Migdal et al, Equation (51)

Time bar (total: 4.8s)

start0.0ms (0%)

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

analyze158.0ms (3.3%)

Memory
20.6MiB live, 224.0MiB allocated; 87ms 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)

sample3.3s (68.8%)

Memory
-136.9MiB live, 3 212.5MiB allocated; 1.9s collecting garbage
Samples
1.8s5 617×1invalid
673.0ms8 256×0valid
177.0ms503×2invalid
28.0ms392×0invalid
24.0ms247×0exit
Precisions
Click to see histograms. Total time spent on operations: 2.2s
adjust: 919.0ms (42.2% of total)
ival-pow: 546.0ms (25.1% of total)
ival-div!: 248.0ms (11.4% of total)
ival-mult!: 234.0ms (10.8% of total)
ival-sqrt: 158.0ms (7.3% of total)
ival-sub!: 72.0ms (3.3% of total)
ival-pi: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

preprocess50.0ms (1%)

Memory
-20.5MiB live, 24.9MiB allocated; 5ms 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
▶99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Symmetry

(abs k)

Compiler

Compiled 32 to 26 computations (18.8% saved)

series81.0ms (1.7%)

Memory
6.3MiB live, 102.6MiB allocated; 13ms 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
35.0ms
n
0
21.0ms
n
-inf
8.0ms
n
inf
2.0ms
k
0
2.0ms
k
-inf

rewrite47.0ms (1%)

Memory
4.2MiB live, 50.1MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01354
02254
19751
068351
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
13 → 142
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (pow.f64 n (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 k) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(sqrt.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)))
(sqrt.f64 k)
(fabs.f64 (neg.f64 (sqrt.f64 k)))
(fabs.f64 (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
k
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (fabs.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(*.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 n (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(fabs.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sinh.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 n (PI.f64)))
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 n (PI.f64)))
(fma.f64 n (PI.f64) (*.f64 n (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 n (PI.f64)))
(+.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (PI.f64)) (+.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (fma.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (PI.f64) (*.f64 #s(literal 1 binary64) (PI.f64)))
(-.f64 (PI.f64) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))
(-.f64 (PI.f64) (*.f64 (neg.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 #s(literal 1 binary64) (PI.f64)))
(+.f64 (PI.f64) (PI.f64))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)))
(log.f64 (*.f64 (exp.f64 (PI.f64)) (exp.f64 (PI.f64))))
#s(literal 2 binary64)
(PI.f64)
n
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) #s(literal 1/2 binary64)) (+.f64 k #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) #s(literal 1/2 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 k #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 k #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) k)) #s(literal 4 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) #s(literal 1 binary64)) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) #s(literal 1 binary64)) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64))))
(neg.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))
(neg.f64 (/.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)))
(neg.f64 (-.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 k #s(literal 1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (neg.f64 k) #s(literal 2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (/.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 k) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 k k) (*.f64 #s(literal 1 binary64) (neg.f64 k)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k))) (neg.f64 (+.f64 k #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k))) (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 k #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 k #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 k k))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k))))
(neg.f64 (-.f64 k #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 k k) k) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 k)))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (neg.f64 k) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 k))

eval18.0ms (0.4%)

Memory
34.5MiB live, 34.5MiB allocated; 0ms collecting garbage
Compiler

Compiled 3 925 to 715 computations (81.8% saved)

prune15.0ms (0.3%)

Memory
-22.8MiB live, 22.8MiB allocated; 3ms collecting garbage
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New15217169
Fresh000
Picked101
Done000
Total15317170
Accuracy
100.0%
Counts
170 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
▶99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
99.4%
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
99.5%
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
99.5%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
▶99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
45.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
▶99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
76.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
96.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
▶96.5%
(*.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.5%
(*.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
50.0%
#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))))
▶45.1%
#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)))
96.5%
#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 798 to 578 computations (27.6% saved)

series167.0ms (3.5%)

Memory
10.5MiB live, 242.3MiB allocated; 36ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04733907
Stop Event
1×iter-limit
Counts
40 → 101
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
#s(literal 1/2 binary64)
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n)
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))
(sqrt.f64 (PI.f64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(*.f64 (log.f64 k) #s(literal 1/2 binary64))
(log.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
Outputs
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (fma.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (fma.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k))))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/48 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k))))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) (fma.f64 #s(literal -1/16 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/48 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k 1/2)) #s(literal 1 binary64))
#s(approx (pow (* n (+ (PI) (PI))) (* k 1/2)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k 1/2)) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal 1/8 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k 1/2)) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal 1/48 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))))))
#s(approx (* k 1/2) (*.f64 #s(literal 1/2 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (fma.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (fma.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (fma.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (- 1 k)) #s(literal 1/2 binary64))
#s(approx (* 1/2 (- 1 k)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (- 1 k) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
Calls

