Migdal et al, Equation (51)

Time bar (total: 53.5s)

start0.0ms (0.0%)

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

analyze168.0ms (0.3%)

Memory
1.9MiB live, 183.7MiB allocated; 26ms collecting garbage
Algorithm
1×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)

sample3.5s (6.6%)

Memory
194.1MiB live, 9 592.2MiB allocated; 1.2s collecting garbage
Samples
1.6s5 432×1invalid
1.1s8 254×0valid
191.0ms517×2invalid
32.0ms230×0exit
26.0ms344×0invalid
1.0ms2×1valid
Precisions
Click to see histograms. Total time spent on operations: 1.9s
ival-pow: 644.0ms (34.4% of total)
ival-mult!: 349.0ms (18.6% of total)
adjust: 269.0ms (14.4% of total)
ival-sqrt: 250.0ms (13.4% of total)
ival-div!: 246.0ms (13.1% of total)
ival-sub!: 114.0ms (6.1% of total)
ival-pi: 0.0ms (0.0% of total)
exact: 0.0ms (0.0% of total)
Bogosity

preprocess41.0ms (0.1%)

Memory
-15.8MiB live, 28.1MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033101
112887
246287
3217586
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.3%
(*.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))))
Symmetry

(abs k)

Compiler

Compiled 32 to 26 computations (18.8% saved)

series94.0ms (0.2%)

Memory
20.5MiB live, 124.8MiB allocated; 36ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0158949
Stop Event
1×iter-limit
Counts
13 → 37
Calls
Call 1
Inputs
#s(literal 1 binary64)
k
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 2 binary64)
(PI.f64)
(*.f64 #s(literal 2 binary64) (PI.f64))
n
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(-.f64 #s(literal 1 binary64) k)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 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 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 (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)) (+.f64 (*.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)) (+.f64 (*.f64 k (+.f64 (*.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)) (+.f64 (*.f64 k (+.f64 (*.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 (+.f64 (*.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 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (+.f64 (*.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))) (+.f64 (*.f64 k (+.f64 (*.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))) (+.f64 (*.f64 k (+.f64 (*.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 (+.f64 (*.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) (*.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 (- 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 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 (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 (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 k) (*.f64 #s(literal -1 binary64) (*.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 (- 1 k) (*.f64 #s(literal -1 binary64) (*.f64 k (-.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 (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 (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 n n)
#s(approx (* (* 2 (PI)) n) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 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 (*.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)))))
#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)))
Calls

6 calls:

TimeVariablePoint
34.0ms
n
-inf
31.0ms
n
0
8.0ms
n
inf
3.0ms
k
0
2.0ms
k
-inf

rewrite123.0ms (0.2%)

