Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze143.0ms (2.6%)

Memory

-7.4MiB live, 136.3MiB allocated; 46ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
50%	25%	25%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
50%	25%	25%	0.1%	0%	50%	0%	6
51.6%	25%	23.4%	0.1%	0%	51.5%	0%	7
52.5%	25%	22.6%	0.1%	0%	52.3%	0%	8
53.8%	25%	21.5%	0.1%	0%	53.5%	0%	9
54.5%	25%	20.9%	0.1%	0%	54%	0%	10
55.3%	25%	20.2%	0.1%	0%	54.7%	0%	11
55.7%	25%	19.9%	0.1%	0%	55.1%	0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.7s (67.5%)

Memory

-48.3MiB live, 4 248.0MiB allocated; 2.2s collecting garbage

Samples

1.6s	8 256×	0	valid
1.3s	5 551×	1	invalid
174.0ms	476×	2	invalid
24.0ms	249×	0	exit
24.0ms	370×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 2.4s

ival-pow: 1.4s (57.1% of total)

ival-mult!: 248.0ms (10.2% of total)

adjust: 243.0ms (10% of total)

ival-div!: 213.0ms (8.8% of total)

ival-sqrt: 172.0ms (7.1% of total)

ival-sub!: 163.0ms (6.7% of total)

ival-pi: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

Bogosity

preprocess54.0ms (1%)

Memory

-30.7MiB live, 60.7MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Symmetry

(abs k)

Compiler

Compiled 30 to 26 computations (13.3% saved)

series88.0ms (1.6%)

Memory

21.6MiB live, 157.9MiB allocated; 31ms 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	Expression
31.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
24.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
20.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
2.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
2.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))

rewrite48.0ms (0.9%)

Memory

10.3MiB live, 54.9MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	97	51
0	683	51

Stop Event

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

Counts

13 → 142

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 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 n (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (.f64 (pow.f64 n (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 #s(literal -1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 k) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(sqrt.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)))
(sqrt.f64 k)
(fabs.f64 (neg.f64 (sqrt.f64 k)))
(fabs.f64 (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
k
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 n (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(.f64 (fabs.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (fabs.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(.f64 (neg.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (neg.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 n (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(.f64 (pow.f64 n (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(/.f64 (pow.f64 (.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))))
(fabs.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (+.f64 #s(literal 0 binary64) (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(+.f64 (cosh.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sinh.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n) (.f64 n (PI.f64)))
(fma.f64 (cbrt.f64 (.f64 (PI.f64) (PI.f64))) (.f64 (cbrt.f64 (PI.f64)) n) (*.f64 n (PI.f64)))
(fma.f64 n (PI.f64) (*.f64 n (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 n (PI.f64)))
(+.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (cbrt.f64 (.f64 (PI.f64) (PI.f64))) (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (PI.f64)) (+.f64 (cbrt.f64 (.f64 (PI.f64) (PI.f64))) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (fma.f64 (.f64 (PI.f64) (PI.f64)) (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) (PI.f64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (PI.f64) (*.f64 #s(literal 1 binary64) (PI.f64)))
(-.f64 (PI.f64) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))
(-.f64 (PI.f64) (.f64 (neg.f64 (cbrt.f64 (.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (.f64 (PI.f64) #s(literal 1 binary64)) (.f64 (PI.f64) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (PI.f64)) (.f64 #s(literal 1 binary64) (PI.f64)))
(+.f64 (PI.f64) (PI.f64))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)))
(log.f64 (*.f64 (exp.f64 (PI.f64)) (exp.f64 (PI.f64))))
#s(literal 2 binary64)
(PI.f64)
n
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 k k)) #s(literal 1/2 binary64)) (+.f64 k #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (*.f64 k k) k)) #s(literal 1/2 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 k #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (fma.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 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) k)) #s(literal 4 binary64))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 k k)) #s(literal 1 binary64)) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 k k) k)) #s(literal 1 binary64)) (.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 k k)) (.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 k k) k)) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64))))
(neg.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))
(neg.f64 (/.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)))
(neg.f64 (-.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 k #s(literal 1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (neg.f64 k) #s(literal 2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 k k)) (/.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (*.f64 k k) k)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 k) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 k k) (.f64 #s(literal 1 binary64) (neg.f64 k)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k))) (neg.f64 (+.f64 k #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 k k) k))) (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 k #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 k k) k)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 k #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 k k))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 k k) k))))
(neg.f64 (-.f64 k #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 k k) k) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 k)))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (neg.f64 k) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 k))

eval23.0ms (0.4%)

