Metrics for Migdal et al, Equation (51)

start0.0ms (0.0%)

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

analyze130.0ms (2.0%)

Memory

-30.6MiB live, 207.3MiB allocated; 44ms 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)

sample3.5s (53.0%)

Memory

9.9MiB live, 4 330.4MiB allocated; 2.1s collecting garbage

Samples

1.3s	8 255×	0	valid
1.2s	5 580×	1	invalid
188.0ms	496×	2	invalid
51.0ms	363×	0	invalid
27.0ms	261×	0	exit
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-pow: 495.0ms (30.9% of total)

ival-mult!: 323.0ms (20.2% of total)

ival-sqrt: 272.0ms (17.0% of total)

adjust: 246.0ms (15.4% of total)

ival-div!: 186.0ms (11.6% of total)

ival-sub!: 78.0ms (4.9% of total)

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

exact: 0.0ms (0.0% of total)

Bogosity

preprocess65.0ms (1.0%)

Memory

-38.2MiB live, 45.1MiB allocated; 52ms 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

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

Calls

Call 1

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

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

Samples

0.0ms

1×

valid

Compiler

Compiled 8 to 6 computations (25.0% saved)

Precisions

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

adjust: 0.0ms (0.0% of total)

series101.0ms (1.5%)

Memory

35.7MiB live, 172.6MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	158	937

Stop Event

1×	iter-limit

Counts

13 → 37

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
50.0ms	n	0
26.0ms	n	-inf
8.0ms	n	inf
2.0ms	k	0
2.0ms	k	-inf

rewrite106.0ms (1.6%)

Memory

-26.8MiB live, 165.2MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	97	51
2	351	51
3	1690	51
0	4159	48

Stop Event

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

Counts

13 → 308

Calls

Call 1

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

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

eval42.0ms (0.6%)

Memory: 16.1MiB live, 111.4MiB allocated; 10ms collecting garbage
Compiler: Compiled 7 466 to 1 284 computations (82.8% saved)

prune20.0ms (0.3%)

Memory

-1.4MiB live, 45.3MiB allocated; 3ms collecting garbage

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	319	18	337
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	320	18	338

Accuracy

100.0%

Counts

338 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
▶	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	99.5%	(.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))))
	43.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 (+.f64 (pow.f64 (.f64 n (PI.f64)) #s(literal 3 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 3 binary64))) (fma.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)) (-.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64))) (.f64 (.f64 n (PI.f64)) (*.f64 n (PI.f64)))))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	45.1%	(.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))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.6%	(.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))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) k))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
	72.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 n n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
▶	72.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	96.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.3%	(.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	96.5%	(.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	45.2%	#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 738 to 540 computations (26.8% saved)

sample0.0ms (0.0%)

Memory

1.0MiB live, 0.9MiB allocated; 0ms collecting garbage

Calls

Call 1

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

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

series247.0ms (3.7%)

Memory

10.7MiB live, 388.8MiB allocated; 64ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	631	5348

Stop Event

1×	iter-limit

Counts

38 → 138

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
68.0ms	n	-inf
66.0ms	n	0
59.0ms	n	inf
9.0ms	k	inf
9.0ms	k	0

rewrite251.0ms (3.8%)

Memory

64.5MiB live, 642.8MiB allocated; 129ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	289
0	79	235
1	299	228
2	964	228
0	4129	228

Stop Event

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

Counts

38 → 2 546

Calls

Call 1

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

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

eval212.0ms (3.2%)

Memory: -23.0MiB live, 542.8MiB allocated; 136ms collecting garbage
Compiler: Compiled 46 689 to 4 626 computations (90.1% saved)

prune42.0ms (0.6%)

Memory

3.2MiB live, 148.7MiB allocated; 9ms collecting garbage

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	1 530	20	1 550
Fresh	11	2	13
Picked	5	0	5
Done	0	0	0
Total	1 546	22	1 568