Memory
28.1MiB live, 159.8MiB allocated; 15ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01354
02254
19751
235151
3169051
0415951
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
13 → 491
Calls
Call 1
Inputs
#s(literal 1 binary64)
k
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 2 binary64)
(PI.f64)
(*.f64 #s(literal 2 binary64) (PI.f64))
n
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(-.f64 #s(literal 1 binary64) k)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
#s(literal 1 binary64)
k
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 k))) (sqrt.f64 (neg.f64 (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 (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))))
(*.f64 (sqrt.f64 k) (pow.f64 k #s(literal 0 binary64)))
(pow.f64 k #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(neg.f64 (neg.f64 (sqrt.f64 k)))
(sqrt.f64 k)
(fabs.f64 (neg.f64 (sqrt.f64 k)))
(fabs.f64 (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 k (/.f64 #s(literal -1/2 binary64) #s(literal 2 binary64))) (pow.f64 k (/.f64 #s(literal -1/2 binary64) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal -1 binary64))
(*.f64 (pow.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 k) #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 k #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 #s(literal -2 binary64) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(fabs.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 0 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 0 binary64) (sqrt.f64 k)))
#s(literal 2 binary64)
(PI.f64)
(*.f64 (*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (PI.f64)) (PI.f64))) (PI.f64))
(*.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
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(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (cbrt.f64 #s(literal 2 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (cbrt.f64 #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (cbrt.f64 #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 8/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)) (cbrt.f64 (*.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 8/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 8/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 8/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))))
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(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 #s(literal 1/2 binary64)) (cbrt.f64 (+.f64 (PI.f64) (PI.f64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
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(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (cbrt.f64 (*.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
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(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/9 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 7/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/9 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 7/9 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/9 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 7/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/9 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 7/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (cbrt.f64 (*.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (cbrt.f64 (*.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) #s(literal 1 binary64) (cbrt.f64 (*.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) #s(literal 1 binary64) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) #s(literal 1 binary64) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64) (cbrt.f64 (PI.f64)) (cbrt.f64 (*.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64) (cbrt.f64 (PI.f64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64) (cbrt.f64 (PI.f64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64) (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))))
(134-z0z1z2z3z4 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64) (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
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(134-z0z1z2z3z4 (*.f64 (cbrt.f64 (PI.f64)) n) (pow.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))) #s(literal 3 binary64)) (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (*.f64 (cbrt.f64 (PI.f64)) n) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 17/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)) (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))
(134-z0z1z2z3z4 (*.f64 (cbrt.f64 (PI.f64)) n) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 17/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/27 binary64)) (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (PI.f64))))
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(134-z0z1z2z3z4 (*.f64 (cbrt.f64 (PI.f64)) n) (pow.f64 (PI.f64) #s(literal 4/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))
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(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) (+.f64 n n)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (+.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 (cbrt.f64 (PI.f64)) n)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (+.f64 n n)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.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 (pow.f64 (+.f64 n n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (PI.f64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (PI.f64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (+.f64 n n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (neg.f64 k))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (pow.f64 n (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(/.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64))
(/.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 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (+.f64 k k) #s(literal 4 binary64))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))))
(neg.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(+.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 0 binary64)))
(+.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (/.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))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (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))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(neg.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))

eval4.9s (9.2%)

Memory
251.0MiB live, 6 718.0MiB allocated; 1.3s collecting garbage
Samples
3.9s60 672×0valid
Compiler

Compiled 13 885 to 2 027 computations (85.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.4s
ival-mult!: 1.1s (77.5% of total)
ival-sub!: 197.0ms (14.4% of total)
adjust: 111.0ms (8.1% of total)

prune54.0ms (0.1%)

Memory
-16.9MiB live, 46.6MiB allocated; 53ms collecting garbage
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New49720517
Fresh000
Picked101
Done000
Total49820518
Accuracy
100.0%
Counts
518 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.3%
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
▶99.3%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
99.3%
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
▶99.4%
(*.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))))
99.2%
(*.f64 (/.f64 #s(literal 1 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))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.2%
(*.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))))
51.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal -1/2 binary64))))
▶99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
76.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
76.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (+.f64 n n) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (PI.f64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
77.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (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))))
▶77.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
96.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
99.3%
(*.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))))
99.2%
(*.f64 (*.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 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.0%
(*.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))))
▶51.5%
#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)))
Compiler

Compiled 820 to 602 computations (26.6% saved)

series249.0ms (0.5%)

