Migdal et al, Equation (51)

Time bar (total: 6.9s)

start0.0ms (0.0%)

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

analyze139.0ms (2.0%)

Memory
25.5MiB live, 223.0MiB allocated; 66ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0.0%0.0%99.9%0.1%0.0%0.0%0.0%0
0.0%0.0%99.9%0.1%0.0%0.0%0.0%1
0.0%0.0%50.0%0.1%0.0%50.0%0.0%2
50.0%25.0%25.0%0.1%0.0%50.0%0.0%3
50.0%25.0%25.0%0.1%0.0%50.0%0.0%4
50.0%25.0%25.0%0.1%0.0%50.0%0.0%5
50.0%25.0%25.0%0.1%0.0%50.0%0.0%6
51.6%25.0%23.4%0.1%0.0%51.5%0.0%7
52.5%25.0%22.6%0.1%0.0%52.3%0.0%8
53.8%25.0%21.5%0.1%0.0%53.5%0.0%9
54.5%25.0%20.9%0.1%0.0%54.0%0.0%10
55.3%25.0%20.2%0.1%0.0%54.7%0.0%11
55.7%25.0%19.9%0.1%0.0%55.1%0.0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.6s (52.0%)

Memory
-54.2MiB live, 5 242.9MiB allocated; 2.2s collecting garbage
Samples
1.5s8 256×0valid
1.2s5 659×1invalid
127.0ms461×2invalid
25.0ms392×0invalid
19.0ms212×0exit
Precisions
Click to see histograms. Total time spent on operations: 1.5s
ival-pow: 529.0ms (35.2% of total)
adjust: 307.0ms (20.5% of total)
ival-mult!: 238.0ms (15.9% of total)
ival-div!: 195.0ms (13.0% of total)
ival-sqrt: 155.0ms (10.3% of total)
ival-sub!: 78.0ms (5.2% of total)
ival-pi: 0.0ms (0.0% of total)
exact: 0.0ms (0.0% of total)
Bogosity

preprocess124.0ms (1.8%)

Memory
-101.5MiB live, 58.0MiB allocated; 136ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

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

(abs k)

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample0.0ms (0.0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Calls
Call 1
Inputs
1
(* 2 (PI))
2
(PI)
Outputs
#s(literal 1 binary64)
#s(literal 884279719003555/140737488355328 binary64)
#s(literal 2 binary64)
#s(literal 884279719003555/281474976710656 binary64)
Samples
0.0ms0valid
Compiler

Compiled 8 to 6 computations (25.0% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
adjust: 0.0ms (0.0% of total)

series85.0ms (1.2%)

Memory
4.4MiB live, 145.0MiB allocated; 20ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

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

6 calls:

TimeVariablePoint
30.0ms
n
0
23.0ms
n
-inf
8.0ms
n
inf
2.0ms
k
0
2.0ms
k
-inf

rewrite107.0ms (1.6%)

Memory
49.3MiB live, 183.9MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01354
02254
19751
235151
3169051
0415948
Stop Event
iter-limit
node-limit
iter-limit
Counts
13 → 308
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
(*.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(neg.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 k (/.f64 #s(literal -1/2 binary64) #s(literal 2 binary64))) (pow.f64 k (/.f64 #s(literal -1/2 binary64) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal -1 binary64))
(*.f64 (pow.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 k) #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 k #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
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#s(literal 2 binary64)
(PI.f64)
n
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eval45.0ms (0.7%)

Memory
-13.5MiB live, 85.9MiB allocated; 19ms collecting garbage
Compiler

Compiled 7 466 to 1 284 computations (82.8% saved)

prune44.0ms (0.6%)

Memory
-14.4MiB live, 31.7MiB allocated; 6ms collecting garbage
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New31918337
Fresh000
Picked101
Done000
Total32018338
Accuracy
100.0%
Counts
338 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
99.6%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
52.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
76.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
76.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
96.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.3%
(*.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.1%
(*.f64 (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))))
52.8%
#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))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
95.8%
#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 794 to 600 computations (24.4% saved)

sample0.0ms (0.0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Calls
Call 1
Inputs
1
(+ (PI) (PI))
(PI)
-1/2
1/2
2
(* 2 (PI))
Outputs
#s(literal 1 binary64)
#s(literal 884279719003555/140737488355328 binary64)
#s(literal 884279719003555/281474976710656 binary64)
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
#s(literal 884279719003555/140737488355328 binary64)
Samples
0.0ms0valid
Compiler

