Metrics for Migdal et al, Equation (51)

start0.0ms (0.0%)

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

analyze155.0ms (2.1%)

Memory

10.1MiB live, 589.9MiB allocated; 66ms 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)

sample3.8s (51.1%)

Memory

54.8MiB live, 28 756.8MiB allocated; 1.0s collecting garbage

Samples

1.6s	5 560×	1	invalid
1.2s	8 256×	0	valid
180.0ms	470×	2	invalid
35.0ms	342×	0	invalid
35.0ms	226×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 2.1s

ival-pow: 694.0ms (32.8% of total)

ival-mult!: 413.0ms (19.5% of total)

ival-sqrt: 319.0ms (15.1% of total)

adjust: 313.0ms (14.8% of total)

ival-div!: 294.0ms (13.9% of total)

ival-sub!: 84.0ms (4.0% of total)

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

exact: 0.0ms (0.0% of total)

Bogosity

preprocess43.0ms (0.6%)

Memory

20.2MiB live, 215.5MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	101
1	128	87
2	462	87
3	2175	86

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Symmetry

(abs k)

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample0.0ms (0.0%)

Memory

3.9MiB live, 3.9MiB 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)

series192.0ms (2.6%)

Memory

-6.0MiB live, 1 363.9MiB allocated; 40ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	158	949

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)) (+.f64 (.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)) (+.f64 (.f64 k (+.f64 (.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)) (+.f64 (.f64 k (+.f64 (.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 (+.f64 (.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))) (+.f64 (.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))) (+.f64 (.f64 k (+.f64 (.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))) (+.f64 (.f64 k (+.f64 (.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 (+.f64 (.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
89.0ms	n	0
47.0ms	n	-inf
20.0ms	n	inf
3.0ms	k	0
3.0ms	k	-inf

rewrite133.0ms (1.8%)

Memory

23.2MiB live, 991.8MiB allocated; 33ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	97	51
2	351	51
3	1690	51
0	4159	51

Stop Event

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

Counts

13 → 254

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

eval38.0ms (0.5%)

Memory: -1.3MiB live, 433.2MiB allocated; 14ms collecting garbage
Compiler: Compiled 6 283 to 1 153 computations (81.6% saved)

prune24.0ms (0.3%)

Memory

5.5MiB live, 248.3MiB allocated; 10ms collecting garbage

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	266	16	282
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	267	16	283

Accuracy

100.0%

Counts

283 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
▶	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	99.4%	(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
▶	99.5%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.3%	(.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))))
	55.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
▶	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 k #s(literal -1/2 binary64))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal -1/2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
	78.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 n n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (PI.f64) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	78.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
	79.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
▶	95.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	99.3%	(.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))))
▶	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))

Compiler

Compiled 644 to 490 computations (23.9% saved)

sample0.0ms (0.0%)

Memory

6.4MiB live, 6.4MiB allocated; 0ms collecting garbage

Calls

Call 1

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

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

Samples

0.0ms

1×

valid

Compiler

Compiled 13 to 9 computations (30.8% saved)

Precisions

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

adjust: 0.0ms (0.0% of total)

series292.0ms (3.9%)

Memory

14.3MiB live, 1 524.1MiB allocated; 187ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	417	3596

Stop Event

1×	iter-limit

Counts

36 → 104

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
61.0ms	k	inf
43.0ms	n	0
34.0ms	n	-inf
32.0ms	n	inf
28.0ms	k	0

rewrite278.0ms (3.8%)

Memory

14.7MiB live, 1 500.4MiB allocated; 142ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	271
0	74	246
1	276	240
2	896	229
0	4351	229

Stop Event

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

Counts

36 → 1 433

Calls

Call 1

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

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

eval123.0ms (1.7%)

Memory: -0.1MiB live, 758.7MiB allocated; 60ms collecting garbage
Compiler: Compiled 23 727 to 3 313 computations (86.0% saved)

prune37.0ms (0.5%)

Memory

25.5MiB live, 268.1MiB allocated; 10ms collecting garbage

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	870	20	890
Fresh	11	0	11
Picked	5	0	5
Done	0	0	0
Total	886	20	906