6 calls:

TimeVariablePoint
45.0ms
n
0
29.0ms
n
-inf
22.0ms
n
inf
19.0ms
k
inf
17.0ms
k
0

rewrite39.0ms (0.8%)

Memory
4.5MiB live, 49.1MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049297
083248
0290248
Stop Event
1×iter-limit
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
40 → 201
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
#s(literal 1/2 binary64)
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n)
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))
(sqrt.f64 (PI.f64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(*.f64 (log.f64 k) #s(literal 1/2 binary64))
(log.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
Outputs
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(exp.f64 (neg.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(pow.f64 (exp.f64 (log.f64 k)) #s(literal 1/2 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
(fabs.f64 (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
k
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
n
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
#s(literal 1/2 binary64)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 n (*.f64 #s(literal 1/2 binary64) k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 n (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (pow.f64 n (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 k #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(neg.f64 (-.f64 k #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) k)
(+.f64 #s(literal 1 binary64) (neg.f64 k))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 n (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (pow.f64 n (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (PI.f64) (PI.f64))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))
(+.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1/2 binary64))
(sqrt.f64 (PI.f64))
(fabs.f64 (sqrt.f64 (PI.f64)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(exp.f64 (neg.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (log.f64 k)) #s(literal 1/2 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
(fabs.f64 (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(*.f64 (log.f64 k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (log.f64 k))
(log.f64 k)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 n (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (pow.f64 n (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (PI.f64) (PI.f64))

eval31.0ms (0.7%)

Memory
13.2MiB live, 58.3MiB allocated; 6ms collecting garbage
Compiler

Compiled 8 229 to 1 109 computations (86.5% saved)

prune22.0ms (0.5%)

Memory
4.2MiB live, 50.7MiB allocated; 4ms collecting garbage
Pruning

22 alts after pruning (20 fresh and 2 done)

PrunedKeptTotal
New24415259
Fresh7512
Picked325
Done000
Total25422276
Accuracy
100.0%
Counts
276 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
▶99.7%
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
✓99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
96.8%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
99.5%
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
▶99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
99.5%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
99.5%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
✓99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
76.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
▶99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
96.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
▶45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
96.5%
#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)))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
▶45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
99.6%
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
Compiler

Compiled 1 044 to 776 computations (25.7% saved)

series114.0ms (2.4%)

Memory
-47.1MiB live, 121.1MiB allocated; 121ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04764054
Stop Event
1×iter-limit
Counts
36 → 107
Calls
Call 1
Inputs
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(literal 1 binary64)
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
(sqrt.f64 k)
k
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
(*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
Outputs
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (fma.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (fma.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k))))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/48 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k))))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k))
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (+.f64 (sqrt.f64 k) (*.f64 #s(literal 1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))))
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (+.f64 (sqrt.f64 k) (*.f64 k (fma.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))))))
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (+.f64 (sqrt.f64 k) (*.f64 k (fma.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal 1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 k))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)))))))))
#s(approx k k)
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(literal 1 binary64))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal 1/8 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal 1/48 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))))))
#s(approx (* 1/2 k) (*.f64 #s(literal 1/2 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))
#s(approx (/ 1 k) (/.f64 #s(literal 1 binary64) k))
#s(approx (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)))) (fma.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)))) (fma.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (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 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))) (fma.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/4 binary64) (/.f64 (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 #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))))))) (*.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 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))) (fma.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.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))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (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 #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))))))))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (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))))))) (*.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 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (* (- 1 k) 1/2) #s(literal 1/2 binary64))
#s(approx (* (- 1 k) 1/2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (- 1 k) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
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#s(approx (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (sqrt k) (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)))) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (/ 1 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2))) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) (/ 1 (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
#s(approx (/ 1 (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))))
Calls

6 calls:

TimeVariablePoint
41.0ms
k
inf
17.0ms
n
inf
12.0ms
n
-inf
11.0ms
n
0
5.0ms
k
-inf

rewrite42.0ms (0.9%)