Compiled 13 to 9 computations (30.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
adjust: 0.0ms (0.0% of total)

series186.0ms (2.7%)

Memory
39.9MiB live, 270.3MiB allocated; 37ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05724684
Stop Event
iter-limit
Counts
40 → 123
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))))
#s(approx (* (pow (* n (+ (PI) (PI))) (* k -1/2)) (pow (* n (+ (PI) (PI))) 1/2)) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) #s(literal 1 binary64))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* k -1/2)) (+.f64 #s(literal 1 binary64) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))))))
#s(approx (* k -1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (fma.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
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#s(approx (/ 1 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)))) (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) (sqrt.f64 k)))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2))) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2)))) (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -1 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (sqrt.f64 k)))
#s(approx (* (pow (* n (PI)) (+ (* k -1/2) 1/2)) (pow 2 (+ (* k -1/2) 1/2))) (*.f64 (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -1 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (pow (* n (PI)) (+ (* k -1/2) 1/2)) (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -1 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
Calls

6 calls:

TimeVariablePoint
79.0ms
n
0
38.0ms
n
-inf
26.0ms
n
inf
8.0ms
k
0
6.0ms
k
-inf

rewrite208.0ms (3.0%)

Memory
-11.8MiB live, 320.7MiB allocated; 76ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
049305
083269
1309260
2884260
33641260
04148260
Stop Event
iter-limit
node-limit
iter-limit
Counts
40 → 2 006
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
Outputs
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 k))) (/.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 k)) (/.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
(*.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))) (pow.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (neg.f64 (sqrt.f64 k))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(pow.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) #s(literal -1 binary64))
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 2 binary64))
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(fma.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fma.f64 (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 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.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 0 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fma.f64 (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) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(+.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(+.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(/.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(neg.f64 (*.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))

eval214.0ms (3.1%)

Memory
9.4MiB live, 380.0MiB allocated; 54ms collecting garbage
Compiler

Compiled 45 256 to 5 570 computations (87.7% saved)

prune69.0ms (1.0%)

Memory
-27.7MiB live, 82.8MiB allocated; 36ms collecting garbage
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1 561141 575
Fresh11213
Picked505
Done000
Total1 577161 593
Accuracy
100.0%
Counts
1 593 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
99.5%
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
99.7%
(/.f64 (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))))
52.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
79.1%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
99.6%
(*.f64 (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))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
52.6%
#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)))
41.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
Compiler

Compiled 708 to 548 computations (22.6% saved)

sample0.0ms (0.0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Calls
Call 1
Inputs
(+ (PI) (PI))
(PI)
1/2
2
1
884279719003555/140737488355328
-1/2
Outputs
#s(literal 884279719003555/140737488355328 binary64)
#s(literal 884279719003555/281474976710656 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(literal 884279719003555/140737488355328 binary64)
#s(literal -1/2 binary64)
Samples
0.0ms0valid
Compiler

Compiled 11 to 9 computations (18.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
adjust: 0.0ms (0.0% of total)

series121.0ms (1.8%)

