Migdal et al, Equation (51)

Time bar (total: 5.7s)

start0.0ms (0%)

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

analyze116.0ms (2%)

Memory
17.8MiB live, 112.8MiB allocated; 47ms collecting garbage
Algorithm
1×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)

sample2.8s (48.3%)

Memory
82.4MiB live, 4 466.3MiB allocated; 1.0s collecting garbage
Samples
1.2s5 426×1invalid
739.0ms8 254×0valid
187.0ms439×2invalid
29.0ms383×0invalid
20.0ms222×0exit
0.0ms2×1valid
Precisions
Click to see histograms. Total time spent on operations: 1.6s
ival-pow: 470.0ms (29.4% of total)
adjust: 308.0ms (19.3% of total)
ival-mult!: 286.0ms (17.9% of total)
ival-div!: 236.0ms (14.8% of total)
ival-sqrt: 226.0ms (14.1% of total)
ival-sub!: 74.0ms (4.6% of total)
ival-pi: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

preprocess43.0ms (0.8%)

Memory
-15.3MiB live, 31.0MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033101
112887
246287
3217586
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Symmetry

(abs k)

Compiler

Compiled 32 to 26 computations (18.8% saved)

series95.0ms (1.7%)

Memory
4.0MiB live, 103.9MiB allocated; 30ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0158937
Stop Event
1×iter-limit
Counts
13 → 37
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) k))
#s(approx (- 1 k) (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal -1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt k) (*.f64 #s(literal -1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (* 2 (PI)) n) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
Calls

6 calls:

TimeVariablePoint
28.0ms
n
0
26.0ms
n
inf
21.0ms
n
-inf
2.0ms
k
-inf
2.0ms
k
0

rewrite102.0ms (1.8%)

Memory
-2.0MiB live, 139.3MiB allocated; 13ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01354
02254
16451
222051
3109651
0409748
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
13 → 785
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 4 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))) (sqrt.f64 k)) #s(literal 4 binary64)))
(*.f64 #s(literal -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))) (sqrt.f64 k)) #s(literal -2 binary64)))
(*.f64 #s(literal -1 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))) (sqrt.f64 k)) #s(literal -1 binary64)))
(*.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 #s(literal 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))) (sqrt.f64 k)) #s(literal 2 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 (/.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 #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 (neg.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 (neg.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)))))) (neg.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k)))))
(/.f64 (neg.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))))) (neg.f64 (*.f64 #s(literal 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))
(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))))
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(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (+.f64 k k)) #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 k k) #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (/.f64 k #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (/.f64 (*.f64 (neg.f64 k) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))
(+.f64 (/.f64 k #s(literal -1 binary64)) #s(literal 1 binary64))
(+.f64 (neg.f64 k) #s(literal 1 binary64))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 k k)) #s(literal 2 binary64)))
(+.f64 (-.f64 #s(literal 1 binary64) k) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 0 binary64)) #s(literal 1 binary64)))
(+.f64 (-.f64 #s(literal 1 binary64) k) (/.f64 (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)))
(+.f64 (-.f64 #s(literal 1 binary64) k) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 0 binary64)))
(+.f64 (-.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
(+.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 0 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (+.f64 k k)) #s(literal 2 binary64)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) k) #s(literal 2 binary64)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (neg.f64 k)) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (neg.f64 k)))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) k))
(+.f64 #s(literal 1 binary64) (/.f64 k #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (neg.f64 k))

eval88.0ms (1.5%)

Memory
19.1MiB live, 154.5MiB allocated; 12ms collecting garbage
Compiler

Compiled 18 288 to 2 751 computations (85% saved)

prune30.0ms (0.5%)

Memory
1.5MiB live, 53.3MiB allocated; 8ms collecting garbage
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New79616812
Fresh000
Picked101
Done000
Total79716813
Accuracy
99.8%
Counts
813 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.1%
(/.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))
99.0%
(*.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)))
▶99.1%
(*.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 0 binary64))) k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.0%
(*.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 k) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 0 binary64))) (*.f64 (neg.f64 (sqrt.f64 k)) (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))))
98.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
98.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
44.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
59.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 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)))))
▶52.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
96.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
▶96.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
99.0%
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.1%
(*.f64 (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))))
48.8%
#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))))
▶45.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
96.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
Compiler

Compiled 1 036 to 686 computations (33.8% saved)

series203.0ms (3.5%)