Memory: -8.1MiB live, 36.6MiB allocated; 7ms collecting garbage
Compiler: Compiled 1 724 to 715 computations (58.5% saved)

prune14.0ms (0.2%)

Memory

27.2MiB live, 27.2MiB allocated; 0ms collecting garbage

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	151	18	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	18	170

Accuracy

100.0%

Counts

170 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
▶	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	76.7%	(.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (.f64 (pow.f64 n (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
	99.5%	(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
▶	99.6%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	46.6%	(.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))))
	96.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
▶	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 k #s(literal 1/2 binary64)))))
	76.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	96.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	76.8%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 n (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
	96.5%	(.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	51.2%	#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))))
▶	46.7%	#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 672 to 578 computations (14% saved)

series265.0ms (4.8%)

Memory

5.3MiB live, 426.2MiB allocated; 124ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	578	4650

Stop Event

1×	iter-limit

Counts

36 → 116

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
101.0ms	n	@	0	((* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2))) (pow (* n (+ (PI) (PI))) 1/2) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) 1/2 (pow (* n (+ (PI) (PI))) (* k 1/2)) (* k 1/2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (pow (* 2 (* n (PI))) 1/2) (* 2 (* n (PI))) 2 (* n (PI)) (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))))) (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (* 1/2 (- 1 k)) (- 1 k) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) -1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow (+ (PI) (PI)) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))
38.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2))) (pow (* n (+ (PI) (PI))) 1/2) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) 1/2 (pow (* n (+ (PI) (PI))) (* k 1/2)) (* k 1/2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (pow (* 2 (* n (PI))) 1/2) (* 2 (* n (PI))) 2 (* n (PI)) (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))))) (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (* 1/2 (- 1 k)) (- 1 k) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) -1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow (+ (PI) (PI)) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))
37.0ms	n	@	inf	((* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2))) (pow (* n (+ (PI) (PI))) 1/2) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) 1/2 (pow (* n (+ (PI) (PI))) (* k 1/2)) (* k 1/2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (pow (* 2 (* n (PI))) 1/2) (* 2 (* n (PI))) 2 (* n (PI)) (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))))) (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (* 1/2 (- 1 k)) (- 1 k) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) -1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow (+ (PI) (PI)) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))
34.0ms	k	@	0	((* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2))) (pow (* n (+ (PI) (PI))) 1/2) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) 1/2 (pow (* n (+ (PI) (PI))) (* k 1/2)) (* k 1/2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (pow (* 2 (* n (PI))) 1/2) (* 2 (* n (PI))) 2 (* n (PI)) (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))))) (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (* 1/2 (- 1 k)) (- 1 k) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) -1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow (+ (PI) (PI)) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))
18.0ms	k	@	inf	((* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2))) (pow (* n (+ (PI) (PI))) 1/2) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) 1/2 (pow (* n (+ (PI) (PI))) (* k 1/2)) (* k 1/2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (pow (* 2 (* n (PI))) 1/2) (* 2 (* n (PI))) 2 (* n (PI)) (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))))) (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (* 1/2 (- 1 k)) (- 1 k) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) -1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow (+ (PI) (PI)) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))

rewrite35.0ms (0.6%)

Memory

9.2MiB live, 54.8MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	274
0	74	246
0	275	246

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

36 → 156

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (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)))
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eval38.0ms (0.7%)

Memory: -8.0MiB live, 81.9MiB allocated; 11ms collecting garbage
Compiler: Compiled 4 624 to 1 230 computations (73.4% saved)

prune23.0ms (0.4%)

Memory

-8.6MiB live, 43.1MiB allocated; 7ms collecting garbage

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	264	17	281
Fresh	10	3	13
Picked	5	0	5
Done	0	0	0
Total	279	20	299

Accuracy

100.0%

Counts

299 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.6%	(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (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)))
▶	99.7%	(/.f64 (.f64 #s(literal 1 binary64) (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))))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
▶	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
	99.5%	(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	96.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	76.8%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (.f64 (pow.f64 n (/.f64 (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 n (/.f64 (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
	46.5%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(approx (* 1/2 (- 1 k)) #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (* 1/2 (- 1 k)) #s(literal 1/2 binary64))))
	99.5%	(.f64 #s(approx (pow k -1/2) (pow.f64 (/.f64 #s(literal 1 binary64) 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))))
	46.6%	#s(approx (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
▶	46.7%	#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)))
	46.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	46.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
	46.6%	#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))))
▶	46.6%	#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))))))
▶	46.4%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/.f64 (.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))