Memory
4.8MiB live, 192.2MiB allocated; 21ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04583203
Stop Event
iter-limit
Counts
35 → 102
Calls
Call 1
Inputs
(/.f64 (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))))
(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))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k)))
(/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))
(*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))
#s(literal 2 binary64)
(/.f64 (PI.f64) n)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 #s(literal 884279719003555/140737488355328 binary64) n)
#s(literal 884279719003555/140737488355328 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(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)
Outputs
#s(approx (/ (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 (/ (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 (/ (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 (/ (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 (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k))
#s(approx (/ (* (+ (PI) (PI)) n) k) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
#s(approx (/ (* n (sqrt (* 2 (/ (PI) n)))) (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 (* 884279719003555/140737488355328 n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #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 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #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 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (sqrt.f64 k)))))) (/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))
#s(approx (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))))
#s(approx (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))))) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))))
#s(approx (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #s(literal 1/2 binary64))))))) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) #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) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* -1/2 k)) (sqrt (/ (* (+ (PI) (PI)) n) k))) (/.f64 (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.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 k (*.f64 n (PI.f64))))))))) k))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* -1/2 k)) (sqrt (/ (* (+ (PI) (PI)) n) k))) (/.f64 (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))))))))) k))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* -1/2 k)) (sqrt (/ (* (+ (PI) (PI)) n) k))) (/.f64 (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64)))))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.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 k (*.f64 n (PI.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 (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 #s(literal 1/8 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))
#s(approx (pow (* (+ (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 (/ (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 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 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 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) 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 (/ (* n (sqrt (* 2 (/ (PI) n)))) (sqrt 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 (* 884279719003555/140737488355328 n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (-.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 (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (-.f64 #s(literal 1 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 (* (pow (* (+ (PI) (PI)) n) (* -1/2 k)) (sqrt (/ (* (+ (PI) (PI)) n) 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 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (* -1/2 k)) (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#s(approx (/ (sqrt (* (+ (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 (/ (* n (sqrt (* 2 (/ (PI) n)))) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2))) (*.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (+.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 (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (+.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 (/ (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 (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 (sqrt (* 2 (/ (PI) n))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) n))
#s(approx (* 2 (/ (PI) n)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))
#s(approx (/ (PI) n) (/.f64 (PI.f64) n))
#s(approx (* (/ 1 (sqrt k)) (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (log.f64 n)) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (log.f64 n)) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* 884279719003555/140737488355328 n) (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* -1/2 k)) (sqrt (/ (* (+ (PI) (PI)) n) 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 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.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 (/ (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 (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (sqrt (* 2 (/ (PI) n))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* 884279719003555/140737488355328 n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 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 (* 884279719003555/140737488355328 n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (*.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) (* -1/2 k)) (sqrt (/ (* (+ (PI) (PI)) n) k))) (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#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 (/ (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 (sqrt (* (+ (PI) (PI)) n)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* -1/2 k)) (sqrt (/ (* (+ (PI) (PI)) n) k))) (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n))))))))
#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))))))))
Calls

6 calls:

TimeVariablePoint
31.0ms
n
0
30.0ms
n
-inf
19.0ms
n
inf
6.0ms
k
0
5.0ms
k
-inf

rewrite119.0ms (1.7%)

Memory
5.8MiB live, 237.5MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048269
075268
1271254
2883246
04400239
Stop Event
iter-limit
node-limit
iter-limit
Counts
35 → 959
Calls
Call 1
Inputs
(/.f64 (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))))
(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))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k)))
(/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))
(*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))
#s(literal 2 binary64)
(/.f64 (PI.f64) n)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 #s(literal 884279719003555/140737488355328 binary64) n)
#s(literal 884279719003555/140737488355328 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(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)
Outputs
(*.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 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 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (neg.f64 (sqrt.f64 k))))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 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 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 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)))
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(/.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 2 binary64))
(/.f64 (*.f64 k #s(literal -1 binary64)) #s(literal 2 binary64))
(/.f64 (/.f64 (neg.f64 k) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 k) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (neg.f64 k)))
(/.f64 k #s(literal -2 binary64))
(neg.f64 (*.f64 #s(literal 1/2 binary64) k))
#s(literal -1/2 binary64)

eval202.0ms (2.9%)

Memory
27.0MiB live, 404.7MiB allocated; 71ms collecting garbage
Compiler

Compiled 49 960 to 5 927 computations (88.1% saved)

prune61.0ms (0.9%)

Memory
-0.3MiB live, 144.3MiB allocated; 9ms collecting garbage
Pruning

39 alts after pruning (39 fresh and 0 done)

PrunedKeptTotal
New1 533371 570
Fresh9211
Picked505
Done000
Total1 547391 586
Accuracy
100.0%
Counts
1 586 → 39
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
52.6%
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
99.7%
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal 1/2 binary64) k))))
99.5%
(*.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
79.1%
(*.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
41.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
52.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
41.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
41.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
41.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
25.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 n (PI.f64)) k (*.f64 (*.f64 n (PI.f64)) k)) (*.f64 k k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
3.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))))
25.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
38.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n) (sqrt.f64 k))))
52.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 k))))
52.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))))
52.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))) (sqrt.f64 k))))
52.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 k))))
52.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
52.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
52.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))
53.1%
#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 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
45.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 n (sqrt.f64 k)))))
52.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (neg.f64 n) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))))
42.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
Compiler

Compiled 2 412 to 1 760 computations (27.0% saved)

sample0.0ms (0.0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Calls
Call 1
Inputs
884279719003555/140737488355328
1/2
(+ (PI) (PI))
(PI)
1
Outputs
#s(literal 884279719003555/140737488355328 binary64)
#s(literal 1/2 binary64)
#s(literal 884279719003555/140737488355328 binary64)
#s(literal 884279719003555/281474976710656 binary64)
#s(literal 1 binary64)
Samples
0.0ms0valid
Compiler

