Migdal et al, Equation (51)

Time bar (total: 6.5s)

start0.0ms (0%)

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

analyze132.0ms (2%)

Memory
-4.4MiB live, 187.3MiB allocated; 46ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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)

sample2.7s (41%)

Memory
122.9MiB live, 4 544.4MiB allocated; 1.0s collecting garbage
Samples
1.1s5 492×1invalid
857.0ms8 254×0valid
129.0ms494×2invalid
31.0ms239×0exit
24.0ms370×0invalid
0.0ms1valid
Precisions
Click to see histograms. Total time spent on operations: 1.6s
ival-pow: 586.0ms (37.6% of total)
ival-mult!: 262.0ms (16.8% of total)
adjust: 229.0ms (14.7% of total)
ival-div!: 217.0ms (13.9% of total)
ival-sqrt: 203.0ms (13% of total)
ival-sub!: 61.0ms (3.9% of total)
ival-pi: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

preprocess42.0ms (0.6%)

Memory
-35.3MiB live, 15.4MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033101
112887
246287
3217586
Stop Event
node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Symmetry

(abs k)

Compiler

Compiled 32 to 26 computations (18.8% saved)

series79.0ms (1.2%)

Memory
22.5MiB live, 110.4MiB allocated; 14ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0158937
Stop Event
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:

TimeVariablePoint
28.0ms
n
0
21.0ms
n
-inf
12.0ms
n
inf
2.0ms
k
0
2.0ms
k
-inf

rewrite109.0ms (1.7%)

Memory
-12.4MiB live, 138.5MiB allocated; 36ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01354
02254
19751
235151
3169051
0416348
Stop Event
iter-limit
node-limit
iter-limit
Counts
13 → 308
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
(*.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(neg.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 k (/.f64 #s(literal -1/2 binary64) #s(literal 2 binary64))) (pow.f64 k (/.f64 #s(literal -1/2 binary64) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal -1 binary64))
(*.f64 (pow.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 k) #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 k #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 #s(literal -2 binary64) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 1 binary64)))
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k
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(-.f64 (PI.f64) (neg.f64 (PI.f64)))
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(+.f64 (PI.f64) (PI.f64))
(log.f64 (exp.f64 (+.f64 (PI.f64) (PI.f64))))
#s(literal 2 binary64)
(PI.f64)
n
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(+.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 0 binary64))
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eval36.0ms (0.6%)

Memory
17.0MiB live, 61.7MiB allocated; 6ms collecting garbage
Compiler

Compiled 7 436 to 1 275 computations (82.9% saved)

prune38.0ms (0.6%)

Memory
-18.6MiB live, 27.6MiB allocated; 4ms collecting garbage
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New31718335
Fresh000
Picked101
Done000
Total31818336
Accuracy
100.0%
Counts
336 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
99.5%
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
99.6%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
48.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal -1/2 binary64))))
99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
75.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
76.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
96.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
96.4%
(*.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
49.3%
#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))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
95.9%
#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 776 to 588 computations (24.2% saved)

series186.0ms (2.8%)

Memory
37.7MiB live, 363.0MiB allocated; 51ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05534494
Stop Event
iter-limit
Counts
40 → 118
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) #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 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.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 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) #s(literal 1 binary64))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))))))
#s(approx (* k -1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (fma.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (fma.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
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#s(approx (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (+ (* k -1/2) 1/2)) (pow n (+ (* k -1/2) 1/2)))) (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (+ (PI) (PI)) (+ (* k -1/2) 1/2)) (pow n (+ (* k -1/2) 1/2))) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
#s(approx (pow (+ (PI) (PI)) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
#s(approx (pow n (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (log.f64 n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#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 (* (/ 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 (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)))) (*.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
#s(approx (+ (* k -1/2) 1/2) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* (* 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) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (+ (* k -1/2) 1/2)) (pow n (+ (* k -1/2) 1/2)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (pow (+ (PI) (PI)) (+ (* k -1/2) 1/2)) (pow n (+ (* k -1/2) 1/2))) (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))))
#s(approx (pow (+ (PI) (PI)) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
#s(approx (pow n (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (/.f64 (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* n (+ (PI) (PI))) (*.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 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (* n (PI)) (*.f64 n (PI.f64)))
#s(approx (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)))) (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (+ (* k -1/2) 1/2)) (pow n (+ (* k -1/2) 1/2)))) (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (/.f64 (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (pow (* n (+ (PI) (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k)))
#s(approx (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)))) (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
#s(approx (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 (+ (PI) (PI)) (+ (* k -1/2) 1/2)) (pow n (+ (* k -1/2) 1/2)))) (/.f64 (*.f64 (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (sqrt.f64 k)))
#s(approx (* (pow (+ (PI) (PI)) (+ (* k -1/2) 1/2)) (pow n (+ (* k -1/2) 1/2))) (*.f64 (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))))
#s(approx (pow n (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (pow (* n (+ (PI) (PI))) 1/2) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)))) (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
#s(approx (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:

TimeVariablePoint
63.0ms
n
-inf
39.0ms
n
0
29.0ms
n
inf
8.0ms
k
0
6.0ms
k
-inf

rewrite206.0ms (3.2%)

Memory
-25.0MiB live, 259.3MiB allocated; 64ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
049305
082269
1304260
2883260
33652260
04163260
Stop Event
iter-limit
node-limit
iter-limit
Counts
40 → 2 005
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) #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 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.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 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
Outputs
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.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 (*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (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 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 k))) (/.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 k)) (/.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(*.f64 (/.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 (neg.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #s(literal -1 binary64))
(*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))) (pow.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (neg.f64 (sqrt.f64 k))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(pow.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) #s(literal -1 binary64))
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 2 binary64)))
(/.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
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(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))))
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(neg.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
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(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(/.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(neg.f64 (neg.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 n (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 n (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 n (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (pow.f64 n (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 n #s(literal 1/2 binary64)))
(*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(/.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (pow.f64 n (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 n #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(neg.f64 (*.f64 #s(literal -1 binary64) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))

eval188.0ms (2.9%)

Memory
51.4MiB live, 418.6MiB allocated; 82ms collecting garbage
Compiler

Compiled 43 967 to 5 408 computations (87.7% saved)

prune72.0ms (1.1%)

Memory
-4.2MiB live, 88.4MiB allocated; 8ms collecting garbage
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1 514151 529
Fresh13013
Picked415
Done000
Total1 531161 547
Accuracy
100.0%
Counts
1 547 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
75.8%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.5%
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
48.7%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
76.8%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
96.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (/.f64 (sqrt.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))))
48.8%
#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)))
36.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
48.4%
#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))))
48.7%
#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))))))
Compiler

Compiled 707 to 545 computations (22.9% saved)

series82.0ms (1.3%)

Memory
20.6MiB live, 163.6MiB allocated; 14ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04993941
Stop Event
iter-limit
Counts
33 → 113
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))
#s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))
Outputs
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.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)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.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)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) #s(literal 1 binary64))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))))))
#s(approx (* k -1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k))
#s(approx (/ (* (+ (PI) (PI)) n) k) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
#s(approx (* (/ 1 (sqrt k)) (sqrt (* (+ (PI) (PI)) n))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
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#s(approx (pow (* (+ (PI) (PI)) n) (+ (* 1/2 k) -1/2)) (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))))
#s(approx (+ (* 1/2 k) -1/2) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* n (+ (PI) (PI))) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
#s(approx n n)
#s(approx (sqrt (* (PI) n)) (sqrt.f64 (*.f64 n (PI.f64))))
#s(approx (* (PI) n) (*.f64 n (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)))) (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
#s(approx (/ (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* 1/2 k) -1/2))) (/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* 1/2 k) -1/2)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))))
#s(approx (sqrt (* (PI) n)) (*.f64 n (sqrt.f64 (/.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (sqrt (* (+ (PI) (PI)) n))) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k)))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)))) (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
#s(approx (/ (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* 1/2 k) -1/2))) (/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* 1/2 k) -1/2)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))) (sqrt.f64 k))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))))))
#s(approx (sqrt (* (PI) n)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (/.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (sqrt (* (+ (PI) (PI)) n))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)))) (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
#s(approx (/ (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* 1/2 k) -1/2))) (/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* 1/2 k) -1/2)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))
Calls

6 calls:

TimeVariablePoint
17.0ms
n
inf
16.0ms
n
-inf
13.0ms
n
0
7.0ms
k
-inf
5.0ms
k
0

rewrite182.0ms (2.8%)

Memory
-59.9MiB live, 203.3MiB allocated; 148ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044261
069256
1294247
2942232
04051223
Stop Event
iter-limit
node-limit
iter-limit
Counts
33 → 1 454
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))
#s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))
Outputs
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))) (pow.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 k)) (/.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
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(*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 k #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))
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(-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))
(-.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(+.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal -1/2 binary64))
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eval245.0ms (3.7%)