Accuracy

100.0%

Counts

1 568 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.5%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
	45.1%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ ( k -1/2) 1/2) #s(literal 1/2 binary64)))))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
	76.2%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
	78.0%	(.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)))
	99.5%	(.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))))
	99.4%	(.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 k)))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	96.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	45.2%	#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)))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))))
	34.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	45.1%	#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))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
▶	33.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #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))))
▶	45.1%	#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))))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2)))) (/.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (PI.f64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))

Compiler

Compiled 1 018 to 782 computations (23.2% saved)

sample0.0ms (0.0%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Calls

Call 1

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

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

Samples

0.0ms

1×

valid

Compiler

Compiled 10 to 8 computations (20.0% saved)

Precisions

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

adjust: 0.0ms (0.0% of total)

series102.0ms (1.6%)

Memory

-16.0MiB live, 241.4MiB allocated; 44ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	371	2745

Stop Event

1×	iter-limit

Counts

35 → 92

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
30.0ms	n	0
16.0ms	n	-inf
16.0ms	n	inf
8.0ms	k	0
8.0ms	k	inf

rewrite192.0ms (2.9%)

Memory

20.8MiB live, 375.5MiB allocated; 80ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	48	288
0	77	292
1	307	280
2	1063	262
0	4122	262

Stop Event

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

Counts

35 → 1 155

Calls

Call 1

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

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

eval245.0ms (3.7%)

Memory: 2.8MiB live, 305.8MiB allocated; 165ms collecting garbage
Compiler: Compiled 40 174 to 5 091 computations (87.3% saved)

prune79.0ms (1.2%)

Memory

6.0MiB live, 98.4MiB allocated; 5ms collecting garbage

Pruning

40 alts after pruning (40 fresh and 0 done)

	Pruned	Kept	Total
New	1 311	33	1 344
Fresh	10	7	17
Picked	5	0	5
Done	0	0	0
Total	1 326	40	1 366

Accuracy

100.0%

Counts

1 366 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	78.0%	(/.f64 (sqrt.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
	45.2%	(/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx ( (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (.f64 #s(literal 1/2 binary64) k))))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	78.0%	(.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)))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
▶	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))))
	34.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	33.3%	#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)))))
	45.1%	#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))))))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
	45.1%	#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))))
	33.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
	45.2%	#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))))
▶	33.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))))
	33.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))))
	22.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 n (PI.f64)) k (.f64 (.f64 n (PI.f64)) k)) (.f64 k k))))
▶	33.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
	23.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
	31.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
	33.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
	33.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
	33.5%	#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))))
	33.5%	#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))))
	31.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
	38.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
	45.1%	#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 n (+.f64 (PI.f64) (PI.f64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k))))))
	34.8%	#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 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))))
	38.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 k (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1 binary64) k)))))))
	38.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	45.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
	45.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
	38.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k)))
	52.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))

Compiler

Compiled 2 400 to 1 766 computations (26.4% saved)

sample0.0ms (0.0%)

Memory

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

Calls

Call 1

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

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

series110.0ms (1.7%)

Memory

-0.3MiB live, 182.3MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	347	2145