Compiled 9 to 7 computations (22.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
adjust: 0.0ms (0.0% of total)

series104.0ms (1.5%)

Memory
-12.3MiB live, 126.5MiB allocated; 10ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04122726
Stop Event
iter-limit
Counts
35 → 85
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal 1/2 binary64) k))))
(sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))
(*.f64 #s(literal 884279719003555/140737488355328 binary64) n)
#s(literal 884279719003555/140737488355328 binary64)
n
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal 1/2 binary64) k)))
(sqrt.f64 k)
k
(pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) 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 #s(literal 884279719003555/140737488355328 binary64) n) k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k))
(/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 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 n (+.f64 (PI.f64) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))) (sqrt.f64 k)))
(/.f64 (*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))) (sqrt.f64 k))
(*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n)))))
(sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))
(*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n)))
(+.f64 n n)
(/.f64 (PI.f64) (*.f64 n n))
(*.f64 n n)
Outputs
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k))))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 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 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k))))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 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 884279719003555/140737488355328 binary64) n)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k))))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)) (*.f64 #s(literal 1/48 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k))))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k))))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (+.f64 (sqrt.f64 k) (*.f64 #s(literal 1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k))))))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 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 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 k))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)))))))
#s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (+.f64 (sqrt.f64 k) (*.f64 k (fma.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (sqrt.f64 k)) (*.f64 k (fma.f64 #s(literal 1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 3 binary64)) (sqrt.f64 k))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(literal 2 binary64)) (sqrt.f64 k)))))))))
#s(approx k k)
#s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) #s(literal 1 binary64))
#s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))))))
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#s(approx (/ (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 (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 (/ (sqrt k) (sqrt (* n (+ (PI) (PI))))) (/.f64 (sqrt.f64 k) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (sqrt (* (+ n n) (/ (PI) (* n n)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))
#s(approx (/ (sqrt (* 884279719003555/140737488355328 n)) (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) n))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 k)))))
#s(approx (sqrt (* 884279719003555/140737488355328 n)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 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 (/ (* 884279719003555/140737488355328 n) k)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
#s(approx (/ (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 (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 (/ 1 (/ (sqrt k) (sqrt (* n (+ (PI) (PI)))))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (/ (sqrt k) (sqrt (* n (+ (PI) (PI))))) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))))
Calls

6 calls:

TimeVariablePoint
22.0ms
n
-inf
22.0ms
n
inf
19.0ms
n
0
6.0ms
k
-inf
5.0ms
k
0

rewrite131.0ms (1.9%)