Memory
-51.0MiB live, 220.2MiB allocated; 142ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04234371
Stop Event
1×iter-limit
Counts
45 → 121
Calls
Call 1
Inputs
(/.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))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
k
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(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 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 0 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 (fma.f64 #s(literal 1 binary64) (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 0 binary64))) k)
(fma.f64 #s(literal 1 binary64) (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 0 binary64)))
(*.f64 (sqrt.f64 k) #s(literal 0 binary64))
#s(literal 0 binary64)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#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))))
(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)))
(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))))))
(*.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)))))
#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))))
(*.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 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))
Outputs
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 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 (* n (+ (PI) (PI))) (+ (* k -1/2) 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 (* n (+ (PI) (PI))) (+ (* k -1/2) 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 (* n (+ (PI) (PI))) (+ (* k -1/2) 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 (* 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))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 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 (* n (+ (PI) (PI))) (+ (* k -1/2) 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 (+ (* k -1/2) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* k -1/2) 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 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
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#s(approx (log (* 2 (* n (PI)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
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#s(approx (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (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 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)))))))))
#s(approx (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)))))))
#s(approx (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
#s(approx (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))))))
#s(approx (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (*.f64 k (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)))))
#s(approx (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))))
#s(approx (pow (log (* 2 (* n (PI)))) 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 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 (* 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 (* (* 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 (pow (* 2 (* n (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) 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 (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (* 2 (* n (PI)))) (- 1 k)) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (log (* 2 (* n (PI)))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))
#s(approx (* (/ (+ (* 1 (sqrt k)) (* (sqrt k) 0)) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.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)) k))
#s(approx (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2)) (*.f64 n (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (+.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 1/8 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64))))))))))
#s(approx (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (+.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 1/8 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64))))))))
#s(approx (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (*.f64 n (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
#s(approx (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 n (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64)))))))
#s(approx (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (*.f64 k (*.f64 n (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64))))))
#s(approx (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (*.f64 n (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64)))))
#s(approx (pow (log (* 2 (* n (PI)))) 2) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64)))
#s(approx (/ (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 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 (* 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 (* (* 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 (pow (* 2 (* n (PI))) 1/2) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (pow (* (* 2 (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 (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (* 2 (* n (PI)))) (- 1 k)) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (log (* 2 (* n (PI)))) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
#s(approx (* (/ (+ (* 1 (sqrt k)) (* (sqrt k) 0)) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.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)) k))
#s(approx (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2)) (*.f64 #s(literal -1 binary64) (*.f64 n (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (+.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 1/8 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))))))))))
#s(approx (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))) (*.f64 #s(literal -1 binary64) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (+.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 1/8 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))))))))
#s(approx (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))) (*.f64 #s(literal -1/8 binary64) (*.f64 k (*.f64 n (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))))))
#s(approx (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (*.f64 #s(literal -1 binary64) (*.f64 k (*.f64 n (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))))))
#s(approx (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64))))))
#s(approx (pow (log (* 2 (* n (PI)))) 2) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))
Calls

6 calls:

TimeVariablePoint
73.0ms
n
-inf
32.0ms
k
inf
31.0ms
k
0
16.0ms
n
0
13.0ms
n
inf

rewrite139.0ms (2.4%)