Memory
15.5MiB live, 380.3MiB allocated; 66ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06085167
Stop Event
1×iter-limit
Counts
36 → 122
Calls
Call 1
Inputs
#s(literal 1 binary64)
k
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
n
(PI.f64)
(+.f64 (PI.f64) (PI.f64))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
#s(literal 1/2 binary64)
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(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))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
#s(literal 2 binary64)
(*.f64 n (PI.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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(-.f64 #s(literal 1 binary64) k)
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
#s(literal -1/2 binary64)
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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 (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))))
(pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
Outputs
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (* 1/2 k) (*.f64 #s(literal 1/2 binary64) k))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 k)) #s(literal 1 binary64))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 k (+.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)))) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 k)) (+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 k (+.f64 (*.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 (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* 1/2 k))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* 1/2 k))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* 1/2 k))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* 1/2 k))) (+.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))) (+.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/48 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))) (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* 1/2 k)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* 1/2 k)))) (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* 1/2 k)))) (+.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k))))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* 1/2 k)))) (+.f64 (*.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.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 (*.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))))))) (+.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k))))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (+.f64 (*.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))) (+.f64 (*.f64 k (+.f64 (*.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))) (+.f64 (*.f64 k (+.f64 (*.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 (+.f64 (*.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 k) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
#s(approx (* 1/2 (- 1 k)) #s(literal 1/2 binary64))
#s(approx (* 1/2 (- 1 k)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (+.f64 (*.f64 k (+.f64 (*.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 (+.f64 (*.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 (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (+.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (*.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 n n)
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#s(approx (pow (* n (+ (PI) (PI))) 1/2) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (pow (* n (+ (PI) (PI))) (* 1/2 k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
#s(approx (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* 1/2 k))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (+ (PI) (PI))) 1/2) (pow (* n (+ (PI) (PI))) (* 1/2 k)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (*.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 (* 2 (* n (PI))) 1/2) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 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 (* n (+ (PI) (PI))) (* 1/2 (- 1 k))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (sqrt k) (pow (* n (+ (PI) (PI))) (* 1/2 (- 1 k)))) (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (* (pow k -1/2) (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)))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (pow (* n (PI)) (* 1/2 (- 1 k))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -1 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* n (PI)) (* 1/2 (- 1 k))) (pow 2 (* 1/2 (- 1 k)))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -1 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)) (* 1/2 (- 1 k))) (pow 2 (* 1/2 (- 1 k))))) (/.f64 (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -1 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)))
Calls

6 calls:

TimeVariablePoint
81.0ms
n
0
43.0ms
n
-inf
38.0ms
n
inf
23.0ms
k
0
16.0ms
k
inf

rewrite622.0ms (1.2%)

Memory
6.6MiB live, 724.9MiB allocated; 215ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
045277
074249
1282237
2828237
33654237
04161237
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
36 → 2 684
Calls
Call 1
Inputs
#s(literal 1 binary64)
k
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
n
(PI.f64)
(+.f64 (PI.f64) (PI.f64))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
#s(literal 1/2 binary64)
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(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))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
#s(literal 2 binary64)
(*.f64 n (PI.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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(-.f64 #s(literal 1 binary64) k)
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
#s(literal -1/2 binary64)
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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 (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))))
(pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
Outputs
#s(literal 1 binary64)
k
(*.f64 (*.f64 (sqrt.f64 k) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.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))))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 k))
(pow.f64 k #s(literal 1/2 binary64))
(/.f64 (*.f64 (sqrt.f64 k) #s(literal 2 binary64)) #s(literal 2 binary64))
(neg.f64 (*.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 k)))
(sqrt.f64 k)
(fabs.f64 (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(fabs.f64 (neg.f64 (sqrt.f64 k)))
(fabs.f64 (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(+.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 0 binary64)))
(+.f64 (sqrt.f64 k) (*.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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 (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 #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) (sqrt.f64 k)))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 #s(literal -2 binary64) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(fabs.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 0 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 0 binary64) (sqrt.f64 k)))
n
(PI.f64)
(*.f64 (*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (PI.f64)) (PI.f64))) (PI.f64))
(*.f64 (cbrt.f64 (fabs.f64 (PI.f64))) (*.f64 (cbrt.f64 (fabs.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (*.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (log.f64 (exp.f64 (PI.f64))))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (PI.f64) (PI.f64)))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (*.f64 (neg.f64 (PI.f64)) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (neg.f64 (PI.f64))))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (neg.f64 (PI.f64))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (+.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (+.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(134-z0z1z2z3z4 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (cbrt.f64 (fabs.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (cbrt.f64 (fabs.f64 (PI.f64))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))))
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(134-z0z1z2z3z4 #s(literal 1/2 binary64) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) n) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)) (*.f64 (neg.f64 (PI.f64)) n) #s(literal 1 binary64))
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(134-z0z1z2z3z4 #s(literal 1/2 binary64) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) n) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) n))
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(134-z0z1z2z3z4 #s(literal 1/2 binary64) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) n) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)) (PI.f64) (neg.f64 n))
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(134-z0z1z2z3z4 #s(literal 1 binary64) (*.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) n))
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(134-z0z1z2z3z4 #s(literal 1 binary64) (*.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 2 binary64) #s(literal -1 binary64) (*.f64 (PI.f64) n))
(134-z0z1z2z3z4 #s(literal 1 binary64) (*.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 2 binary64) (PI.f64) (neg.f64 n))
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(134-z0z1z2z3z4 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) n)) (cbrt.f64 (PI.f64)) (PI.f64) (neg.f64 n))
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(134-z0z1z2z3z4 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) n) (PI.f64) (*.f64 (neg.f64 (PI.f64)) n) #s(literal 1 binary64))
(134-z0z1z2z3z4 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) n) (PI.f64) (neg.f64 (PI.f64)) n)
(134-z0z1z2z3z4 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) n) (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) n))
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(134-z0z1z2z3z4 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) n) (PI.f64) (PI.f64) (neg.f64 n))
(134-z0z1z2z3z4 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) n) (PI.f64) n (neg.f64 (PI.f64)))
(134-z0z1z2z3z4 #s(literal 1 binary64) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) n) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)) (*.f64 (neg.f64 n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
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(/.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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))) (neg.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 (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 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1 binary64) (pow.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(neg.f64 (*.f64 (neg.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))))
(neg.f64 (*.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)) #s(literal 1 binary64)))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(neg.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal -1 binary64)))
(neg.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(neg.f64 (/.f64 (neg.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))))
(neg.f64 (/.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)) (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal -1 binary64)))
(+.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)) (*.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(+.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 #s(literal 0 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k))))

