Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze142.0ms (3%)

Memory

-15.5MiB live, 185.4MiB allocated; 36ms 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)

sample3.2s (66.3%)

Memory

0.5MiB live, 3 303.7MiB allocated; 1.9s collecting garbage

Samples

1.7s	5 426×	1	invalid
738.0ms	8 254×	0	valid
142.0ms	439×	2	invalid
31.0ms	383×	0	invalid
20.0ms	222×	0	exit
0.0ms	2×	1	valid

Precisions

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

adjust: 829.0ms (40.4% of total)

ival-pow: 525.0ms (25.6% of total)

ival-mult!: 261.0ms (12.7% of total)

ival-div!: 225.0ms (11% of total)

ival-sqrt: 151.0ms (7.4% of total)

ival-sub!: 60.0ms (2.9% of total)

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

exact: 0.0ms (0% of total)

Bogosity

preprocess62.0ms (1.3%)

Memory

-46.9MiB live, 55.7MiB allocated; 33ms 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
▶	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Symmetry

(abs k)

Compiler

Compiled 32 to 26 computations (18.8% saved)

series82.0ms (1.7%)

Memory

13.8MiB live, 98.4MiB allocated; 22ms 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
34.0ms	n	0
21.0ms	n	-inf
8.0ms	n	inf
2.0ms	k	0
2.0ms	k	-inf

rewrite59.0ms (1.2%)

Memory

35.3MiB live, 74.7MiB allocated; 30ms 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))

eval44.0ms (0.9%)

Memory: -18.1MiB live, 53.8MiB allocated; 47ms collecting garbage
Compiler: Compiled 3 925 to 715 computations (81.8% saved)

prune41.0ms (0.9%)

Memory

-9.0MiB live, 36.1MiB allocated; 9ms collecting garbage

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	150	19	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	19	170

Accuracy

100.0%

Counts

170 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(/.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))
▶	99.1%	(/.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)))))
	98.9%	(.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))))
	99.0%	(.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)))
	99.1%	(.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))))
	98.9%	(.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)))
▶	98.9%	(.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))))
	44.9%	(.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))))
▶	96.2%	(.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))))
▶	99.3%	(.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)))))
	75.1%	(.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)))))
	96.2%	(.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)))))
	52.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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)))))
	96.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
	99.0%	(.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))))
	98.9%	(.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	75.1%	(.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))))
▶	45.0%	#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)))
	96.2%	#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)))

Compiler

Compiled 890 to 648 computations (27.2% saved)

series181.0ms (3.8%)

Memory

5.0MiB live, 235.6MiB allocated; 40ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	467	3923

Stop Event

1×	iter-limit

Counts

36 → 100

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

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

Calls

6 calls:

Time	Variable	Point
63.0ms	n	-inf
31.0ms	n	0
28.0ms	n	inf
27.0ms	k	-inf
6.0ms	k	0

rewrite36.0ms (0.8%)

Memory

27.0MiB live, 72.2MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	285
0	75	239
0	284	239

Stop Event

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

Counts

36 → 187

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

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

eval43.0ms (0.9%)

Memory: -30.9MiB live, 65.8MiB allocated; 15ms collecting garbage
Compiler: Compiled 8 992 to 1 205 computations (86.6% saved)

prune45.0ms (0.9%)

Memory

8.9MiB live, 54.8MiB allocated; 4ms collecting garbage

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	280	14	294
Fresh	9	5	14
Picked	3	2	5
Done	0	0	0
Total	292	21	313

Accuracy

100.0%

Counts

313 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(/.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))
	99.3%	(/.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)))
▶	99.3%	(/.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))))
✓	99.1%	(/.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)))))
	96.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
	52.7%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #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))))))
▶	99.0%	(/.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))))))
	99.0%	(.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)))
	98.9%	(.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))))
	99.1%	(.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))))
	98.9%	(.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)))
✓	98.9%	(.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))))
▶	99.3%	(.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)))))
	75.1%	(.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)))))
	96.2%	(.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)))))
▶	45.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
	44.9%	#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)))))
	44.9%	#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))))
	45.3%	#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))))
▶	44.9%	#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))))))
	99.2%	#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 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))))))