Stop Event

1×	iter-limit

Counts

33 → 79

Calls

Call 1

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

Outputs
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k))))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (fma.f64 k (-.f64 (.f64 #s(literal -1 binary64) (.f64 k (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k))))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (fma.f64 k (-.f64 (.f64 k (-.f64 (.f64 #s(literal -1 binary64) (.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k))))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)) (.f64 #s(literal 1/48 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k))))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k))))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (+.f64 (sqrt.f64 k) (.f64 #s(literal 1/2 binary64) (.f64 k (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k))))))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (+.f64 (sqrt.f64 k) (.f64 k (fma.f64 #s(literal 1/8 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 k))) (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)))))))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (+.f64 (sqrt.f64 k) (.f64 k (fma.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)) (.f64 k (fma.f64 #s(literal 1/48 binary64) (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (sqrt.f64 k))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 k)))))))))
#s(approx k k)
#s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) #s(literal 1 binary64))
#s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))))))
#s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (.f64 k (fma.f64 #s(literal 1/8 binary64) (.f64 k (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)))))))
#s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (.f64 k (fma.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (.f64 k (fma.f64 #s(literal 1/48 binary64) (.f64 k (pow.f64 (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64))) (.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)))))))))
#s(approx (* 1/2 k) (*.f64 #s(literal 1/2 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n))) k))
#s(approx (/ (* 884279719003555/140737488355328 n) k) (*.f64 #s(literal 884279719003555/140737488355328 binary64) (/.f64 n k)))
#s(approx (* (sqrt 2) (sqrt (/ (* n (PI)) k))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64))))) k))
#s(approx (sqrt (/ (* n (PI)) k)) (/.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) k))
#s(approx (/ (* n (PI)) k) (/.f64 (*.f64 n (PI.f64)) k))
#s(approx (/ (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (sqrt (sqrt k))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) (sqrt.f64 k)))))
#s(approx (/ (* (+ (PI) (PI)) n) (sqrt k)) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) (sqrt.f64 k))))
#s(approx (sqrt (sqrt k)) (sqrt.f64 (sqrt.f64 k)))
#s(approx (/ (sqrt (sqrt k)) (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k)))) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) (sqrt.f64 k))))))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (.f64 k (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (.f64 k (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (*.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 (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 (/ (* 884279719003555/140737488355328 n) k)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) (/.f64 n k))))
#s(approx (* (sqrt 2) (sqrt (/ (* n (PI)) k))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))))
#s(approx (sqrt (/ (* n (PI)) k)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
#s(approx (/ (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (sqrt (sqrt k))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))) (.f64 k (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (/ (* (+ (PI) (PI)) n) (sqrt k)) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (sqrt (sqrt k)) (*.f64 k (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))
#s(approx (/ (sqrt (sqrt k)) (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k)))) (/.f64 (.f64 k (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (.f64 k (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (.f64 #s(literal -1 binary64) (.f64 k (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (sqrt k) (.f64 #s(literal -1 binary64) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (sqrt (sqrt k))) (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal -2 binary64) (/.f64 (.f64 n (PI.f64)) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))) (.f64 k (sqrt.f64 (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (sqrt.f64 (.f64 #s(literal -2 binary64) (/.f64 (.f64 n (PI.f64)) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (/ (* (+ (PI) (PI)) n) (sqrt k)) (.f64 #s(literal -2 binary64) (/.f64 (.f64 n (PI.f64)) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (sqrt (sqrt k)) (.f64 #s(literal -1 binary64) (.f64 k (sqrt.f64 (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))))
#s(approx (/ (sqrt (sqrt k)) (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k)))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 k (sqrt.f64 (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)))) (sqrt.f64 (.f64 #s(literal -2 binary64) (/.f64 (.f64 n (PI.f64)) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (log.f64 n))))) (sqrt.f64 k))))
#s(approx (sqrt (* 884279719003555/140737488355328 n)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)))
#s(approx (* 884279719003555/140737488355328 n) (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))
#s(approx n n)
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (log.f64 n))))) (sqrt.f64 k)))
#s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (log.f64 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (* n (PI)) (*.f64 n (PI.f64)))
#s(approx (* (+ (PI) (PI)) n) (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (/.f64 (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 k))))
#s(approx (sqrt (* 884279719003555/140737488355328 n)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) n))))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 k)))
#s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (.f64 k n)))))
#s(approx (* (sqrt 2) (sqrt (/ (* n (PI)) k))) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (sqrt (/ (* n (PI)) k)) (.f64 n (sqrt.f64 (/.f64 (PI.f64) (.f64 k n)))))
#s(approx (/ (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (sqrt (sqrt k))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k)))))))
#s(approx (/ (sqrt (sqrt k)) (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k)))) (/.f64 (sqrt.f64 (sqrt.f64 k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (sqrt.f64 k))))))))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 k)))))
#s(approx (sqrt (* 884279719003555/140737488355328 n)) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (/.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 (.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 (/ (* 884279719003555/140737488355328 n) k)) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
#s(approx (* (sqrt 2) (sqrt (/ (* n (PI)) k))) (.f64 #s(literal -1 binary64) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (.f64 k n)))))))
#s(approx (sqrt (/ (* n (PI)) k)) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (/ (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (sqrt (sqrt k))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (.f64 n (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k)))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k))) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (.f64 n (sqrt.f64 k))))))))
#s(approx (/ (sqrt (sqrt k)) (sqrt (/ (* (+ (PI) (PI)) n) (sqrt k)))) (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (.f64 n (sqrt.f64 k)))))))))