Memory
29.9MiB live, 266.1MiB allocated; 23ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
054320
082313
1325299
21066297
04094295
Stop Event
iter-limit
node-limit
iter-limit
Counts
35 → 894
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal 1/2 binary64) k))))
(sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))
(*.f64 #s(literal 884279719003555/140737488355328 binary64) n)
#s(literal 884279719003555/140737488355328 binary64)
n
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal 1/2 binary64) k)))
(sqrt.f64 k)
k
(pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) 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 #s(literal 884279719003555/140737488355328 binary64) n) k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k))
(/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
#s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 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 n (+.f64 (PI.f64) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))) (sqrt.f64 k)))
(/.f64 (*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))) (sqrt.f64 k))
(*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n)))))
(sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))
(*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n)))
(+.f64 n n)
(/.f64 (PI.f64) (*.f64 n n))
(*.f64 n n)
Outputs
(*.f64 (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))) (/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 k)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)))))
(*.f64 (/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))) (neg.f64 (/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 k #s(literal -2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) #s(literal 1 binary64))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (neg.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))) (neg.f64 (neg.f64 (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k))))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))) #s(literal 1 binary64)) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))) (neg.f64 (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))) (*.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))) (neg.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) (neg.f64 (neg.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)))) (neg.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k))) (neg.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k))) (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (neg.f64 (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (*.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(neg.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) (neg.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k))))
(neg.f64 (neg.f64 (/.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))) (sqrt.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
(*.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))))
(*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 #s(literal 884279719003555/140737488355328 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 884279719003555/140737488355328 binary64) #s(literal 1/2 binary64)) (pow.f64 n #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64)) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64)))
(pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))
(fabs.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
(fabs.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
(fabs.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))) (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))
(*.f64 n #s(literal 884279719003555/140737488355328 binary64))
(*.f64 #s(literal 884279719003555/140737488355328 binary64) n)
(pow.f64 (*.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))
(fabs.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
(fabs.f64 (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (neg.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
(fabs.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))
#s(literal 884279719003555/140737488355328 binary64)
n
(*.f64 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k))
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))
(*.f64 (pow.f64 k (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))) (pow.f64 k (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))))
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
(fabs.f64 (neg.f64 (neg.f64 (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 (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64))))
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(*.f64 (neg.f64 (neg.f64 (fabs.f64 n))) (neg.f64 (neg.f64 (fabs.f64 n))))
(*.f64 (neg.f64 (neg.f64 (neg.f64 n))) (neg.f64 (neg.f64 (neg.f64 n))))
(*.f64 (pow.f64 (fabs.f64 n) #s(literal 1 binary64)) (pow.f64 (fabs.f64 n) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fabs.f64 n) #s(literal 1 binary64)) (fabs.f64 n))
(*.f64 (pow.f64 (neg.f64 n) #s(literal 1 binary64)) (pow.f64 (neg.f64 n) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 n) #s(literal 1 binary64)) (neg.f64 n))
(*.f64 (pow.f64 n (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 n (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(*.f64 (neg.f64 (fabs.f64 n)) (neg.f64 (fabs.f64 n)))
(*.f64 (neg.f64 (neg.f64 n)) (neg.f64 (neg.f64 n)))
(*.f64 (pow.f64 n #s(literal 1 binary64)) (pow.f64 n #s(literal 1 binary64)))
(*.f64 (pow.f64 n #s(literal 1 binary64)) n)
(*.f64 (fabs.f64 n) (fabs.f64 n))
(*.f64 (neg.f64 n) (neg.f64 n))
(*.f64 n n)
(pow.f64 (neg.f64 (fabs.f64 n)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 n)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 n) #s(literal 2 binary64))
(pow.f64 (neg.f64 n) #s(literal 2 binary64))
(pow.f64 (*.f64 n n) #s(literal 1 binary64))
(pow.f64 n #s(literal 2 binary64))
(/.f64 (pow.f64 (fabs.f64 n) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fabs.f64 n)))
(/.f64 (pow.f64 (neg.f64 n) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) n))
(/.f64 (pow.f64 n #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) n))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 n n)))
(neg.f64 (*.f64 (neg.f64 n) n))
(sqrt.f64 (*.f64 (*.f64 n n) (*.f64 n n)))
(fabs.f64 (*.f64 (neg.f64 n) n))
(fabs.f64 (*.f64 n n))
(exp.f64 (*.f64 (log.f64 (fabs.f64 n)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 n)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 n) #s(literal 2 binary64)))

eval192.0ms (2.8%)

Memory
13.9MiB live, 295.8MiB allocated; 208ms collecting garbage
Compiler

Compiled 34 969 to 4 635 computations (86.7% saved)

prune56.0ms (0.8%)

Memory
-9.0MiB live, 131.3MiB allocated; 28ms collecting garbage
Pruning

43 alts after pruning (41 fresh and 2 done)

PrunedKeptTotal
New93327960
Fresh201434
Picked325
Done000
Total95643999
Accuracy
100.0%
Counts
999 → 43
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
52.4%
(/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
52.5%
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
52.4%
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
52.6%
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
99.7%
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal 1/2 binary64) k))))
62.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (*.f64 (sqrt.f64 k) #s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))))))))
52.6%
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k)))
99.5%
(*.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
79.1%
(*.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
52.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
52.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))))
41.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
41.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
52.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
41.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
41.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
41.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
3.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
25.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k) (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
38.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) #s(literal 1/2 binary64))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n) (sqrt.f64 k))))
52.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 k))))
52.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n n))))) (sqrt.f64 k))))
46.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 n n))))) (sqrt.f64 k))))
52.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 k))))
52.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))))
45.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 n (sqrt.f64 k)))))
46.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (*.f64 n n)) (+.f64 n n)) k)) n)))
42.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))) k)))
53.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
Compiler

Compiled 1 219 to 914 computations (25.0% saved)

regimes710.0ms (10.3%)