Compiler

Compiled 828 to 734 computations (11.4% saved)

series126.0ms (2.3%)

Memory

8.9MiB live, 289.4MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	519	4172

Stop Event

1×	iter-limit

Counts

38 → 109

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
32.0ms	n	@	inf	((/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (* 1 (sqrt (* (+ (PI) (PI)) n))) 1 (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt k) k (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (+ (PI) (PI)) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (sqrt (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (* n (PI)) (* k (sqrt (/ 1 k))) (sqrt (/ 1 k)) (/ 1 k) (/ 1 (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))))) (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)))) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))) (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (* (- 1 k) 1/2) (- 1 k) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (pow n 1/2) (pow (* 2 (PI)) 1/2) (* 2 (PI)))
29.0ms	n	@	-inf	((/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (* 1 (sqrt (* (+ (PI) (PI)) n))) 1 (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt k) k (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (+ (PI) (PI)) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (sqrt (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (* n (PI)) (* k (sqrt (/ 1 k))) (sqrt (/ 1 k)) (/ 1 k) (/ 1 (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))))) (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)))) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))) (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (* (- 1 k) 1/2) (- 1 k) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (pow n 1/2) (pow (* 2 (PI)) 1/2) (* 2 (PI)))
28.0ms	n	@	0	((/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (* 1 (sqrt (* (+ (PI) (PI)) n))) 1 (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt k) k (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (+ (PI) (PI)) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (sqrt (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (* n (PI)) (* k (sqrt (/ 1 k))) (sqrt (/ 1 k)) (/ 1 k) (/ 1 (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))))) (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)))) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))) (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (* (- 1 k) 1/2) (- 1 k) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (pow n 1/2) (pow (* 2 (PI)) 1/2) (* 2 (PI)))
9.0ms	k	@	-inf	((/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (* 1 (sqrt (* (+ (PI) (PI)) n))) 1 (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt k) k (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (+ (PI) (PI)) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (sqrt (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (* n (PI)) (* k (sqrt (/ 1 k))) (sqrt (/ 1 k)) (/ 1 k) (/ 1 (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))))) (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)))) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))) (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (* (- 1 k) 1/2) (- 1 k) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (pow n 1/2) (pow (* 2 (PI)) 1/2) (* 2 (PI)))
5.0ms	k	@	0	((/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (* 1 (sqrt (* (+ (PI) (PI)) n))) 1 (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt k) k (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (+ (PI) (PI)) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (sqrt (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (* n (PI)) (* k (sqrt (/ 1 k))) (sqrt (/ 1 k)) (/ 1 k) (/ 1 (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))))) (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)))) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))) (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (* (- 1 k) 1/2) (- 1 k) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (pow n 1/2) (pow (* 2 (PI)) 1/2) (* 2 (PI)))

rewrite37.0ms (0.7%)

Memory

14.4MiB live, 59.9MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	348
0	90	313
0	353	313

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

38 → 177

Calls

Call 1

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

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

eval45.0ms (0.8%)

Memory: -25.0MiB live, 77.8MiB allocated; 34ms collecting garbage
Compiler: Compiled 4 264 to 1 246 computations (70.8% saved)

prune18.0ms (0.3%)

Memory

2.5MiB live, 49.1MiB allocated; 1ms collecting garbage

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	239	15	254
Fresh	9	6	15
Picked	4	1	5
Done	0	0	0
Total	252	22	274

Accuracy

100.0%

Counts

274 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 (-.f64 #s(literal 1 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) (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
	54.9%	(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (.f64 (sqrt.f64 k) #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))))))))))
	81.4%	(/.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
▶	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
	99.5%	(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	96.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
✓	46.7%	#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)))
	46.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	46.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	46.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
	46.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))))
▶	36.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	41.9%	#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 (+.f64 (PI.f64) (PI.f64)) n)) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
▶	46.6%	#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))))
	46.6%	#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 (+.f64 (PI.f64) (PI.f64)) n)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
	46.6%	#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))))))
	46.5%	#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 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
	46.4%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/.f64 #s(approx (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
	46.4%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/.f64 #s(approx (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
▶	46.5%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) #s(approx (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))