Memory
4.3MiB live, 49.6MiB allocated; 8ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049337
079313
0303313
Stop Event
1×iter-limit
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
36 → 169
Calls
Call 1
Inputs
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(literal 1 binary64)
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
(sqrt.f64 k)
k
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
(*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
Outputs
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k))))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(fabs.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/2 binary64)))
#s(literal 1 binary64)
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(fabs.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(fma.f64 n (PI.f64) (*.f64 n (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 n (PI.f64)))
(+.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k))
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
(fabs.f64 (sqrt.f64 k))
k
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(fabs.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(fma.f64 n (PI.f64) (*.f64 n (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 n (PI.f64)))
(+.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)
(*.f64 k (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 k #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) k)
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 k) #s(literal 1 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (pow.f64 n (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 k #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(neg.f64 (-.f64 k #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) k)
(+.f64 #s(literal 1 binary64) (neg.f64 k))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k))))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) #s(literal -1 binary64))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))

eval35.0ms (0.7%)

Memory
12.0MiB live, 65.2MiB allocated; 10ms collecting garbage
Compiler

Compiled 9 979 to 1 286 computations (87.1% saved)

prune30.0ms (0.6%)

Memory
-14.0MiB live, 32.9MiB allocated; 5ms collecting garbage
Pruning

21 alts after pruning (19 fresh and 2 done)

PrunedKeptTotal
New27812290
Fresh8715
Picked415
Done112
Total29121312
Accuracy
100.0%
Counts
312 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
99.6%
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
56.3%
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))
▶99.7%
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
79.8%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
✓99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
96.8%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
▶99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
99.5%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
96.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
✓45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
▶34.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
39.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
▶45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
▶45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
45.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
Compiler

Compiled 1 170 to 857 computations (26.8% saved)

series71.0ms (1.5%)

Memory
25.2MiB live, 116.4MiB allocated; 10ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04623557
Stop Event
1×iter-limit
Counts
38 → 108
Calls
Call 1
Inputs
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(literal 1 binary64)
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(*.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
#s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
k
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))
(/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (fma.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
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#s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ 1 (* (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (sqrt k))) (/.f64 #s(literal 1 binary64) (*.f64 k (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (sqrt k)) (*.f64 k (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (neg (* (- 1 k) 1/2)) (*.f64 k (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (- 1 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (* (- 1 k) 1/2) (*.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) k))
#s(approx (- 1 k) (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))))
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 #s(literal -1 binary64) (*.f64 k (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (sqrt k) (*.f64 #s(literal -1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) k) (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal -1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ 1 (* (/ 1 (sqrt k)) k)) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (/ 1 (* (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (sqrt k))) (/.f64 #s(literal -1 binary64) (*.f64 k (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (sqrt k)) (*.f64 #s(literal -1 binary64) (*.f64 k (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
#s(approx (neg (* (- 1 k) 1/2)) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))
#s(approx (* (- 1 k) 1/2) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 k))))
#s(approx (* 1 (sqrt (* (+ (PI) (PI)) n))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (* (+ (PI) (PI)) n) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
#s(approx n n)
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (/ 1 (* (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (sqrt k))) (/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))))
#s(approx (* (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (sqrt k)) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 k))))
#s(approx (* 1 (sqrt (* (+ (PI) (PI)) n))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k)))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) k))
#s(approx (/ 1 (* (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (sqrt k))) (/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))))
#s(approx (* (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (sqrt k)) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (* 1 (sqrt (* (+ (PI) (PI)) n))) (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (sqrt.f64 k)))))
#s(approx (* 1 (sqrt (* (+ (PI) (PI)) n))) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) k)))
#s(approx (/ 1 (* (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (sqrt k))) (/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))))
#s(approx (* (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (sqrt k)) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* n (+ (PI) (PI))) (neg (* (- 1 k) 1/2))) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
Calls

6 calls:

TimeVariablePoint
14.0ms
n
0
14.0ms
n
-inf
12.0ms
n
inf
6.0ms
k
-inf
5.0ms
k
0

rewrite39.0ms (0.8%)