Memory
25.4MiB live, 212.8MiB allocated; 16ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
054545
093498
1225480
2790448
04239448
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
45 → 1 609
Calls
Call 1
Inputs
(/.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))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
k
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(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 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 0 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 (fma.f64 #s(literal 1 binary64) (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 0 binary64))) k)
(fma.f64 #s(literal 1 binary64) (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 0 binary64)))
(*.f64 (sqrt.f64 k) #s(literal 0 binary64))
#s(literal 0 binary64)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#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))))
(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)))
(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))))))
(*.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)))))
#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))))
(*.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 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))
Outputs
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 2 binary64))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(*.f64 (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) k))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) k))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (neg.f64 (sqrt.f64 k)) (*.f64 (/.f64 #s(literal -1 binary64) k) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (neg.f64 (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 k)))
(*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal -1 binary64)) (neg.f64 k))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 1 binary64)) k)
(/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)) k)
(/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (*.f64 k (sqrt.f64 k))) (*.f64 k k))
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) k)
(/.f64 (*.f64 (*.f64 k (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) (*.f64 k k))
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)) (neg.f64 k))
(/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) k)
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k)))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (neg.f64 k)))
(neg.f64 (/.f64 (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)) k))
(neg.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k))))
(fma.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 0 binary64))
(fma.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 0 binary64))
(fma.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) k) #s(literal 0 binary64))
(fma.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) k) #s(literal 0 binary64))
(fma.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 k)) (*.f64 (/.f64 #s(literal -1 binary64) k) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 k)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 0 binary64))
(fma.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))) #s(literal 0 binary64))
(-.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))) #s(literal 0 binary64)))
(-.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(+.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 0 binary64))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (neg.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (exp.f64 (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64))))
(pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(pow.f64 (exp.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (-.f64 #s(literal 2 binary64) (+.f64 k k))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
(pow.f64 (E.f64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (sqrt.f64 (E.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) #s(literal 2 binary64))
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(*.f64 (*.f64 k (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) #s(literal 1/8 binary64)))
(*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) k)) (neg.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (neg.f64 k))
(*.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) k) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) k)) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))
(*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) k)
(*.f64 (*.f64 #s(literal -1/8 binary64) k) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (*.f64 (neg.f64 (*.f64 k (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) #s(literal -1/8 binary64))
(*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) k) (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) #s(literal 1/8 binary64)))
(*.f64 (*.f64 #s(literal 1/8 binary64) k) (neg.f64 (*.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (log.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(*.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 #s(literal -1/8 binary64) (*.f64 (neg.f64 (*.f64 k (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) k) #s(literal 1/8 binary64))
(*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 #s(literal 1/8 binary64) k))
(*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 k (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) #s(literal 1/8 binary64))))
(*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) k) #s(literal 1/8 binary64)))
(*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (*.f64 #s(literal 1/8 binary64) k)))
(*.f64 #s(literal 1/8 binary64) (neg.f64 (*.f64 (neg.f64 (*.f64 k (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))))
(*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) k))
(*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (*.f64 #s(literal 1/8 binary64) k)))
(*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 #s(literal 1/8 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) k) #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 #s(literal 1/8 binary64) k)))
(*.f64 k (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(*.f64 k (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) #s(literal 1/8 binary64)))
(neg.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) k)))
(log.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (*.f64 #s(literal 1/8 binary64) k) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))
#s(literal 1/8 binary64)
(*.f64 (*.f64 k (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (*.f64 k (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) k)))
(*.f64 (neg.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (neg.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) k)))
(*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) k) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))
(*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) k)
(*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 k (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) k))
(*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) k))
(*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) k))
(*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) k))
(*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(log.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 k (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(*.f64 (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (neg.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))
(*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (log.f64 (*.f64 (+.f64 n n) (PI.f64))))
(*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(log.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(log.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(log.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (fabs.f64 (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (fabs.f64 (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(*.f64 (neg.f64 (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (neg.f64 (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(*.f64 (neg.f64 (neg.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (neg.f64 (neg.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(*.f64 (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (neg.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (neg.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64))))
(pow.f64 (fabs.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) #s(literal 2 binary64))
(pow.f64 (neg.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) #s(literal 2 binary64))
(pow.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) #s(literal 2 binary64))
(neg.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (neg.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(neg.f64 (*.f64 (neg.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(fabs.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(log.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))))

eval202.0ms (3.5%)

Memory
32.0MiB live, 403.9MiB allocated; 47ms collecting garbage
Compiler

Compiled 71 950 to 6 188 computations (91.4% saved)

prune46.0ms (0.8%)

Memory
-13.5MiB live, 78.0MiB allocated; 8ms collecting garbage
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New1 579221 601
Fresh11011
Picked505
Done000
Total1 595221 617
Accuracy
100.0%
Counts
1 617 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.8%
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
96.1%
(/.f64 (pow.f64 (sqrt.f64 (E.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k))
▶95.9%
(/.f64 (pow.f64 (E.f64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
99.0%
(/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) k)
▶99.3%
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (exp.f64 (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))) (sqrt.f64 k))
99.1%
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
96.2%
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
52.8%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (-.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))) k (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k))
52.7%
(*.f64 (/.f64 (sqrt.f64 k) k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
99.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))))
96.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(approx (- 1 k) (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))))))))
23.6%
(*.f64 (*.f64 (*.f64 k (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (*.f64 k k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
99.0%
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) k))
▶93.2%
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k))
44.9%
#s(approx (* (/ (+ (* 1 (sqrt k)) (* (sqrt k) 0)) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) k))
45.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
42.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (exp.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
▶42.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
45.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
44.9%
#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 n n) (PI.f64)))))
▶35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
44.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
Compiler

Compiled 1 264 to 872 computations (31% saved)

series193.0ms (3.4%)