Calls

6 calls:

Time	Variable	Point
30.0ms	n	0
21.0ms	n	inf
20.0ms	n	-inf
9.0ms	k	-inf
5.0ms	k	0

rewrite129.0ms (2.0%)

Memory

36.5MiB live, 222.4MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	267
0	65	240
1	249	231
2	863	225
0	4200	220

Stop Event

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

Counts

33 → 1 143

Calls

Call 1

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

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

eval157.0ms (2.4%)

Memory: -5.6MiB live, 283.4MiB allocated; 59ms collecting garbage
Compiler: Compiled 41 076 to 4 600 computations (88.8% saved)

prune78.0ms (1.2%)

Memory

-1.7MiB live, 141.6MiB allocated; 11ms collecting garbage

Pruning

57 alts after pruning (55 fresh and 2 done)

	Pruned	Kept	Total
New	1 174	41	1 215
Fresh	21	14	35
Picked	3	2	5
Done	0	0	0
Total	1 198	57	1 255

Accuracy

100.0%

Counts

1 255 → 57

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	78.0%	(/.f64 (sqrt.f64 (/.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)))
	54.1%	(/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (.f64 (sqrt.f64 k) #s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))))))))
	45.2%	(/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx ( (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k)))
	99.4%	(.f64 (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	78.0%	(.f64 (sqrt.f64 (/.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) (pow.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (.f64 #s(literal -1/2 binary64) k)))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	39.6%	#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 n n) (/.f64 (PI.f64) (sqrt.f64 k)))))) (sqrt.f64 (sqrt.f64 k))))
	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (/.f64 n (sqrt.f64 k))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 k))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (sqrt.f64 k))))) (sqrt.f64 (sqrt.f64 k))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 k))))
	40.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 k) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (sqrt.f64 k))))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (sqrt.f64 k))))))))
✓	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
	33.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
	33.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 k)))))
	33.3%	#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))))
	45.1%	#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 #s(literal 884279719003555/140737488355328 binary64)))))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
	45.1%	#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))))
	33.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
	33.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
	45.2%	#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))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))))
	33.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))))
	33.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n k)))))
	4.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (.f64 (PI.f64) n))) k))))
	33.4%	#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) k) n))))
	33.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))))
	51.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (/ ( n (PI)) k)) (.f64 n (sqrt.f64 (/.f64 (PI.f64) (.f64 k n)))))))
	33.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(literal 6369051672525773/4503599627370496 binary64) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))))
	22.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 n (PI.f64)) k (.f64 (.f64 n (PI.f64)) k)) (.f64 k k))))
✓	33.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
	23.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))) k)))
	31.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
	33.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
	33.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
	33.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal -884279719003555/140737488355328 binary64) (.f64 n (/.f64 #s(literal -1 binary64) k)))))
	18.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) k) (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
	31.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) #s(literal 1/2 binary64))))
	38.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
	45.1%	#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 n (+.f64 (PI.f64) (PI.f64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k))))))
	34.8%	#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 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))))
	38.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 k (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1 binary64) k)))))))
	45.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
	38.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (/ (* n (PI)) k))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64))))) k)))
	51.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (/ (* n (PI)) k))) (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
	38.6%	#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)))
	52.0%	#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 1 678 to 1 261 computations (24.9% saved)

regimes489.0ms (7.4%)