Memory
-18.5MiB live, 32.4MiB allocated; 9ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
052399
083377
0315377
Stop Event
1×iter-limit
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
38 → 167
Calls
Call 1
Inputs
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(literal 1 binary64)
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(*.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
#s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
k
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))
(/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
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#s(literal 1 binary64)
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(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(fma.f64 n (PI.f64) (*.f64 n (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 n (PI.f64)))
(+.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
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(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(*.f64 #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
#s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)
(*.f64 k (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 1 binary64) k) (sqrt.f64 k))
k
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 k #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) k)
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))
(fabs.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1 binary64) k))
(*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))
(/.f64 (neg.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (neg.f64 k))
(/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)
(/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(fma.f64 n (PI.f64) (*.f64 n (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 n (PI.f64)))
(+.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k)
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(fabs.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)
(*.f64 k (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 1 binary64) k) (sqrt.f64 k))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
(fabs.f64 (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k)
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k)
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k))))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k))
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 n (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 k #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(neg.f64 (-.f64 k #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) k)
(+.f64 #s(literal 1 binary64) (neg.f64 k))

eval29.0ms (0.6%)

Memory
24.0MiB live, 68.3MiB allocated; 6ms collecting garbage
Compiler

Compiled 9 103 to 1 202 computations (86.8% saved)

prune24.0ms (0.5%)

Memory
-28.9MiB live, 63.1MiB allocated; 8ms collecting garbage
Pruning

34 alts after pruning (31 fresh and 3 done)

PrunedKeptTotal
New22521246
Fresh41014
Picked415
Done022
Total23334267
Accuracy
100.0%
Counts
267 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
99.4%
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))) (sqrt.f64 k))
56.3%
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))
79.8%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
99.7%
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
✓99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k)))
45.1%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (neg (* (- 1 k) 1/2)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
96.8%
(/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))) (sqrt.f64 k)))
96.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
✓45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
✓34.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
34.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
34.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1 binary64) k))))
34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
34.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 #s(approx (/ (* n (+ (PI) (PI))) k) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k)))
39.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k))))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k)))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k)))))))
45.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) k))))
45.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
35.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
47.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
Compiler

Compiled 1 134 to 804 computations (29.1% saved)

regimes373.0ms (7.8%)

Memory
35.6MiB live, 588.2MiB allocated; 111ms collecting garbage
Accuracy

Total -0.1b remaining (-0%)

Threshold costs -0.1b (-0%)

Counts
3 → 1
5 → 1
31 → 2
48 → 1
51 → 1
66 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 #s(approx (/ (* n (+ (PI) (PI))) k) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
Call 2
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 #s(approx (/ (* n (+ (PI) (PI))) k) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1 binary64) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
Call 3
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 #s(approx (/ (* n (+ (PI) (PI))) k) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (neg (* (- 1 k) 1/2)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
Call 4
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 #s(approx (/ (* n (+ (PI) (PI))) k) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (neg (* (- 1 k) 1/2)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))
#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 #s(literal 1 binary64) (/.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
Outputs
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
Call 5
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 #s(approx (/ (* n (+ (PI) (PI))) k) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (neg (* (- 1 k) 1/2)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))
#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 #s(literal 1 binary64) (/.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
Call 6
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 #s(approx (/ (* n (+ (PI) (PI))) k) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* n (+ (PI) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 k (sqrt.f64 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) #s(approx (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (neg (* (- 1 k) 1/2)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))
#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 #s(literal 1 binary64) (/.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* k 1/2)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(*.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #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))))
Outputs
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
Calls

24 calls:

57.0ms
k
37.0ms
k
33.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
26.0ms
k
20.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
34.3%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))))
34.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
34.3%1n
34.3%1k
45.1%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))))
45.1%1k
45.1%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
45.1%1n
58.4%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
58.4%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
58.4%2k
58.4%2n
99.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%1k
99.5%1n
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%1k
99.6%1n
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1k
99.7%1n
Compiler

Compiled 2 121 to 470 computations (77.8% saved)

bsearch23.0ms (0.5%)

Memory
-21.3MiB live, 31.3MiB allocated; 11ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
22.0ms
4.471835052103547e+30
9.806331772938429e+31
Samples
17.0ms112×0valid
Compiler

Compiled 446 to 347 computations (22.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-pow: 2.0ms (39.6% of total)
ival-sqrt: 1.0ms (19.8% of total)
ival-div!: 1.0ms (19.8% of total)
ival-mult!: 1.0ms (19.8% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

derivations14.0ms (0.3%)

Memory
25.9MiB live, 25.9MiB allocated; 0ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 171 to 56 computations (67.3% saved)

preprocess78.0ms (1.6%)

Memory
19.7MiB live, 149.5MiB allocated; 26ms collecting garbage
Remove

(abs k)

Compiler

Compiled 529 to 299 computations (43.5% saved)

end0.0ms (0%)

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

Profiling

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