eval21.8s (40.8%)

Memory
-51.7MiB live, 100 430.9MiB allocated; 15.1s collecting garbage
Samples
17.9s173 056×0valid
Compiler

Compiled 78 153 to 9 483 computations (87.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.7s
ival-mult!: 3.5s (74.1% of total)
ival-sub!: 685.0ms (14.5% of total)
adjust: 543.0ms (11.5% of total)

prune86.0ms (0.2%)

Memory
16.7MiB live, 817.8MiB allocated; 35ms collecting garbage
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2 356152 371
Fresh15015
Picked505
Done000
Total2 376152 391
Accuracy
100.0%
Counts
2 391 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.3%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
77.0%
(/.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
79.1%
(/.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)))
▶99.7%
(/.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)))
99.3%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
99.3%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
▶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)))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
51.5%
#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)))
▶51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
51.5%
#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))))
▶40.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
51.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
51.5%
#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 704 to 526 computations (25.3% saved)

series135.0ms (0.3%)

Memory
-0.8MiB live, 1 207.4MiB allocated; 64ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03962941
Stop Event
1×iter-limit
Counts
27 → 90
Calls
Call 1
Inputs
(PI.f64)
(+.f64 (PI.f64) (PI.f64))
n
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(literal 1/2 binary64)
k
(*.f64 #s(literal 1/2 binary64) k)
(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) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/2 binary64) k)
(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) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
Outputs
#s(approx k k)
#s(approx (* 1/2 k) (*.f64 #s(literal 1/2 binary64) 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 (+.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)))) (*.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 (+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 k (+.f64 (*.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 (sqrt k) (sqrt.f64 k))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (+.f64 (sqrt.f64 k) (*.f64 k (+.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 k)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (+.f64 (sqrt.f64 k) (*.f64 k (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (*.f64 k (+.f64 (*.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 (/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (+.f64 (*.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)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (+.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (*.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)) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (+.f64 (*.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.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 (*.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))))))) (+.f64 (*.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 (/ (* (+ (PI) (PI)) n) k) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.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 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (+.f64 (*.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))))
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#s(approx (* (- 1 k) 1/2) #s(literal 1/2 binary64))
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#s(approx n n)
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#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (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 k) (sqrt (* (+ (PI) (PI)) n))) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))))
#s(approx (/ 1 (/ (sqrt k) (sqrt (* (+ (PI) (PI)) n)))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (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 (* (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))))))))
Calls