Memory
26.9MiB live, 400.4MiB allocated; 53ms collecting garbage
Compiler

Compiled 46 448 to 5 252 computations (88.7% saved)

prune63.0ms (1%)

Memory
5.6MiB live, 145.1MiB allocated; 22ms collecting garbage
Pruning

34 alts after pruning (30 fresh and 4 done)

PrunedKeptTotal
New1 618221 640
Fresh2810
Picked235
Done011
Total1 622341 656
Accuracy
100.0%
Counts
1 656 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
75.8%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.5%
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
96.1%
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
76.8%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
96.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
48.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
48.7%
#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)))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
48.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
45.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
22.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 k k))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
34.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
48.4%
#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))))
48.7%
#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))))))
35.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
46.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
48.7%
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
Compiler

Compiled 1 723 to 1 307 computations (24.1% saved)

series200.0ms (3.1%)

Memory
11.5MiB live, 379.8MiB allocated; 93ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02891798
Stop Event
iter-limit
Counts
31 → 74
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
(sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))
(*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))
(/.f64 n k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
#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)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64)))
(*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))
(log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
Outputs
#s(approx (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (+ (* -1/2 k) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* -1/2 k) 1/2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (sqrt (* (/ n k) (+ (PI) (PI)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k))
#s(approx (* (/ n k) (+ (PI) (PI))) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
#s(approx (/ n k) (/.f64 n k))
#s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) k))
#s(approx (sqrt (* (/ n k) (PI))) (/.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) k))
#s(approx (* (/ n k) (PI)) (/.f64 (*.f64 n (PI.f64)) k))
#s(approx (/ 1 (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal -1 binary64) (log.f64 k)))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal -1 binary64) (log.f64 k))))
#s(approx (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (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 k) (+ (PI) (PI)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (sqrt (* (/ n k) (PI))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
#s(approx (/ 1 (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n))) (/.f64 (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (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 (/ 1 (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n)))) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k))))
#s(approx (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
#s(approx (* (+ (PI) (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 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
#s(approx (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
#s(approx (* (/ 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 k) (+ (PI) (PI)))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (sqrt (* (/ n k) (PI))) (*.f64 n (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))
#s(approx (/ 1 (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n)))) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k)))
#s(approx (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n))) (/.f64 (sqrt.f64 k) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))
#s(approx (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
#s(approx (* (/ 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 k) (+ (PI) (PI)))) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (sqrt (* (/ n k) (PI))) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (/ 1 (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n))) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
Calls

6 calls:

TimeVariablePoint
55.0ms
n
-inf
31.0ms
k
-inf
28.0ms
n
0
23.0ms
k
0
20.0ms
n
inf

rewrite151.0ms (2.3%)