Accuracy

100.0%

Counts

906 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
	99.2%	(/.f64 (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
	99.4%	(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	81.7%	(.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)))
	79.1%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (.f64 (pow.f64 (.f64 n (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	99.2%	(.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)))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
▶	55.1%	#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)))
	55.1%	#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)))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	55.3%	#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)))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
	55.3%	#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)))))
▶	55.3%	#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))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 2 binary64) (sqrt.f64 k))))
▶	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	55.2%	#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))))))
▶	55.3%	#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (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)))))

Compiler

Compiled 1 034 to 782 computations (24.4% saved)

sample0.0ms (0.0%)

Memory

3.6MiB live, 3.6MiB allocated; 0ms collecting garbage

Calls

Call 1

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

Outputs
#s(literal 884279719003555/281474976710656 binary64)
#s(literal 884279719003555/140737488355328 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2822212540896131/1125899906842624 binary64)
#s(literal 2 binary64)
#s(literal -1/2 binary64)

Samples

0.0ms

1×

valid

Compiler

Compiled 14 to 9 computations (35.7% saved)

Precisions

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

adjust: 0.0ms (0.0% of total)

series259.0ms (3.5%)

Memory

-14.9MiB live, 1 242.0MiB allocated; 180ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	329	2447

Stop Event

1×	iter-limit

Counts

33 → 90

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
115.0ms	n	0
29.0ms	k	-inf
24.0ms	n	inf
23.0ms	n	-inf
20.0ms	k	0

rewrite196.0ms (2.6%)

Memory

42.9MiB live, 1 291.2MiB allocated; 57ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	280
0	73	245
1	294	239
2	1007	237
0	4171	237

Stop Event

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

Counts

33 → 1 138

Calls

Call 1

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

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

eval218.0ms (2.9%)

Memory: -22.2MiB live, 1 423.7MiB allocated; 132ms collecting garbage
Compiler: Compiled 31 749 to 4 095 computations (87.1% saved)

prune77.0ms (1.0%)

Memory

11.6MiB live, 643.6MiB allocated; 18ms collecting garbage

Pruning

45 alts after pruning (45 fresh and 0 done)

	Pruned	Kept	Total
New	1 001	38	1 039
Fresh	8	7	15
Picked	5	0	5
Done	0	0	0
Total	1 014	45	1 059

Accuracy

100.0%

Counts

1 059 → 45

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
	81.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (.f64 n (+.f64 (PI.f64) (PI.f64))))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) k))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
	99.4%	(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	81.7%	(.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)))
	99.2%	(.f64 (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))
▶	99.7%	(.f64 (sqrt.f64 n) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64))))))
	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (sqrt.f64 n)))) (sqrt.f64 k)))
	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
	54.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
	55.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) #s(approx (sqrt n) (.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
	55.1%	#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)))
▶	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	55.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
	55.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64)) (sqrt.f64 n)) (sqrt.f64 k)))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(literal 2822212540896131/1125899906842624 binary64) (sqrt.f64 n)) (sqrt.f64 k)))
	46.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
	55.3%	#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)))))
	55.1%	#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))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
	55.2%	#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))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
▶	28.5%	#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 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k))))
	55.2%	#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 n)) (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))))))
▶	46.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
	55.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (sqrt.f64 k) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	46.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 k n)))))
	45.6%	#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)))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	45.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
	55.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))))
	26.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 (.f64 n (PI.f64)) k)) (*.f64 k k))))
▶	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (/.f64 n k))))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))))
	55.2%	#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))))))
	38.3%	#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)))
	49.1%	#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 2 552 to 1 904 computations (25.4% saved)

sample0.0ms (0.0%)

Memory

2.3MiB live, 2.3MiB allocated; 0ms collecting garbage

Calls

Call 1

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

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

Samples

0.0ms

1×

valid

Compiler

Compiled 12 to 9 computations (25.0% saved)

Precisions

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

adjust: 0.0ms (0.0% of total)

series160.0ms (2.2%)

Memory

-5.9MiB live, 1 370.0MiB allocated; 52ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	392	2791