Memory
2.0MiB live, 241.8MiB allocated; 64ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05344728
Stop Event
1×iter-limit
Counts
30 → 118
Calls
Call 1
Inputs
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (exp.f64 (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (exp.f64 (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))))
(sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))
(*.f64 (+.f64 n n) (PI.f64))
(+.f64 n n)
n
(PI.f64)
(exp.f64 (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(neg.f64 k)
k
(log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k)))
(*.f64 (+.f64 n n) (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
(/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k)
(sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
(/.f64 (pow.f64 (E.f64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(pow.f64 (E.f64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(E.f64)
(*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
Outputs
#s(approx (/ (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (sqrt k)) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (log.f64 (sqrt.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 1/2 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (sqrt.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 (/ (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (log.f64 (sqrt.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 -1/6 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (sqrt.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 1/2 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (sqrt.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 (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal -1 binary64) (*.f64 k (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
#s(approx (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1 binary64) (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (sqrt.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 (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1 binary64) (*.f64 (log.f64 (sqrt.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 -1/6 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (sqrt.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 1/2 binary64) (*.f64 (pow.f64 (log.f64 (sqrt.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 (exp (* (neg k) (log (sqrt (* (+ n n) (PI)))))) #s(literal 1 binary64))
#s(approx (exp (* (neg k) (log (sqrt (* (+ n n) (PI)))))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 k (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
#s(approx (exp (* (neg k) (log (sqrt (* (+ n n) (PI)))))) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal -1 binary64) (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 k (pow.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) #s(literal 2 binary64))))))))
#s(approx (exp (* (neg k) (log (sqrt (* (+ n n) (PI)))))) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal -1 binary64) (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 k (fma.f64 #s(literal -1/6 binary64) (*.f64 k (pow.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (pow.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) #s(literal 2 binary64)))))))))
#s(approx (* (neg k) (log (sqrt (* (+ n n) (PI))))) (*.f64 #s(literal -1 binary64) (*.f64 k (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#s(approx (neg k) (*.f64 #s(literal -1 binary64) k))
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k))
#s(approx (* (+ n n) (/ (PI) k)) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
#s(approx (/ (PI) k) (/.f64 (PI.f64) k))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) k))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (fma.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (*.f64 (sqrt.f64 k) (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) k))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (fma.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 k (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (*.f64 (sqrt.f64 k) (-.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (sqrt.f64 k) (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))) (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) k))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k) (/.f64 (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) k))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k) (/.f64 (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.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 1/2 binary64) (/.f64 (*.f64 k (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.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))))))))) k))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k) (/.f64 (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.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 1/2 binary64) (/.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.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))))))))))) k))
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#s(approx (/ (pow (E) (* (log (sqrt (* (+ n n) (PI)))) (- 1 k))) (sqrt k)) (/.f64 (exp.f64 (*.f64 (log.f64 (E.f64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (* (log (sqrt (* (+ n n) (PI)))) (- 1 k)) (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (sqrt k)) (/.f64 (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 (sqrt (* (+ n n) (PI))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (exp (* (neg k) (log (sqrt (* (+ n n) (PI)))))) (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (* (neg k) (log (sqrt (* (+ n n) (PI))))) (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
#s(approx (log (sqrt (* (+ n n) (PI)))) (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 n) (/ (PI) k))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (/ (exp (log (sqrt (* (+ n n) (PI))))) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k)))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.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 #s(literal 1 binary64) k))))) k))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k) (/.f64 (sqrt.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 #s(literal 1 binary64) k)))) k))
#s(approx (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt.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 #s(literal 1 binary64) k)))))
#s(approx (pow (* (+ n n) (PI)) (- 1 k)) (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 #s(literal 1 binary64) k))))
#s(approx (/ (pow (E) (* (log (sqrt (* (+ n n) (PI)))) (- 1 k))) (sqrt k)) (/.f64 (exp.f64 (*.f64 (log.f64 (E.f64)) (*.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 (E) (* (log (sqrt (* (+ n n) (PI)))) (- 1 k))) (exp.f64 (*.f64 (log.f64 (E.f64)) (*.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (log (sqrt (* (+ n n) (PI)))) (- 1 k)) (*.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 (* (sqrt (* (+ n n) (PI))) (exp (* (neg k) (log (sqrt (* (+ n n) (PI))))))) (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 (sqrt (* (+ n n) (PI))) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (exp (* (neg k) (log (sqrt (* (+ n n) (PI)))))) (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (* (neg k) (log (sqrt (* (+ n n) (PI))))) (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
#s(approx (log (sqrt (* (+ n n) (PI)))) (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 n) (/ (PI) k))) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (/ (exp (log (sqrt (* (+ n n) (PI))))) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.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 #s(literal 1 binary64) k))))) k))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k) (/.f64 (sqrt.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 #s(literal 1 binary64) k)))) k))
#s(approx (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt.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 #s(literal 1 binary64) k)))))
#s(approx (pow (* (+ n n) (PI)) (- 1 k)) (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 #s(literal 1 binary64) k))))
#s(approx (/ (pow (E) (* (log (sqrt (* (+ n n) (PI)))) (- 1 k))) (sqrt k)) (/.f64 (exp.f64 (*.f64 (log.f64 (E.f64)) (*.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 (E) (* (log (sqrt (* (+ n n) (PI)))) (- 1 k))) (exp.f64 (*.f64 (log.f64 (E.f64)) (*.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (log (sqrt (* (+ n n) (PI)))) (- 1 k)) (*.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))
Calls

6 calls:

TimeVariablePoint
42.0ms
k
0
35.0ms
n
-inf
31.0ms
n
0
29.0ms
n
inf
15.0ms
k
-inf

rewrite123.0ms (2.1%)