Memory
8.1MiB live, 202.2MiB allocated; 36ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
040253
062238
1251225
2877225
04181225
Stop Event
iter-limit
node-limit
iter-limit
Counts
31 → 1 466
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
(sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))
(*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))
(/.f64 n k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
#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)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64)))
(*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))
(log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
Outputs
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 (+.f64 n n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (+.f64 n n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (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) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(neg.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(+.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(+.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) (*.f64 n (PI.f64)))
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (+.f64 n n) (PI.f64))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (neg.f64 n))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (neg.f64 (PI.f64)) n))
(*.f64 (neg.f64 n) (*.f64 #s(literal -2 binary64) (PI.f64)))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (fma.f64 (cbrt.f64 (PI.f64)) n (*.f64 (cbrt.f64 (PI.f64)) n)))
(*.f64 (cbrt.f64 (PI.f64)) (fma.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
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(fma.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (/.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 0 binary64)))
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(sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))
(-.f64 (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64)) (neg.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))))
(-.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))) (/.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal -2 binary64)))
(fabs.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(fabs.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))
(fabs.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(fabs.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(hypot.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
(hypot.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(hypot.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
(hypot.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(exp.f64 (*.f64 (log.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(+.f64 (*.f64 #s(literal 1 binary64) (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1 binary64) (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))))
(+.f64 (*.f64 #s(literal 1 binary64) (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))) (*.f64 #s(literal 1 binary64) (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64))))
(+.f64 (*.f64 (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (*.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))) #s(literal 1 binary64)))
(+.f64 (*.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))) #s(literal 1 binary64)) (*.f64 (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+.f64 (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64)) (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))) (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64)))
(+.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 0 binary64)))
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#s(literal 1 binary64)
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(*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 k) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))
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(pow.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/2 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 k) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
(/.f64 (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (neg.f64 k)) (sqrt.f64 (*.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) n)))
(/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
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(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 k k) (fma.f64 (*.f64 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)
(neg.f64 (*.f64 (/.f64 (neg.f64 n) k) (+.f64 (PI.f64) (PI.f64))))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(neg.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal -2 binary64)))
(neg.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal -2 binary64) (PI.f64))))
(neg.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
(neg.f64 (-.f64 (*.f64 (/.f64 (neg.f64 n) k) (PI.f64)) (*.f64 (/.f64 n k) (PI.f64))))
(neg.f64 (*.f64 #s(literal -2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(fma.f64 (/.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) k) (cbrt.f64 (PI.f64)) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) k) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (*.f64 (neg.f64 (PI.f64)) n) (/.f64 #s(literal -1 binary64) k) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 1 binary64) k) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64))))
(fma.f64 (neg.f64 n) (/.f64 (PI.f64) (neg.f64 k)) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (*.f64 (cbrt.f64 (PI.f64)) n) k) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(fma.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(fma.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 1 binary64) (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 1 binary64)))
(fma.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))))
(fma.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64))))
(fma.f64 (/.f64 n k) (PI.f64) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 #s(literal 1 binary64) (*.f64 (/.f64 n k) (PI.f64)) (*.f64 #s(literal 1 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(fma.f64 n (/.f64 (PI.f64) k) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (PI.f64) (/.f64 n k) (*.f64 (/.f64 n k) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(-.f64 (cosh.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (neg.f64 (sinh.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
(-.f64 (*.f64 (/.f64 n k) (PI.f64)) (*.f64 (/.f64 (neg.f64 n) k) (PI.f64)))
(fabs.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
(fabs.f64 (-.f64 (*.f64 (/.f64 (neg.f64 n) k) (PI.f64)) (*.f64 (/.f64 n k) (PI.f64))))
(fabs.f64 (*.f64 #s(literal -2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(fabs.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64))) (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64))))
(+.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 1 binary64)))
(+.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64))))
(+.f64 (*.f64 #s(literal 1 binary64) (*.f64 (/.f64 n k) (PI.f64))) (*.f64 #s(literal 1 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(+.f64 (*.f64 (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (*.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(+.f64 (*.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (*.f64 (*.f64 (-.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(+.f64 (/.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) k) k) (*.f64 (/.f64 n k) (PI.f64)))
(+.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) k) (*.f64 k k)) (/.f64 (*.f64 k (*.f64 n (PI.f64))) (*.f64 k k)))
(+.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) k) (*.f64 k k)) (/.f64 (*.f64 (*.f64 n (PI.f64)) k) (*.f64 k k)))
(+.f64 (cosh.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (sinh.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(+.f64 (*.f64 (/.f64 n k) (PI.f64)) (*.f64 (/.f64 n k) (PI.f64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (+.f64 n n) k)))
(log.f64 (pow.f64 (exp.f64 (+.f64 (PI.f64) (PI.f64))) (/.f64 n k)))
(log.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64))) #s(literal 2 binary64)))
(log.f64 (*.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64))) (exp.f64 (*.f64 (/.f64 n k) (PI.f64)))))

eval126.0ms (1.9%)

Memory
-3.5MiB live, 223.4MiB allocated; 36ms collecting garbage
Compiler

Compiled 32 530 to 3 955 computations (87.8% saved)

prune69.0ms (1.1%)

Memory
-3.9MiB live, 102.3MiB allocated; 51ms collecting garbage
Pruning

50 alts after pruning (42 fresh and 8 done)

PrunedKeptTotal
New1 011221 033
Fresh52025
Picked145
Done044
Total1 017501 067
Accuracy
100.0%
Counts
1 067 → 50
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
75.8%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
54.1%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
99.5%
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
96.1%
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 k))
99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
76.8%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
96.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
48.7%
#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)))))
48.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
48.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
48.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
48.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
48.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
15.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
34.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))) #s(literal 1/2 binary64)))))
45.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
22.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k k))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
34.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
34.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
48.4%
#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))))
48.7%
#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))))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) k)))
46.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
35.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
46.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
48.7%
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
Compiler