Stop Event

1×	iter-limit

Counts

38 → 97

Calls

Call 1

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

Outputs
#s(approx k k)
#s(approx (* -1/2 k) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (pow (* n (+ (PI) (PI))) (* -1/2 k)) #s(literal 1 binary64))
#s(approx (pow (* n (+ (PI) (PI))) (* -1/2 k)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* -1/2 k)) (+.f64 #s(literal 1 binary64) (.f64 k (+.f64 (.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))) (* -1/2 k)) (+.f64 #s(literal 1 binary64) (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (.f64 k (+.f64 (.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 (/ k (+ (PI) (PI))) (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64))))
#s(approx (sqrt (/ k (+ (PI) (PI)))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI))))) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI))))) (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 k (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI))))) (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))) (.f64 k (+.f64 (.f64 #s(literal -1/48 binary64) (/.f64 (.f64 k (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (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 1/2 binary64) (/.f64 k (PI.f64)))))))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))))
#s(approx (* (sqrt n) (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI)))))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64))))))
#s(approx (* (sqrt n) (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI)))))) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 n))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))))
#s(approx (* (sqrt n) (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI)))))) (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))) (.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 n))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))))
#s(approx (* (sqrt n) (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI)))))) (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))) (.f64 k (+.f64 (.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 n))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))) (.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 n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))))))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))))
#s(approx (/ (* 884279719003555/140737488355328 n) k) (*.f64 #s(literal 884279719003555/140737488355328 binary64) (/.f64 n k)))
#s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (+.f64 (.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))) (+.f64 (.f64 k (+.f64 (.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))) (+.f64 (.f64 k (+.f64 (.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 (+.f64 (.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 (/ k (* n (+ (PI) (PI)))) (.f64 #s(literal 1/2 binary64) (/.f64 k (.f64 n (PI.f64)))))
#s(approx (sqrt (/ k (* n (+ (PI) (PI))))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (.f64 n (PI.f64))))))
#s(approx (/ 1 (sqrt (/ k (* n (+ (PI) (PI)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (.f64 n (PI.f64)))))))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (/ (* (sqrt (* n (PI))) (sqrt 2)) (sqrt k)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k)) (/.f64 (sqrt.f64 k) (sqrt.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (/ 1 (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k)))
#s(approx (pow (* n (+ (PI) (PI))) (* -1/2 k)) (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))))))
#s(approx (sqrt (/ k (+ (PI) (PI)))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 k (PI.f64))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI))))) (/.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 k (PI.f64)))))))
#s(approx (* (sqrt n) (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI)))))) (/.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 n)) (.f64 k (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 k (PI.f64)))))))
#s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) (/.f64 n 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 (* n (+ (PI) (PI))))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 k (*.f64 n (PI.f64)))))))
#s(approx (/ 1 (sqrt (/ k (* n (+ (PI) (PI)))))) (/.f64 #s(literal 1 binary64) (.f64 k (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 k (*.f64 n (PI.f64))))))))
#s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* (sqrt (* n (PI))) (sqrt 2)) (sqrt k)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k)) (/.f64 (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (/ 1 (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt (/ k (+ (PI) (PI)))) (.f64 #s(literal -1 binary64) (.f64 k (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 k (PI.f64)))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI))))) (.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 k (PI.f64))))))))
#s(approx (* (sqrt n) (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI)))))) (.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 n)) (.f64 k (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 k (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (sqrt (/ k (* n (+ (PI) (PI))))) (.f64 #s(literal -1 binary64) (.f64 k (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 k (.f64 n (PI.f64))))))))
