 → 1

68 → 2

70 → 2

95 → 1

Calls

Call 1

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

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

Call 2

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

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

Call 3

Inputs
#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 (PI.f64) (/.f64 (+.f64 n 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(literal 6369051672525773/4503599627370496 binary64) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fabs.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.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)) k)) (sqrt.f64 n)))
#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 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#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))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.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 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.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)) (.f64 (sqrt.f64 (+.f64 n n)) #s(literal 7982422502469483/4503599627370496 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (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 (fabs.f64 (.f64 (+.f64 (PI.f64) (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))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) (sqrt.f64 (+.f64 n n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 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 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (fabs.f64 (+.f64 n n))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 n (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (fma.f64 (PI.f64) k (.f64 (PI.f64) k)) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.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))) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#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 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (sqrt (+ n n)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 (.f64 (PI.f64) n) k)) (.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #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) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#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))) #s(approx (* (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (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)) (.f64 (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 n n) (+.f64 n n)))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 n (sqrt.f64 k))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.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 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.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 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))

Outputs

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

#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)))))))

Call 4

Inputs
#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 (PI.f64) (/.f64 (+.f64 n 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(literal 6369051672525773/4503599627370496 binary64) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fabs.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.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)) k)) (sqrt.f64 n)))
#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 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#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))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.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 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.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)) (.f64 (sqrt.f64 (+.f64 n n)) #s(literal 7982422502469483/4503599627370496 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (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 (fabs.f64 (.f64 (+.f64 (PI.f64) (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))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) (sqrt.f64 (+.f64 n n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 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 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (fabs.f64 (+.f64 n n))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 n (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (fma.f64 (PI.f64) k (.f64 (PI.f64) k)) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.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))) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#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 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (sqrt (+ n n)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 (.f64 (PI.f64) n) k)) (.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #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) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#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))) #s(approx (* (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (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)) (.f64 (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 n n) (+.f64 n n)))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 n (sqrt.f64 k))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.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 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.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 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(approx (+ ( k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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)))))

Outputs

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

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

Call 5

Inputs
#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 (PI.f64) (/.f64 (+.f64 n 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(literal 6369051672525773/4503599627370496 binary64) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fabs.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.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)) k)) (sqrt.f64 n)))
#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 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#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))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.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 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.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)) (.f64 (sqrt.f64 (+.f64 n n)) #s(literal 7982422502469483/4503599627370496 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (PI) (/ n k)))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (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 (fabs.f64 (.f64 (+.f64 (PI.f64) (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))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) (sqrt.f64 (+.f64 n n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 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 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (fabs.f64 (+.f64 n n))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 n (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (fma.f64 (PI.f64) k (.f64 (PI.f64) k)) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.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))) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#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 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ 1 (sqrt k)) (* (sqrt (+ n n)) (sqrt (PI)))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (sqrt (+ n n)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 (.f64 (PI.f64) n) k)) (.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #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) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#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))) #s(approx (* (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))) (neg.f64 (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (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)) (.f64 (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 n n) (+.f64 n n)))) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 n (sqrt.f64 k))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (/.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 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.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 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(approx (+ ( k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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)))))
(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
#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)))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (+ (PI) (PI))) (+ (* 1/2 k) -1/2)))) (/.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)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal -1/2 binary64))) (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 (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 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (pow.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 #s(literal 1 binary64) (sqrt.f64 k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 (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 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (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 (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 (* (/ 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)))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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))))))))))
(.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 (/.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 (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))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

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

Calls

20 calls:

61.0ms	(.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))))
40.0ms	k
38.0ms	n
34.0ms	(.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))))
28.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
39.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
39.3%	1	`k`
39.3%	1	`n`
39.3%	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))))`
52.3%	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))))`
52.3%	1	`k`
52.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
52.3%	1	`n`
62.9%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
62.9%	2	`n`
62.9%	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))))`
62.9%	2	`k`
71.0%	4	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.1%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.1%	2	`k`
71.0%	4	`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 2 784 to 560 computations (79.9% saved)

bsearch24.0ms (0.4%)

Memory

2.2MiB live, 46.6MiB allocated; 6ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
22.0ms	7.038084805290388e-11	219.76676632422755

Samples

15.0ms

160×

valid

Compiler

Compiled 439 to 378 computations (13.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-div!: 6.0ms (52.3% of total)

ival-pow: 3.0ms (26.2% of total)

ival-sqrt: 1.0ms (8.7% of total)

ival-mult!: 1.0ms (8.7% of total)

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

adjust: 0.0ms (0.0% of total)

bsearch2.0ms (0.0%)

Memory

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

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
2.0ms	8.277109267095004e-44	4.3661813707200205e-33

Samples

1.0ms

16×

valid

Compiler

Compiled 81 to 67 computations (17.3% saved)

Precisions

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

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-pow: 0.0ms (0.0% of total)

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

derivations158.0ms (2.4%)

Memory

8.9MiB live, 165.8MiB allocated; 98ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 174 to 63 computations (63.8% saved)

preprocess52.0ms (0.8%)

Memory: -27.2MiB live, 110.8MiB allocated; 25ms collecting garbage
Compiler: Compiled 538 to 314 computations (41.6% saved)

end0.0ms (0.0%)

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

start0.0ms (0.0%)

analyze131.0ms (2.0%)

sample2.6s (39.9%)

preprocess50.0ms (0.8%)

sample0.0ms (0.0%)

series120.0ms (1.8%)

rewrite130.0ms (2.0%)

eval55.0ms (0.9%)

prune77.0ms (1.2%)

sample0.0ms (0.0%)

series130.0ms (2.0%)

rewrite265.0ms (4.1%)

eval175.0ms (2.7%)

prune48.0ms (0.7%)

sample0.0ms (0.0%)

series296.0ms (4.6%)

rewrite168.0ms (2.6%)

eval166.0ms (2.6%)

prune94.0ms (1.5%)

sample3.0ms (0.0%)

series99.0ms (1.5%)

rewrite217.0ms (3.3%)

eval197.0ms (3.0%)

prune129.0ms (2.0%)

regimes1.1s (17.1%)

bsearch24.0ms (0.4%)

bsearch2.0ms (0.0%)

derivations158.0ms (2.4%)

preprocess52.0ms (0.8%)

end0.0ms (0.0%)

Profiling