Compiler

Compiled 1 044 to 734 computations (29.7% saved)

series78.0ms (1.6%)

Memory

32.5MiB live, 169.8MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	476	4134

Stop Event

1×	iter-limit

Counts

36 → 108

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)
(.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(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 (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)))

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

Calls

6 calls:

Time	Variable	Point
18.0ms	n	inf
15.0ms	n	-inf
12.0ms	n	0
7.0ms	k	inf
5.0ms	k	-inf

rewrite99.0ms (2.1%)

Memory

-30.2MiB live, 56.7MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	342
0	79	319
0	309	319

Stop Event

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

Counts

36 → 175

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)
(.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(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 (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)))

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

eval58.0ms (1.2%)

Memory: 5.0MiB live, 61.5MiB allocated; 48ms collecting garbage
Compiler: Compiled 10 160 to 1 293 computations (87.3% saved)

prune24.0ms (0.5%)

Memory

7.5MiB live, 50.8MiB allocated; 9ms collecting garbage

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	283	13	296
Fresh	7	7	14
Picked	4	1	5
Done	1	1	2
Total	295	22	317

Accuracy

100.0%

Counts

317 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(/.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))
▶	99.3%	(/.f64 (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))
	99.2%	(/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
	79.0%	(/.f64 (sqrt.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
✓	99.1%	(/.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)))))
	96.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
	99.1%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
	99.0%	(.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)))
	44.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (pow ( (+ (PI) (PI)) n) (* 1/2 k)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	96.2%	(.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)))))
✓	45.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
	44.9%	#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))))))
	44.9%	#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)))))
	44.9%	#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))))
▶	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
	39.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
	45.3%	#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))))
▶	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
	44.9%	#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))))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))))))
▶	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (/.f64 (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))

Compiler

Compiled 1 220 to 887 computations (27.3% saved)

series75.0ms (1.6%)

Memory

-7.7MiB live, 183.9MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	359	2628

Stop Event

1×	iter-limit

Counts

30 → 84

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
18.0ms	n	inf
12.0ms	n	0
11.0ms	n	-inf
10.0ms	k	inf
5.0ms	k	-inf

rewrite35.0ms (0.7%)

Memory

13.7MiB live, 58.2MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	326
0	67	306
0	258	306

Stop Event

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

Counts

30 → 120

Calls

Call 1

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

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

eval38.0ms (0.8%)

Memory: -12.7MiB live, 76.9MiB allocated; 21ms collecting garbage
Compiler: Compiled 9 768 to 1 119 computations (88.5% saved)

prune27.0ms (0.6%)

Memory

20.9MiB live, 64.5MiB allocated; 7ms collecting garbage

Pruning

35 alts after pruning (30 fresh and 5 done)

	Pruned	Kept	Total
New	248	20	268
Fresh	5	10	15
Picked	1	4	5
Done	1	1	2
Total	255	35	290

Accuracy

100.0%

Counts

290 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.1%	(/.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))
	56.8%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx ( (- 1 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
✓	99.3%	(/.f64 (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))
	99.2%	(/.f64 (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
	79.0%	(/.f64 (sqrt.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
	96.2%	(/.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))
	96.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (exp.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
	99.0%	(.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)))
✓	45.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
	44.9%	#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))))))
	44.9%	#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)))))
	44.9%	#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))))
✓	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
	35.5%	#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))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 #s(approx (/ (* n (+ (PI) (PI))) k) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))))
	44.8%	#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)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k)))
	39.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
	45.3%	#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))))
✓	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
	45.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 k #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(approx (sqrt (* n (+ (PI) (PI)))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
	45.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k)))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k)))))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (/ 1 (* (/ 1 (sqrt k)) k)) (/.f64 (sqrt.f64 k) k)))))
	45.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (/ 1 (* (/ 1 (sqrt k)) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (.f64 #s(approx (sqrt ( n (+ (PI) (PI)))) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (.f64 n (.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) k))))
	33.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 k (*.f64 n (PI.f64))))) k)))
	46.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (.f64 n (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))