Memory
23.7MiB live, 160.4MiB allocated; 11ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040269
065271
1168254
2588230
33307230
04266230
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
30 → 784
Calls
Call 1
Inputs
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (exp.f64 (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (exp.f64 (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))))
(sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))
(*.f64 (+.f64 n n) (PI.f64))
(+.f64 n n)
n
(PI.f64)
(exp.f64 (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))
(*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(neg.f64 k)
k
(log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k)))
(*.f64 (+.f64 n n) (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
(/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k)
(sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
(/.f64 (pow.f64 (E.f64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(pow.f64 (E.f64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(E.f64)
(*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
Outputs
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k))))
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) (neg.f64 (sqrt.f64 k))))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k) (sqrt.f64 k)))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))))
(neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(fma.f64 (/.f64 (cosh.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (/.f64 (*.f64 (-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(fma.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (*.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(fma.f64 (/.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (/.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (neg.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
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(fma.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))) (*.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (*.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 0 binary64)))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) (*.f64 #s(literal 0 binary64) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))))
(-.f64 (cosh.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sinh.f64 (*.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))))
(-.f64 (cosh.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sinh.f64 (*.f64 #s(literal 1 binary64) (*.f64 (-.f64 k #s(literal 1 binary64)) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))))
(-.f64 (cosh.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sinh.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(-.f64 (/.f64 (cosh.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)) (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) (*.f64 (-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (cosh.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)) (*.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))))
(-.f64 (/.f64 (cosh.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)) (neg.f64 (/.f64 (*.f64 (-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))))
(-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)))))
(-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (*.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(fabs.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))))
(fabs.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) #s(literal 0 binary64)))
(exp.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(+.f64 (cosh.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) #s(literal 0 binary64))) (sinh.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) #s(literal 0 binary64))))
(+.f64 (cosh.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sinh.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(+.f64 (/.f64 (*.f64 (-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)) (/.f64 (cosh.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))
(+.f64 (*.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(+.f64 (/.f64 (cosh.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)) (/.f64 (*.f64 (-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(+.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 0 binary64)))
(+.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal 0 binary64) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))))
(E.f64)
(*.f64 (neg.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (-.f64 k #s(literal 1 binary64)))
(*.f64 (-.f64 k #s(literal 1 binary64)) (neg.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(*.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (-.f64 #s(literal 1 binary64) k))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) #s(literal 2 binary64))
(neg.f64 (*.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 (-.f64 k #s(literal 1 binary64)) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(neg.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(fma.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) #s(literal 1/2 binary64)) #s(literal 2 binary64) (*.f64 #s(literal 1 binary64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))))
(fma.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) #s(literal 1/2 binary64)) #s(literal 2 binary64) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)) #s(literal 1 binary64)))
(fma.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) #s(literal 1/2 binary64)) #s(literal 2 binary64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)))
(fma.f64 (neg.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) k (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(fma.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 #s(literal 1 binary64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))))
(fma.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)))
(fma.f64 #s(literal 1 binary64) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 #s(literal 1 binary64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))))
(fma.f64 #s(literal 1 binary64) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)))
(fma.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))))
(fma.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) #s(literal 1 binary64) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)) #s(literal 1 binary64)))
(fma.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) #s(literal 1 binary64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)))
(fma.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(fma.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(-.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)) (neg.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(-.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) k))
(+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(+.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 #s(literal 1 binary64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k))))
(+.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)) #s(literal 1 binary64)))
(+.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (neg.f64 k)))
(log.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (-.f64 k #s(literal 1 binary64))))
(log.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) k)))
(log.f64 (pow.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(log.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) #s(literal 1 binary64))))
(log.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) #s(literal 1 binary64)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))))
(log.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(log.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k)))
(log.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 k #s(literal 1 binary64)))))
(log.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)))
(log.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)))

eval179.0ms (3.1%)

Memory
5.7MiB live, 238.9MiB allocated; 38ms collecting garbage
Compiler

Compiled 35 629 to 4 515 computations (87.3% saved)

prune49.0ms (0.9%)

Memory
-21.6MiB live, 109.9MiB allocated; 23ms collecting garbage
Pruning

28 alts after pruning (25 fresh and 3 done)

PrunedKeptTotal
New1 139171 156
Fresh9817
Picked235
Done000
Total1 150281 178
Accuracy
100.0%
Counts
1 178 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.8%
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
▶99.1%
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
79.0%
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))
87.7%
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 #s(literal 1 binary64) k)) k)) k)
96.2%
(/.f64 (exp.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
▶99.0%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
52.7%
(*.f64 (/.f64 (sqrt.f64 k) k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
87.6%
(*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 #s(literal 1 binary64) k)) k)))
✓93.2%
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k))
39.1%
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 #s(approx (pow (* (+ n n) (PI)) (- 1 k)) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
79.0%
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
45.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
42.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (exp.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
✓42.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
45.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
44.9%
#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 n n) (PI.f64)))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 k))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
▶35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
✓35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
▶35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n)))))
35.5%
#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))))
28.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
44.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
▶33.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
44.9%
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
Compiler