Compiler

Compiled 1 055 to 954 computations (9.6% saved)

series176.0ms (3.2%)

Memory

24.8MiB live, 343.9MiB allocated; 58ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	562	4375

Stop Event

1×	iter-limit

Counts

40 → 123

Calls

Call 1

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

Outputs
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (fma.f64 k (-.f64 (.f64 #s(literal -1 binary64) (.f64 k (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 k)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (fma.f64 k (-.f64 (.f64 k (-.f64 (.f64 #s(literal -1 binary64) (.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 k))))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 k)) (.f64 #s(literal 1/48 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 k))))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 k)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 k)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (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 k 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))))
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#s(approx (neg (* (- 1 k) 1/2)) (.f64 k (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (- 1 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (* (- 1 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 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 (/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (/ (* n (sqrt (* 2 (/ (PI) n)))) (sqrt 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 (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 n) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k)))))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k))) (/.f64 #s(literal -1 binary64) (.f64 k (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k)) (.f64 #s(literal -1 binary64) (.f64 k (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (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 (neg (* (- 1 k) 1/2)) (.f64 #s(literal -1 binary64) (.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))
#s(approx (* (- 1 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 k) (.f64 #s(literal -1 binary64) (.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 k))))
#s(approx (sqrt (* (+ (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 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (sqrt (* 2 (/ (PI) n))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) n))
#s(approx (* 2 (/ (PI) n)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))
#s(approx (/ (PI) n) (/.f64 (PI.f64) n))
#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/.f64 (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 n) (-.f64 #s(literal 1 binary64) k)))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))) (sqrt.f64 k)))
#s(approx (* (sqrt n) (sqrt (* 2 (PI)))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
#s(approx (sqrt n) (sqrt.f64 n))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k))) (/.f64 #s(literal 1 binary64) (.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 (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k)) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (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 (/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 k))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (sqrt (* 2 (/ (PI) n))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))
#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/.f64 (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (/.f64 #s(literal 1 binary64) n)) (-.f64 #s(literal 1 binary64) k)))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))) (sqrt.f64 k)))
#s(approx (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (/.f64 (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))) (sqrt.f64 k)))
#s(approx (/ (* (sqrt n) (sqrt (* 2 (PI)))) (* k (sqrt (/ 1 k)))) (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (sqrt n) (sqrt (* 2 (PI)))) (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))))
#s(approx (sqrt n) (*.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k))) (/.f64 #s(literal 1 binary64) (.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 (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k)) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (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 (/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (sqrt.f64 k)))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))) (sqrt.f64 k))))
#s(approx (/ (* (sqrt n) (sqrt (* 2 (PI)))) (* k (sqrt (/ 1 k)))) (.f64 #s(literal -1 binary64) (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (sqrt n) (sqrt (* 2 (PI)))) (.f64 #s(literal -1 binary64) (.f64 n (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))))
#s(approx (sqrt n) (.f64 #s(literal -1 binary64) (.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k))) (/.f64 #s(literal 1 binary64) (.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 (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k)) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (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	Expression
42.0ms	n	@	-inf	((/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/ (* n (sqrt (* 2 (/ (PI) n)))) (sqrt k)) (* n (sqrt (* 2 (/ (PI) n)))) (sqrt (* 2 (/ (PI) n))) (* 2 (/ (PI) n)) 2 (/ (PI) n) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (* k (sqrt (/ 1 k)))) (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt n) (sqrt (* 2 (PI))) (* 2 (PI)) (* k (sqrt (/ 1 k))) (sqrt (/ 1 k)) (/ 1 k) 1 (/ 1 (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k))) (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k)) (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (neg (* (- 1 k) 1/2)) (* (- 1 k) 1/2) (- 1 k))
36.0ms	n	@	inf	((/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/ (* n (sqrt (* 2 (/ (PI) n)))) (sqrt k)) (* n (sqrt (* 2 (/ (PI) n)))) (sqrt (* 2 (/ (PI) n))) (* 2 (/ (PI) n)) 2 (/ (PI) n) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (* k (sqrt (/ 1 k)))) (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt n) (sqrt (* 2 (PI))) (* 2 (PI)) (* k (sqrt (/ 1 k))) (sqrt (/ 1 k)) (/ 1 k) 1 (/ 1 (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k))) (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k)) (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (neg (* (- 1 k) 1/2)) (* (- 1 k) 1/2) (- 1 k))
30.0ms	n	@	0	((/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/ (* n (sqrt (* 2 (/ (PI) n)))) (sqrt k)) (* n (sqrt (* 2 (/ (PI) n)))) (sqrt (* 2 (/ (PI) n))) (* 2 (/ (PI) n)) 2 (/ (PI) n) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (* k (sqrt (/ 1 k)))) (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt n) (sqrt (* 2 (PI))) (* 2 (PI)) (* k (sqrt (/ 1 k))) (sqrt (/ 1 k)) (/ 1 k) 1 (/ 1 (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k))) (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k)) (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (neg (* (- 1 k) 1/2)) (* (- 1 k) 1/2) (- 1 k))
24.0ms	k	@	-inf	((/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/ (* n (sqrt (* 2 (/ (PI) n)))) (sqrt k)) (* n (sqrt (* 2 (/ (PI) n)))) (sqrt (* 2 (/ (PI) n))) (* 2 (/ (PI) n)) 2 (/ (PI) n) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (* k (sqrt (/ 1 k)))) (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt n) (sqrt (* 2 (PI))) (* 2 (PI)) (* k (sqrt (/ 1 k))) (sqrt (/ 1 k)) (/ 1 k) 1 (/ 1 (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k))) (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k)) (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (neg (* (- 1 k) 1/2)) (* (- 1 k) 1/2) (- 1 k))
7.0ms	k	@	0	((/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/ (* n (sqrt (* 2 (/ (PI) n)))) (sqrt k)) (* n (sqrt (* 2 (/ (PI) n)))) (sqrt (* 2 (/ (PI) n))) (* 2 (/ (PI) n)) 2 (/ (PI) n) (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (* k (sqrt (/ 1 k)))) (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt n) (sqrt (* 2 (PI))) (* 2 (PI)) (* k (sqrt (/ 1 k))) (sqrt (/ 1 k)) (/ 1 k) 1 (/ 1 (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k))) (* (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (sqrt k)) (pow (* (+ (PI) (PI)) n) (neg (* (- 1 k) 1/2))) (neg (* (- 1 k) 1/2)) (* (- 1 k) 1/2) (- 1 k))