Memory
80.0MiB live, 978.9MiB allocated; 253ms collecting garbage
Counts
1 → 1
2 → 1
3 → 1
5 → 1
9 → 1
23 → 2
48 → 2
66 → 2
75 → 1
97 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
Call 2
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
Call 3
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
Call 4
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
Call 5
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
Outputs
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k)))
Call 6
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
Call 7
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 n (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 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 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k) (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (neg.f64 n) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
Call 8
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 n (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 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 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k) (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (neg.f64 n) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (*.f64 n n)) (+.f64 n n)) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.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 (*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 n (PI.f64)) k (*.f64 (*.f64 n (PI.f64)) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.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))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 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 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (*.f64 n n)) (+.f64 n n)) k)) n)))
Call 9
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 n (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 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 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k) (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (neg.f64 n) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (*.f64 n n)) (+.f64 n n)) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.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 (*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 n (PI.f64)) k (*.f64 (*.f64 n (PI.f64)) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.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))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 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 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
(/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 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) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (*.f64 (sqrt.f64 k) #s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))))))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
(/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
Call 10
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 884279719003555/140737488355328 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 884279719003555/140737488355328 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) #s(approx (* (sqrt k) (pow (* 884279719003555/140737488355328 n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (*.f64 n (sqrt.f64 (/.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* 884279719003555/140737488355328 n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) (*.f64 k n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 n (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 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 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k) (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (neg.f64 n) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (*.f64 n n)) (+.f64 n n)) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (* (sqrt k) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.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 (*.f64 n (sqrt.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 n (PI.f64)) k (*.f64 (*.f64 n (PI.f64)) k)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.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))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 n n))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 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 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n #s(literal 884279719003555/140737488355328 binary64)) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (log.f64 (exp.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
(/.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 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) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* k -1/2) 1/2) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (*.f64 (sqrt.f64 k) #s(approx (pow (* 884279719003555/140737488355328 n) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n))))))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(/.f64 (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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (/.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (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 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
#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))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
Outputs
(/.f64 (sqrt.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 884279719003555/140737488355328 binary64) n) (*.f64 #s(literal 1/2 binary64) k))))
Calls

39 calls:

206.0ms
k
74.0ms
k
34.0ms
k
28.0ms
k
27.0ms
n
Results
AccuracySegmentsBranch
41.2%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))))
41.2%1k
41.2%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
41.2%1n
41.2%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))))
41.2%1k
41.2%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
41.2%1n
41.2%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
41.2%1k
41.2%1n
41.2%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))))
52.6%1k
52.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
52.6%1n
52.6%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))))
52.6%1k
52.6%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))))
52.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
52.6%1n
64.8%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
64.8%2n
64.7%2k
64.8%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
64.8%2n
64.8%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))))
64.8%2k
78.1%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
66.4%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
78.1%2k
66.4%3n
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 2 863 to 671 computations (76.6% saved)

bsearch20.0ms (0.3%)

Memory
-12.1MiB live, 33.6MiB allocated; 3ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
19.0ms
2.3147350563628684
294319465.2148352
Samples
13.0ms144×0valid
Compiler

Compiled 631 to 477 computations (24.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-sqrt: 4.0ms (43.2% of total)
ival-pow: 3.0ms (32.4% of total)
ival-div!: 1.0ms (10.8% of total)
ival-mult!: 1.0ms (10.8% of total)
ival-sub!: 0.0ms (0.0% of total)
adjust: 0.0ms (0.0% of total)

bsearch6.0ms (0.1%)

Memory
11.7MiB live, 11.7MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
predicate-same
Steps
TimeLeftRight
5.0ms
4.84419195593875e-46
6.202175254542491e-46
Samples
3.0ms48×0valid
Compiler

Compiled 193 to 159 computations (17.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-pow: 1.0ms (47.2% of total)
ival-sub!: 0.0ms (0.0% of total)
adjust: 0.0ms (0.0% of total)
ival-sqrt: 0.0ms (0.0% of total)
ival-div!: 0.0ms (0.0% of total)
ival-mult!: 0.0ms (0.0% of total)

bsearch2.0ms (0.0%)

Memory
4.3MiB live, 4.3MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
predicate-same
Steps
TimeLeftRight
2.0ms
1.588831918374789e+29
8.993035529906934e+31
Samples
1.0ms16×0valid
Compiler

Compiled 74 to 62 computations (16.2% saved)

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

derivations164.0ms (2.4%)

Memory
-17.5MiB live, 172.7MiB allocated; 16ms collecting garbage
Stop Event
fuel
Compiler

Compiled 330 to 87 computations (73.6% saved)

preprocess189.0ms (2.8%)

Memory
8.0MiB live, 195.4MiB allocated; 139ms collecting garbage
Compiler

Compiled 1 006 to 526 computations (47.7% saved)

end0.0ms (0.0%)

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

Profiling

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