Memory

-4.5MiB live, 708.4MiB allocated; 69ms collecting garbage

Counts

1 → 1

2 → 1

3 → 1

5 → 1

9 → 1

12 → 2

72 → 2

76 → 3

88 → 1

113 → 1

Calls

Call 1

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

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

Call 2

Inputs

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

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

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

Call 3

Inputs

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

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

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

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

Call 4

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

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

Call 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))) (*.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))))
(/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx ( (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 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
(/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx ( (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 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))) (*.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))))
(/.f64 (sqrt.f64 (.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx ( (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 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 -884279719003555/140737488355328 binary64) (.f64 n (/.f64 #s(literal -1 binary64) 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 7

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

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

Call 8

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

Outputs

#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))))))

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

Call 9

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

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

Call 10

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

Outputs

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

Calls

37 calls:

43.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
30.0ms	n
29.0ms	k
29.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
28.0ms	n

Results

Accuracy	Segments	Branch
33.5%	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))))`
33.5%	1	`k`
33.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
33.5%	1	`n`
33.5%	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))))`
33.5%	1	`k`
33.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
33.5%	1	`n`
33.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
33.5%	1	`n`
33.5%	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))))`
33.5%	1	`k`
45.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.2%	1	`n`
45.2%	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))))`
45.2%	1	`k`
45.2%	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))))`
45.2%	1	`k`
45.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.2%	1	`n`
58.5%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
58.5%	2	`n`
58.5%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
58.5%	2	`n`
58.4%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
62.4%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
69.5%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
58.4%	2	`k`
62.4%	2	`n`
99.5%	1	`k`
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	`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 3 241 to 727 computations (77.6% saved)

bsearch1.0ms (0.0%)

Memory

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

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.7221797299887704e+290	+inf
0.0ms	0.0	2.1743653746663587e-192

Compiler

Compiled 34 to 29 computations (14.7% saved)

bsearch6.0ms (0.1%)

Memory

13.2MiB live, 13.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
5.0ms	14030127410914.934	139152286843603.48

Samples

3.0ms

48×

valid

Compiler

Compiled 190 to 156 computations (17.9% saved)

Precisions

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

ival-pow: 1.0ms (44.2% of total)

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

adjust: 0.0ms (0.0% of total)

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

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

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

bsearch1.0ms (0.0%)

Memory

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

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	14030127410914.934	139152286843603.48

Compiler

Compiled 184 to 150 computations (18.5% saved)

derivations146.0ms (2.2%)

Memory

-6.5MiB live, 184.0MiB allocated; 12ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 391 to 96 computations (75.4% saved)

preprocess141.0ms (2.1%)

Memory: -12.0MiB live, 225.8MiB allocated; 37ms collecting garbage
Compiler: Compiled 1 189 to 585 computations (50.8% saved)

end0.0ms (0.0%)

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

start0.0ms (0.0%)

analyze130.0ms (2.0%)

sample3.5s (53.0%)

preprocess65.0ms (1.0%)

sample0.0ms (0.0%)

series101.0ms (1.5%)

rewrite106.0ms (1.6%)

eval42.0ms (0.6%)

prune20.0ms (0.3%)

sample0.0ms (0.0%)

series247.0ms (3.7%)

rewrite251.0ms (3.8%)

eval212.0ms (3.2%)

prune42.0ms (0.6%)

sample0.0ms (0.0%)

series102.0ms (1.6%)

rewrite192.0ms (2.9%)

eval245.0ms (3.7%)

prune79.0ms (1.2%)

sample0.0ms (0.0%)

series110.0ms (1.7%)

rewrite129.0ms (2.0%)

eval157.0ms (2.4%)

prune78.0ms (1.2%)

regimes489.0ms (7.4%)

bsearch1.0ms (0.0%)

bsearch6.0ms (0.1%)

bsearch1.0ms (0.0%)

derivations146.0ms (2.2%)

preprocess141.0ms (2.1%)

end0.0ms (0.0%)

Profiling