rewrite45.0ms (0.8%)

Memory

23.9MiB live, 67.0MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	377
0	99	351
0	385	351

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

40 → 160

Calls

Call 1

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

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

eval56.0ms (1%)

Memory: -22.0MiB live, 76.0MiB allocated; 33ms collecting garbage
Compiler: Compiled 4 622 to 1 399 computations (69.7% saved)

prune47.0ms (0.9%)

Memory

3.6MiB live, 52.3MiB allocated; 4ms collecting garbage

Pruning

36 alts after pruning (33 fresh and 3 done)

	Pruned	Kept	Total
New	268	19	287
Fresh	2	14	16
Picked	3	2	5
Done	0	1	1
Total	273	36	309

Accuracy

100.0%

Counts

309 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 (-.f64 #s(literal 1 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) (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
	81.4%	(/.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
✓	99.7%	(/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
	54.9%	(/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (.f64 #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)))))))) (sqrt.f64 k)))
	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k)))
	46.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (neg (* (- 1 k) 1/2)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
	96.6%	(/.f64 #s(literal 1 binary64) (.f64 (exp.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))) (sqrt.f64 k)))
	99.5%	(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
✓	46.7%	#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)))
	46.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	46.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	46.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
	46.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))))
✓	36.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	36.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	36.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
	36.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 #s(approx (/ (* (+ (PI) (PI)) n) k) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))))
	41.9%	#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 (+.f64 (PI.f64) (PI.f64)) n)) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
	46.6%	#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 (+.f64 (PI.f64) (PI.f64)) n)) n) (sqrt.f64 k))))
	46.5%	#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 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
	46.6%	#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) (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k))))
	46.6%	#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 (+.f64 (PI.f64) (PI.f64)) n)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
	46.6%	#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))))))
	46.5%	#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 (+.f64 (PI.f64) (PI.f64)) n)) n) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
	46.5%	#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 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
	46.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 n (/.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))))
	36.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k)))
	49.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
	46.4%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/.f64 #s(approx (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
	46.4%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) (/.f64 #s(approx (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (.f64 n (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))))) (sqrt.f64 k)))
	46.5%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) #s(approx (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (/.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	46.5%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) #s(approx (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
	46.4%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) #s(approx (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (/.f64 (.f64 #s(approx (sqrt n) (.f64 n (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	41.7%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) #s(approx (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (*.f64 (/.f64 (sqrt.f64 n) k) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))))
	46.4%	#s(approx (* (* (/ 1 (sqrt k)) (pow (+ (PI) (PI)) (* 1/2 (- 1 k)))) (pow n (* 1/2 (- 1 k)))) #s(approx (/ (* (pow n 1/2) (pow (* 2 (PI)) 1/2)) (sqrt k)) (.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))