Compiled 1 410 to 1 017 computations (27.9% saved)

series212.0ms (3.7%)

Memory
25.9MiB live, 410.2MiB allocated; 94ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04163030
Stop Event
1×iter-limit
Counts
32 → 93
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))
(*.f64 (+.f64 n n) (PI.f64))
(+.f64 n n)
n
(PI.f64)
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64)))
(*.f64 (/.f64 (+.f64 n n) k) (PI.f64))
(/.f64 (+.f64 n n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64)))))
(*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))
#s(literal 2 binary64)
(*.f64 k (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (PI.f64) (+.f64 n n))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
Outputs
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt k)) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))) (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt k)) (fma.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 k (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#s(approx (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.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 1/2 binary64) (/.f64 (*.f64 k (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.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 (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.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 1/2 binary64) (/.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (pow.f64 (sqrt.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 n) (PI)) (- 1 k)) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
#s(approx (pow (* (+ n n) (PI)) (- 1 k)) (fma.f64 #s(literal -2 binary64) (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (pow (* (+ n n) (PI)) (- 1 k)) (fma.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)) (*.f64 k (fma.f64 #s(literal -2 binary64) (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))))))
#s(approx (pow (* (+ n n) (PI)) (- 1 k)) (fma.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)) (*.f64 k (fma.f64 #s(literal -2 binary64) (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 k (fma.f64 #s(literal -1/3 binary64) (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (sqrt (* (/ (+ n n) k) (PI))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k))
#s(approx (* (/ (+ n n) k) (PI)) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
#s(approx (/ (+ n n) k) (*.f64 #s(literal 2 binary64) (/.f64 n k)))
#s(approx (sqrt (* 2 (* k (* n (PI))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))))
#s(approx (* 2 (* k (* n (PI)))) (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64)))))
#s(approx (* k (* n (PI))) (*.f64 k (*.f64 n (PI.f64))))
#s(approx (sqrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* (PI) (+ n n)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (sqrt.f64 k) #s(literal 2 binary64))))))
#s(approx (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* (PI) (+ n n))) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (sqrt.f64 k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 2 binary64))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (* (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (/ 1 (sqrt k))) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (/ 1 (sqrt k))) (fma.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (log.f64 (sqrt.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 1/2 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (sqrt.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 (* (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (/ 1 (sqrt k))) (fma.f64 k (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (log.f64 (sqrt.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 -1/6 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (sqrt.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 1/2 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (sqrt.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 (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal -1 binary64) (*.f64 k (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
#s(approx (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1 binary64) (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (sqrt.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 (sqrt (* (PI) (+ n n))) (- 1 k)) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1 binary64) (*.f64 (log.f64 (sqrt.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 -1/6 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (sqrt.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 1/2 binary64) (*.f64 (pow.f64 (log.f64 (sqrt.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 (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt k)) (/.f64 (sqrt.f64 (exp.f64 (*.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 (pow (* (+ n n) (PI)) (- 1 k))) (sqrt.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (pow (* (+ n n) (PI)) (- 1 k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) k))
#s(approx (- 1 k) (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))))
#s(approx (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 n) k) (PI))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (sqrt (* 2 (* k (* n (PI))))) (*.f64 k (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
#s(approx (sqrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* (PI) (+ n n)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))))) k))
#s(approx (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* (PI) (+ n n))) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 (pow.f64 k #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 k #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64)))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.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 (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
#s(approx (pow (* (+ n n) (PI)) (- 1 k)) (exp.f64 (*.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 (sqrt k) (*.f64 #s(literal -1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (sqrt (* 2 (* k (* n (PI))))) k) (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
#s(approx (sqrt (* 2 (* k (* n (PI))))) (*.f64 #s(literal -1 binary64) (*.f64 k (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))))
#s(approx (sqrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* (PI) (+ n n)))) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))))) k)))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal -1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (/ 1 (sqrt k))) (*.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.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 (sqrt (* (PI) (+ n n))) (- 1 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt k)) (/.f64 (sqrt.f64 (exp.f64 (*.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 (pow (* (+ n n) (PI)) (- 1 k))) (sqrt.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (pow (* (+ n n) (PI)) (- 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (+ n n) (*.f64 #s(literal 2 binary64) n))
#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 (* (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt k)) (/.f64 (sqrt.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 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt.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 #s(literal 1 binary64) k)))))
#s(approx (pow (* (+ n n) (PI)) (- 1 k)) (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 #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 (sqrt (* (/ (+ n n) k) (PI))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (/ (sqrt (* 2 (* k (* n (PI))))) k) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n)))) k))
#s(approx (sqrt (* 2 (* k (* n (PI))))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n)))))
#s(approx (sqrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* (PI) (+ n n)))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (pow.f64 (sqrt.f64 k) #s(literal 2 binary64))))))))
#s(approx (* (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 (sqrt (* (PI) (+ n n))) (- 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (PI) (+ n n))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt k)) (/.f64 (sqrt.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 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (pow (* (+ n n) (PI)) (- 1 k))) (sqrt.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 #s(literal 1 binary64) k)))))
#s(approx (pow (* (+ n n) (PI)) (- 1 k)) (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 #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 (sqrt (* (/ (+ n n) k) (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 (* k (* n (PI))))) k) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n)))) k)))
#s(approx (sqrt (* 2 (* k (* n (PI))))) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))))
#s(approx (sqrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* (PI) (+ n n)))) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (pow.f64 (sqrt.f64 k) #s(literal 2 binary64)))))))))
#s(approx (* (pow (sqrt (* (PI) (+ n n))) (- 1 k)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 (sqrt (* (PI) (+ n n))) (- 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (PI) (+ n n))) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
Calls