#s(approx (/ 1 (sqrt (/ k (* n (+ (PI) (PI)))))) (/.f64 #s(literal -1 binary64) (.f64 k (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 k (*.f64 n (PI.f64))))))))
#s(approx (sqrt k) (.f64 #s(literal -1 binary64) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (* (sqrt (* n (PI))) (sqrt 2)) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64)))))))))
#s(approx (/ 1 (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k))) (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64)))))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx n n)
#s(approx (sqrt n) (sqrt.f64 n))
#s(approx (* n (+ (PI) (PI))) (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))
#s(approx (pow (* n (+ (PI) (PI))) (* -1/2 k)) (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI))))) (/.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64))))))
#s(approx (* (sqrt n) (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI)))))) (/.f64 (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64))))))
#s(approx (* 884279719003555/140737488355328 n) (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (/ k (* n (+ (PI) (PI))))) (/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 k n) (PI.f64)))) n))
#s(approx (/ 1 (sqrt (/ k (* n (+ (PI) (PI)))))) (/.f64 n (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 k n) (PI.f64))))))
#s(approx (* n (PI)) (*.f64 n (PI.f64)))
#s(approx (sqrt (* n (PI))) (sqrt.f64 (*.f64 n (PI.f64))))
#s(approx (* (sqrt (* n (PI))) (sqrt 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))))
#s(approx (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI)))) (.f64 #s(literal 4 binary64) (.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) (.f64 n (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI)))))) (sqrt.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))))))
#s(approx (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (/ 1 (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k))) (/.f64 (sqrt.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k)))
#s(approx (sqrt n) (*.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))
#s(approx (pow (* n (+ (PI) (PI))) (* -1/2 k)) (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI))))) (/.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 1/2 binary64) (/.f64 k (PI.f64))))))
#s(approx (* (sqrt n) (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI)))))) (/.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 1 binary64) n)))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64))))))
#s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (* n (PI))) (*.f64 n (sqrt.f64 (/.f64 (PI.f64) n))))
#s(approx (* (sqrt (* n (PI))) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))))
#s(approx (/ (* (sqrt (* n (PI))) (sqrt 2)) (sqrt k)) (/.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (sqrt.f64 k)))
#s(approx (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI)))))) (.f64 n (sqrt.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))) n))))
#s(approx (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (/.f64 #s(literal 1 binary64) (.f64 n (sqrt.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))) n)))))
#s(approx (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k)) (/.f64 (sqrt.f64 k) (.f64 n (sqrt.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))) n)))))
#s(approx (/ 1 (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k))) (/.f64 (.f64 n (sqrt.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))) n))) (sqrt.f64 k)))
#s(approx (sqrt n) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))))
#s(approx (pow (* n (+ (PI) (PI))) (* -1/2 k)) (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI))))) (/.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 1/2 binary64) (/.f64 k (PI.f64))))))
#s(approx (* (sqrt n) (/ (pow (* n (+ (PI) (PI))) (* -1/2 k)) (sqrt (/ k (+ (PI) (PI)))))) (.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 1 binary64) n)))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))))
#s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (* n (PI))) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (/.f64 (PI.f64) n)))))
#s(approx (* (sqrt (* n (PI))) (sqrt 2)) (.f64 #s(literal -1 binary64) (.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))))
#s(approx (/ (* (sqrt (* n (PI))) (sqrt 2)) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (*.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))))))
#s(approx (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI)))))) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))) n))))))
#s(approx (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (/.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))) n))))))
#s(approx (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (.f64 n (sqrt.f64 (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))) n)))))))
#s(approx (/ 1 (* (/ 1 (sqrt (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))))) (sqrt k))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2 binary64)))) n)))) (sqrt.f64 k))))