Compiler

Compiled 1 762 to 1 206 computations (31.6% saved)

regimes265.0ms (4.8%)

Memory

-35.9MiB live, 139.7MiB allocated; 194ms collecting garbage

Counts

70 → 1

Calls

Call 1

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

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

Calls

4 calls:

178.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
43.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
23.0ms	n
17.0ms	k

Results

Accuracy	Segments	Branch
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 22 to 23 computations (-4.5% saved)

regimes55.0ms (1%)

Memory

16.4MiB live, 113.1MiB allocated; 10ms collecting garbage

Counts

48 → 1

Calls

Call 1

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

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

Calls

4 calls:

16.0ms	n
12.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
12.0ms	k

Results

Accuracy	Segments	Branch
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.6%	1	`k`
99.6%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes42.0ms (0.8%)

Memory

4.5MiB live, 96.9MiB allocated; 10ms collecting garbage

Counts

33 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

12.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
10.0ms	n
9.0ms	k
9.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
60.8%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
60.7%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
60.7%	2	`k`
60.8%	2	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes34.0ms (0.6%)

Memory

-17.1MiB live, 19.8MiB allocated; 17ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs
#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)))

Calls

4 calls:

2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
2.0ms	k
2.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
46.7%	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))))`
46.7%	1	`k`
46.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
46.7%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes7.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

4 calls:

2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
1.0ms	k
1.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
36.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
36.7%	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))))`
36.7%	1	`n`
36.7%	1	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes5.0ms (0.1%)

Memory

14.1MiB live, 14.1MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

4 calls:

1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	n
1.0ms	k
1.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
36.7%	1	`k`
36.7%	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))))`
36.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
36.7%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes6.0ms (0.1%)

Memory

-37.1MiB live, 11.2MiB allocated; 3ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	k
1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
1.0ms	n

Results

Accuracy	Segments	Branch
36.7%	1	`k`
36.7%	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))))`
36.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
36.7%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch10.0ms (0.2%)

Memory

16.6MiB live, 16.6MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
9.0ms	3.655658346691168e-11	1.5459626680077064e-10

Samples

6.0ms

80×

valid

Compiler

Compiled 259 to 253 computations (2.3% saved)

Precisions

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

ival-pow: 2.0ms (51.6% of total)

ival-sqrt: 1.0ms (25.8% of total)

ival-div!: 1.0ms (25.8% of total)

ival-mult!: 1.0ms (25.8% of total)

ival-sub!: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

derivations16.0ms (0.3%)

Memory

26.6MiB live, 26.6MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 99 to 59 computations (40.4% saved)

preprocess76.0ms (1.4%)

Memory: -15.5MiB live, 131.2MiB allocated; 34ms collecting garbage
Remove: (abs k)
Compiler: Compiled 424 to 352 computations (17% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze143.0ms (2.6%)

sample3.7s (67.5%)

preprocess54.0ms (1%)

series88.0ms (1.6%)

rewrite48.0ms (0.9%)

eval23.0ms (0.4%)

prune14.0ms (0.2%)

series265.0ms (4.8%)

rewrite35.0ms (0.6%)

eval38.0ms (0.7%)

prune23.0ms (0.4%)

series126.0ms (2.3%)

rewrite37.0ms (0.7%)

eval45.0ms (0.8%)

prune18.0ms (0.3%)

series176.0ms (3.2%)

rewrite45.0ms (0.8%)

eval56.0ms (1%)

prune47.0ms (0.9%)

regimes265.0ms (4.8%)

regimes55.0ms (1%)

regimes42.0ms (0.8%)

regimes34.0ms (0.6%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch10.0ms (0.2%)

derivations16.0ms (0.3%)

preprocess76.0ms (1.4%)

end0.0ms (0%)

Profiling