6 calls:

TimeVariablePoint
79.0ms
k
inf
42.0ms
n
0
36.0ms
n
-inf
24.0ms
n
inf
6.0ms
k
-inf

rewrite159.0ms (2.8%)

Memory
-3.4MiB live, 320.8MiB allocated; 46ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
045296
070264
1182251
2622247
33528247
04734247
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
32 → 1 688
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))
(*.f64 (+.f64 n n) (PI.f64))
(+.f64 n n)
n
(PI.f64)
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64)))
(*.f64 (/.f64 (+.f64 n n) k) (PI.f64))
(/.f64 (+.f64 n n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64)))))
(*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))
#s(literal 2 binary64)
(*.f64 k (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (PI.f64) (+.f64 n n))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
Outputs
(*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)))))
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(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1 binary64))
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(fma.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 0 binary64)))
(fma.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 0 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal 0 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(+.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(+.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 0 binary64)))
(+.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal 0 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(fabs.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(fabs.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(fabs.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))

eval251.0ms (4.4%)

Memory
14.3MiB live, 560.8MiB allocated; 171ms collecting garbage
Compiler

Compiled 51 125 to 6 965 computations (86.4% saved)

prune74.0ms (1.3%)

Memory
18.7MiB live, 205.8MiB allocated; 29ms collecting garbage
Pruning

40 alts after pruning (35 fresh and 5 done)

PrunedKeptTotal
New1 614201 634
Fresh51520
Picked325
Done033
Total1 622401 662
Accuracy
100.0%
Counts
1 662 → 40
Alt Table
Click to see full alt table
StatusAccuracyProgram
79.0%
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))
87.7%
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 #s(literal 1 binary64) k)) k)) k)
96.2%
(/.f64 (exp.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (sqrt.f64 k))
✓99.0%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
52.7%
(*.f64 (/.f64 (sqrt.f64 k) k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
87.6%
(*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 #s(literal 1 binary64) k)) k)))
✓93.2%
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k))
39.1%
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 #s(approx (pow (* (+ n n) (PI)) (- 1 k)) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
89.7%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k))
79.0%
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
33.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 k)) (sqrt.f64 k)))
33.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 k)))
45.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
33.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
42.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (exp.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
✓42.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
45.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
33.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
33.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
44.9%
#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 n n) (PI.f64)))))
33.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (+.f64 n n)) (sqrt.f64 k))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
22.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 k k))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 k)) (*.f64 (PI.f64) (+.f64 n n)))))
✓35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (neg.f64 (sqrt.f64 k))) (/.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)) (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) n))))
✓35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (PI.f64) (+.f64 n n)))))
35.5%
#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))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
15.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
44.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (/ (+ n n) k) (PI))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
33.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) k)))
25.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k)))
48.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
44.9%
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
Compiler

Compiled 1 135 to 822 computations (27.6% saved)

regimes429.0ms (7.5%)

Memory
-7.9MiB live, 809.5MiB allocated; 248ms collecting garbage
Accuracy

Total -0.1b remaining (-0.1%)

Threshold costs -0.1b (-0.1%)