Compiled 1 369 to 1 052 computations (23.2% saved)

regimes554.0ms (8.5%)

Memory
21.8MiB live, 905.5MiB allocated; 116ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
4 → 1
8 → 1
13 → 1
20 → 2
45 → 2
47 → 3
51 → 2
53 → 1
69 → 1
74 → 1
78 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
Call 2
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
Call 3
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
Call 4
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.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 5
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
Call 6
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
Call 7
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
Call 8
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (+ (* -1/2 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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
Call 9
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (+ (* -1/2 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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
Outputs
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
Call 10
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (+ (* -1/2 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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 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) #s(approx (sqrt k) (*.f64 k (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
Call 11
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (+ (* -1/2 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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 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) #s(approx (sqrt k) (*.f64 k (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
Call 12
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 n n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt 2) (sqrt (* (/ n k) (PI)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #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))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (* (sqrt (* (PI) n)) (sqrt 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (+ (* -1/2 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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 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) #s(approx (sqrt k) (*.f64 k (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal -1/2 binary64))))
#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))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
Calls

45 calls:

27.0ms
(*.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))))
26.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms
n
22.0ms
n
21.0ms
k
Results
AccuracySegmentsBranch
36.8%1k
36.8%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
36.8%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.8%1n
36.8%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.8%1k
36.8%1n
36.8%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))))
48.8%1k
48.8%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
48.8%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))))
48.8%1n
48.8%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))))
48.8%1k
48.8%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
48.8%1n
60.6%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
60.6%2n
60.5%2k
60.6%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
60.6%2n
62.8%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
62.8%3n
60.5%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))))
62.2%3k
65.4%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
98.2%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))))
98.2%2k
65.4%2n
99.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%1k
99.5%1n
99.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%1k
99.5%1n
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%1k
99.6%1n
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1k
99.7%1n
Compiler

Compiled 2 260 to 606 computations (73.2% saved)

bsearch14.0ms (0.2%)

Memory
16.3MiB live, 16.3MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
12.0ms
0.0764086566270794
6.796037868165734
Samples
7.0ms112×0valid
Compiler

Compiled 341 to 291 computations (14.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-pow: 2.0ms (40% of total)
ival-sqrt: 1.0ms (20% of total)
ival-div!: 1.0ms (20% of total)
ival-mult!: 1.0ms (20% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch36.0ms (0.5%)

Memory
1.5MiB live, 51.4MiB allocated; 10ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
13.0ms
2.7178496787239455e+30
1.0559660036793747e+33
19.0ms
664.7171019505735
2039122.420358386
Samples
22.0ms256×0valid
Compiler

Compiled 955 to 778 computations (18.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-pow: 4.0ms (36.3% of total)
ival-sqrt: 2.0ms (18.2% of total)
ival-div!: 2.0ms (18.2% of total)
ival-mult!: 2.0ms (18.2% of total)
ival-sub!: 1.0ms (9.1% of total)
adjust: 0.0ms (0% of total)

bsearch22.0ms (0.3%)

Memory
-22.6MiB live, 21.6MiB allocated; 9ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
20.0ms
4.133759111664395e-50
3.521172713179575e-47
Samples
15.0ms128×0valid
Compiler

Compiled 531 to 418 computations (21.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-mult!: 7.0ms (59.8% of total)
ival-pow: 2.0ms (17.1% of total)
ival-sqrt: 1.0ms (8.5% of total)
ival-div!: 1.0ms (8.5% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch13.0ms (0.2%)

Memory
21.4MiB live, 21.4MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
12.0ms
9.386994674757752e+27
2.01312992971684e+30
Samples
7.0ms112×0valid
Compiler

Compiled 446 to 347 computations (22.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-pow: 2.0ms (41.4% of total)
ival-sqrt: 1.0ms (20.7% of total)
ival-div!: 1.0ms (20.7% of total)
ival-mult!: 1.0ms (20.7% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

derivations889.0ms (13.6%)

Memory
-85.9MiB live, 284.3MiB allocated; 1.3s collecting garbage
Stop Event
fuel
Compiler

Compiled 454 to 94 computations (79.3% saved)

preprocess125.0ms (1.9%)

Memory
-43.6MiB live, 293.3MiB allocated; 61ms collecting garbage
Remove

(abs k)

Compiler

Compiled 1 378 to 675 computations (51% saved)

end0.0ms (0%)

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

Profiling

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