Compiler

Compiled 1 225 to 863 computations (29.6% saved)

regimes317.0ms (6.7%)

Memory

-2.1MiB live, 589.7MiB allocated; 191ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

3 → 1

5 → 1

33 → 2

35 → 2

47 → 1

67 → 1

Calls

Call 1

Inputs

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

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

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

Call 2

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

Call 3

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

Outputs

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

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

Call 4

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

Call 5

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

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))

Call 6

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

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

Calls

24 calls:

65.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	n
23.0ms	n
23.0ms	(.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))))
20.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
35.5%	1	`k`
35.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
35.5%	1	`n`
35.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
45.0%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
45.0%	1	`k`
45.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.0%	1	`n`
58.6%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
58.6%	2	`n`
58.5%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
58.5%	2	`k`
67.0%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
97.0%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
97.3%	2	`k`
67.0%	3	`n`
99.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.1%	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))))`
99.1%	1	`k`
99.1%	1	`n`
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.3%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.3%	1	`k`
99.3%	1	`n`

Compiler

Compiled 2 243 to 463 computations (79.4% saved)

bsearch18.0ms (0.4%)

Memory

-8.3MiB live, 34.7MiB allocated; 6ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	0.34724957136033513	9.337830966900018

Samples

12.0ms

112×

valid

Compiler

Compiled 418 to 333 computations (20.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-pow: 6.0ms (65.4% of total)

ival-sqrt: 1.0ms (10.9% of total)

ival-div!: 1.0ms (10.9% of total)

ival-mult!: 1.0ms (10.9% of total)

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

adjust: 0.0ms (0% of total)

bsearch18.0ms (0.4%)

Memory

-9.3MiB live, 33.5MiB allocated; 12ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	8.334793548571993e+27	5.8159764962530186e+28

Samples

6.0ms

96×

valid

Compiler

Compiled 385 to 300 computations (22.1% saved)

Precisions

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

ival-pow: 2.0ms (47.2% of total)

ival-sqrt: 1.0ms (23.6% of total)

ival-div!: 1.0ms (23.6% of total)

ival-mult!: 1.0ms (23.6% of total)

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

adjust: 0.0ms (0% of total)

derivations32.0ms (0.7%)

Memory

7.4MiB live, 57.3MiB allocated; 16ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 210 to 71 computations (66.2% saved)

preprocess52.0ms (1.1%)

Memory: 25.5MiB live, 164.1MiB allocated; 12ms collecting garbage
Remove: (abs k)
Compiler: Compiled 646 to 356 computations (44.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze142.0ms (3%)

sample3.2s (66.3%)

preprocess62.0ms (1.3%)

series82.0ms (1.7%)

rewrite59.0ms (1.2%)

eval44.0ms (0.9%)

prune41.0ms (0.9%)

series181.0ms (3.8%)

rewrite36.0ms (0.8%)

eval43.0ms (0.9%)

prune45.0ms (0.9%)

series78.0ms (1.6%)

rewrite99.0ms (2.1%)

eval58.0ms (1.2%)

prune24.0ms (0.5%)

series75.0ms (1.6%)

rewrite35.0ms (0.7%)

eval38.0ms (0.8%)

prune27.0ms (0.6%)

regimes317.0ms (6.7%)

bsearch18.0ms (0.4%)

bsearch18.0ms (0.4%)

derivations32.0ms (0.7%)

preprocess52.0ms (1.1%)

end0.0ms (0%)

Profiling