Calls

6 calls:

Time	Variable	Point
33.0ms	n	0
30.0ms	n	-inf
28.0ms	n	inf
15.0ms	k	-inf
15.0ms	k	0

rewrite259.0ms (3.5%)

Memory

17.8MiB live, 2 089.9MiB allocated; 63ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	345
0	75	290
1	283	275
2	1092	268
0	4126	268

Stop Event

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

Counts

38 → 1 342

Calls

Call 1

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

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

eval236.0ms (3.2%)

Memory: 8.7MiB live, 2 069.5MiB allocated; 85ms collecting garbage
Compiler: Compiled 44 265 to 6 138 computations (86.1% saved)

prune107.0ms (1.4%)

Memory

22.3MiB live, 1 055.1MiB allocated; 22ms collecting garbage

Pruning

51 alts after pruning (50 fresh and 1 done)

	Pruned	Kept	Total
New	1 222	24	1 246
Fresh	14	26	40
Picked	5	0	5
Done	-1	1	0
Total	1 240	51	1 291

Accuracy

100.0%

Counts

1 291 → 51

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
	81.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (.f64 n (+.f64 (PI.f64) (PI.f64))))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) k))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
	99.4%	(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	81.7%	(.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)))
	99.2%	(.f64 (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))
	99.7%	(.f64 (sqrt.f64 n) (/.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k #s(literal 884279719003555/140737488355328 binary64)))))
	55.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (sqrt.f64 n)))) (sqrt.f64 k)))
	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
	54.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
	55.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) #s(approx (sqrt n) (.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
	55.1%	#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)))
	55.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
	55.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
	55.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64)) (sqrt.f64 n)) (sqrt.f64 k)))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(literal 2822212540896131/1125899906842624 binary64) (sqrt.f64 n)) (sqrt.f64 k)))
	46.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)))
	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
	55.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* n (PI))) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
	46.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
	55.3%	#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)))))
	55.2%	#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))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
	28.4%	#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 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64))))))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
	28.5%	#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 (sqrt.f64 (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 n #s(literal 884279719003555/140737488355328 binary64)))))) (sqrt.f64 k))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))))
	1.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 (-.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 (neg.f64 (PI.f64)) n) (.f64 (neg.f64 (PI.f64)) n))) (+.f64 (.f64 (PI.f64) n) (.f64 (neg.f64 (PI.f64)) n)))))))
	46.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
	55.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (sqrt.f64 k) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	46.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 k n)))))
	45.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
	55.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))))
	45.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
	55.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	26.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 (.f64 n (PI.f64)) k)) (*.f64 k k))))
✓	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (/.f64 n k))))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))))
	55.2%	#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))))))
	38.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))) k)))
	49.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))))))

Compiler

Compiled 1 469 to 1 092 computations (25.7% saved)

regimes618.0ms (8.3%)

Memory

-8.8MiB live, 5 132.8MiB allocated; 143ms collecting garbage

Counts

2 → 1

6 → 1

71 → 2

80 → 1

83 → 1

99 → 1

Calls

Call 1

Inputs

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

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

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

Call 2

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

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

Call 3

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(literal 2822212540896131/1125899906842624 binary64) (sqrt.f64 n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n 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)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.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 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64)) (sqrt.f64 n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 (.f64 n (PI.f64)) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 n 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 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 #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 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))))
#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 #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 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* n (PI))) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (sqrt.f64 k) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (/.f64 n k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) #s(approx (sqrt n) (.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 2 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#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))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 k n)))))
#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 (sqrt.f64 (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 n #s(literal 884279719003555/140737488355328 binary64)))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) 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 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.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 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (sqrt.f64 n)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 (-.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 (neg.f64 (PI.f64)) n) (.f64 (neg.f64 (PI.f64)) n))) (+.f64 (.f64 (PI.f64) n) (.f64 (neg.f64 (PI.f64)) n)))))))
#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 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64))))))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))

Outputs

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

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

Call 4

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(literal 2822212540896131/1125899906842624 binary64) (sqrt.f64 n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n 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)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.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 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64)) (sqrt.f64 n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 (.f64 n (PI.f64)) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 n 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 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 #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 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))))
#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 #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 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* n (PI))) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (sqrt.f64 k) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (/.f64 n k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) #s(approx (sqrt n) (.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 2 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#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))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 k n)))))
#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 (sqrt.f64 (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 n #s(literal 884279719003555/140737488355328 binary64)))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) 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 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.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 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (sqrt.f64 n)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 (-.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 (neg.f64 (PI.f64)) n) (.f64 (neg.f64 (PI.f64)) n))) (+.f64 (.f64 (PI.f64) n) (.f64 (neg.f64 (PI.f64)) n)))))))
#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 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64))))))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) -1/2))) (/.f64 #s(literal 1 binary64) (.f64 (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))))
(/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.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)))

Outputs
(/.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 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 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(literal 2822212540896131/1125899906842624 binary64) (sqrt.f64 n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n 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)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.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 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64)) (sqrt.f64 n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 (.f64 n (PI.f64)) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 n 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 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 #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 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))))
#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 #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 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* n (PI))) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (sqrt.f64 k) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (/.f64 n k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) #s(approx (sqrt n) (.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 2 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#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))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 k n)))))
#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 (sqrt.f64 (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 n #s(literal 884279719003555/140737488355328 binary64)))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) 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 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.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 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (sqrt.f64 n)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 (-.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 (neg.f64 (PI.f64)) n) (.f64 (neg.f64 (PI.f64)) n))) (+.f64 (.f64 (PI.f64) n) (.f64 (neg.f64 (PI.f64)) n)))))))
#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 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64))))))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) -1/2))) (/.f64 #s(literal 1 binary64) (.f64 (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))))
(/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.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 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64)))))