Counts
5 → 1
9 → 1
19 → 2
38 → 2
42 → 2
63 → 1
76 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.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 n n) (/.f64 (PI.f64) k))))
Call 2
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.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 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
Call 3
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.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 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (/ (+ n n) k) (PI))) (*.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))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 #s(approx (pow (* (+ n n) (PI)) (- 1 k)) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
Call 4
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.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 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (/ (+ n n) k) (PI))) (*.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))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 #s(approx (pow (* (+ n n) (PI)) (- 1 k)) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (+.f64 n n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)) (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (neg.f64 (sqrt.f64 k))) (/.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 k)) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (exp.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
Call 5
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.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 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (/ (+ n n) k) (PI))) (*.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))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 #s(approx (pow (* (+ n n) (PI)) (- 1 k)) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (+.f64 n n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)) (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (neg.f64 (sqrt.f64 k))) (/.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 k)) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (exp.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ (+ (* 1 (sqrt k)) (* (sqrt k) 0)) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k))
Call 6
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.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 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (/ (+ n n) k) (PI))) (*.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))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 #s(approx (pow (* (+ n n) (PI)) (- 1 k)) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (+.f64 n n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)) (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (neg.f64 (sqrt.f64 k))) (/.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 k)) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (exp.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ (+ (* 1 (sqrt k)) (* (sqrt k) 0)) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (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 (sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 #s(literal 1 binary64) k)) k)) k)
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) k)
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (exp.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (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 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
(/.f64 (pow.f64 (E.f64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (E.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
(*.f64 (/.f64 #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))))
Outputs
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
Call 7
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.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 (*.f64 (+.f64 n n) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (/ (+ n n) k) (PI))) (*.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))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))
#s(approx (* (sqrt k) (/ (sqrt (pow (* (+ n n) (PI)) (- 1 k))) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 #s(approx (pow (* (+ n n) (PI)) (- 1 k)) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* n (PI))) 1/2) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 #s(approx (sqrt (* 2 (* k (* n (PI))))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 k (PI.f64)) n))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (+.f64 n n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)) (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (neg.f64 (sqrt.f64 k))) (/.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 k)) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (PI.f64) (+.f64 n n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (log.f64 (exp.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ n n) (/ (PI) k))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (exp.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ (+ (* 1 (sqrt k)) (* (sqrt k) 0)) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (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 (sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 #s(literal 1 binary64) k)) k)) k)
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) k)
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (exp.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (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 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (+.f64 n n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (+.f64 n n)) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
(/.f64 (pow.f64 (E.f64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (E.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
(*.f64 (/.f64 #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 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (exp.f64 (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(approx (- 1 k) (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))))))))
(*.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 0 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 (fma.f64 #s(literal -1 binary64) (sqrt.f64 k) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 0 binary64))) (*.f64 (neg.f64 (sqrt.f64 k)) (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)) (pow.f64 (*.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (-.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 n n) (PI.f64))) (log.f64 (*.f64 (+.f64 n n) (PI.f64)))) k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64)))))) k (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 k) k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#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))))
(*.f64 (*.f64 (*.f64 k (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (*.f64 k k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 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)))))
Outputs
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))) (exp.f64 (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 n n) (PI.f64))))))) (sqrt.f64 k))
Calls

28 calls:

91.0ms
k
27.0ms
k
24.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms
(*.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))))
22.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
35.5%1k
35.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
35.5%1n
35.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
45.0%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
45.0%1k
45.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
45.0%1n
58.5%2k
58.5%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
58.6%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
58.6%2n
70.8%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
70.8%2n
70.4%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))))
62.4%4k
95.8%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.2%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))))
99.4%2k
95.8%2n
99.1%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.1%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.1%1k
99.1%1n
99.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.3%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.3%1k
99.3%1n
Compiler

Compiled 2 373 to 537 computations (77.4% saved)

bsearch18.0ms (0.3%)

Memory
37.7MiB live, 37.7MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
16.0ms
8.972881271757691e-19
3.268383758051101e-10
Samples
10.0ms144×0valid
Compiler

Compiled 451 to 369 computations (18.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-pow: 3.0ms (45.1% of total)
ival-sqrt: 1.0ms (15% of total)
ival-div!: 1.0ms (15% of total)
ival-mult!: 1.0ms (15% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch28.0ms (0.5%)

Memory
-54.8MiB live, 10.0MiB allocated; 25ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
27.0ms
7.001993089453205
24.314415794905386
Samples
2.0ms32×0valid
Compiler

Compiled 185 to 138 computations (25.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
ival-pow: 1.0ms (70% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
ival-div!: 0.0ms (0% of total)
ival-mult!: 0.0ms (0% of total)

bsearch4.0ms (0.1%)

Memory
10.8MiB live, 10.8MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
3.0ms
8.334793548571993e+27
5.8159764962530186e+28
Samples
2.0ms32×0valid
Compiler

Compiled 141 to 112 computations (20.6% saved)

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

derivations118.0ms (2%)

Memory
16.1MiB live, 208.8MiB allocated; 11ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 289 to 84 computations (70.9% saved)

preprocess72.0ms (1.3%)

Memory
7.2MiB live, 191.4MiB allocated; 27ms collecting garbage
Remove

(abs k)

Compiler

Compiled 883 to 449 computations (49.2% saved)

end0.0ms (0%)

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

Profiling

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