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

Call 6

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(literal 2822212540896131/1125899906842624 binary64) (sqrt.f64 n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n 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)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.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 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal 6369051672525773/4503599627370496 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64)) (sqrt.f64 n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 (.f64 n (PI.f64)) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 n 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 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 #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 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))))
#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 #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 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (* n (PI))) (sqrt 2)) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (sqrt.f64 k) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (/.f64 n k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) #s(approx (sqrt n) (.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 2 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#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))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 k n)))))
#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 (sqrt.f64 (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 n #s(literal 884279719003555/140737488355328 binary64)))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) 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 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.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 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (sqrt.f64 n)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 (-.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (PI.f64))) (.f64 (.f64 (neg.f64 (PI.f64)) n) (.f64 (neg.f64 (PI.f64)) n))) (+.f64 (.f64 (PI.f64) n) (.f64 (neg.f64 (PI.f64)) n)))))))
#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 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64))))))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) -1/2))) (/.f64 #s(literal 1 binary64) (.f64 (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))))
(/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.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 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 n) (/.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k #s(literal 884279719003555/140737488355328 binary64)))))
(.f64 (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(.f64 (sqrt.f64 n) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (.f64 n (+.f64 (PI.f64) (PI.f64))))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal -1/2 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 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 n n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (PI.f64) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 k #s(literal -1/2 binary64))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal -1/2 binary64))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (.f64 (pow.f64 (.f64 n (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.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))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) n) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))

Outputs

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

Calls

24 calls:

46.0ms	n
45.0ms	(.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))))
37.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
36.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
35.0ms	k

Results

Accuracy	Segments	Branch
45.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
45.9%	1	`k`
45.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.9%	1	`n`
45.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
45.9%	1	`k`
45.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.9%	1	`n`
67.6%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
67.5%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
67.5%	2	`k`
67.6%	2	`n`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.5%	1	`k`
99.5%	1	`n`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.5%	1	`k`
99.5%	1	`n`
99.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.7%	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))))`
99.7%	1	`k`
99.7%	1	`n`

Compiler

Compiled 2 813 to 578 computations (79.5% saved)

bsearch4.0ms (0.1%)

Memory

-14.3MiB live, 33.5MiB allocated; 1ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
3.0ms	7.230204168863625	109.55910259830918

Samples

1.0ms

16×

valid

Compiler

Compiled 74 to 62 computations (16.2% 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)

derivations110.0ms (1.5%)

Memory

17.2MiB live, 307.8MiB allocated; 5ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 148 to 57 computations (61.5% saved)

preprocess63.0ms (0.9%)

Memory: -0.4MiB live, 431.2MiB allocated; 15ms collecting garbage
Compiler: Compiled 460 to 276 computations (40.0% saved)

end0.0ms (0.0%)

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

start0.0ms (0.0%)

analyze155.0ms (2.1%)

sample3.8s (51.1%)

preprocess43.0ms (0.6%)

sample0.0ms (0.0%)

series192.0ms (2.6%)

rewrite133.0ms (1.8%)

eval38.0ms (0.5%)

prune24.0ms (0.3%)

sample0.0ms (0.0%)

series292.0ms (3.9%)

rewrite278.0ms (3.8%)

eval123.0ms (1.7%)

prune37.0ms (0.5%)

sample0.0ms (0.0%)

series259.0ms (3.5%)

rewrite196.0ms (2.6%)

eval218.0ms (2.9%)

prune77.0ms (1.0%)

sample0.0ms (0.0%)

series160.0ms (2.2%)

rewrite259.0ms (3.5%)

eval236.0ms (3.2%)

prune107.0ms (1.4%)

regimes618.0ms (8.3%)

bsearch4.0ms (0.1%)

derivations110.0ms (1.5%)

preprocess63.0ms (0.9%)

end0.0ms (0.0%)

Profiling