6 calls:

TimeVariablePoint
26.0ms
n
inf
25.0ms
n
0
22.0ms
n
-inf
11.0ms
k
-inf
9.0ms
k
0

rewrite399.0ms (0.7%)

Memory
42.4MiB live, 615.6MiB allocated; 207ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
037216
057211
1223196
2703196
33557196
04082196
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
27 → 1 260
Calls
Call 1
Inputs
(PI.f64)
(+.f64 (PI.f64) (PI.f64))
n
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(literal 1/2 binary64)
k
(*.f64 #s(literal 1/2 binary64) k)
(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) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/2 binary64) k)
(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) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
Outputs
(PI.f64)
(*.f64 (*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (PI.f64)) (PI.f64))) (PI.f64))
(*.f64 (cbrt.f64 (fabs.f64 (PI.f64))) (*.f64 (cbrt.f64 (fabs.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (*.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (log.f64 (exp.f64 (PI.f64))))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 #s(literal 1 binary64) (+.f64 (PI.f64) (PI.f64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))
(*.f64 (PI.f64) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (*.f64 (neg.f64 (PI.f64)) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (neg.f64 (PI.f64))))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (neg.f64 (PI.f64))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (+.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (+.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(134-z0z1z2z3z4 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(134-z0z1z2z3z4 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (cbrt.f64 (fabs.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (cbrt.f64 (fabs.f64 (PI.f64))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (cbrt.f64 (PI.f64))) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (cbrt.f64 (fabs.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (cbrt.f64 (fabs.f64 (PI.f64))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (cbrt.f64 (PI.f64))) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (cbrt.f64 (fabs.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (cbrt.f64 (fabs.f64 (PI.f64))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (PI.f64))) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (fabs.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (cbrt.f64 (fabs.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (cbrt.f64 (fabs.f64 (PI.f64))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (PI.f64))) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (cbrt.f64 (PI.f64)) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))) (cbrt.f64 (fabs.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (cbrt.f64 (PI.f64))))
(134-z0z1z2z3z4 (cbrt.f64 (PI.f64)) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (neg.f64 (neg.f64 (cbrt.f64 (PI.f64)))) (cbrt.f64 (fabs.f64 (PI.f64))) (neg.f64 (cbrt.f64 (fabs.f64 (PI.f64)))))
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#s(literal 1/2 binary64)
k
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(134-z0z1z2z3z4 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n) (PI.f64) (neg.f64 n))
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(134-z0z1z2z3z4 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) n) (neg.f64 n) (PI.f64))
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(134-z0z1z2z3z4 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) n (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (neg.f64 (*.f64 (cbrt.f64 (PI.f64)) n)))
(134-z0z1z2z3z4 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) n (PI.f64) n (neg.f64 (PI.f64)))
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(134-z0z1z2z3z4 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (PI.f64) n (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (neg.f64 (*.f64 (cbrt.f64 (PI.f64)) n)))
(134-z0z1z2z3z4 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (PI.f64) n n (neg.f64 (PI.f64)))
(134-z0z1z2z3z4 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (PI.f64) n (PI.f64) (neg.f64 n))
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(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 (neg.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))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(neg.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))

eval9.6s (17.9%)

Memory
411.6MiB live, 12 811.2MiB allocated; 3.6s collecting garbage
Samples
7.1s112 332×0valid
126.0ms2 356×0invalid
Compiler

Compiled 96 428 to 8 541 computations (91.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.5s
ival-mult!: 1.9s (76.5% of total)
ival-sub!: 369.0ms (14.5% of total)
adjust: 230.0ms (9.0% of total)

prune100.0ms (0.2%)

Memory
-30.6MiB live, 207.9MiB allocated; 28ms collecting garbage
Pruning

42 alts after pruning (39 fresh and 3 done)

PrunedKeptTotal
New2 909322 941
Fresh3710
Picked505
Done-330
Total2 914422 956
Accuracy
100.0%
Counts
2 956 → 42
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.3%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
79.1%
(/.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)))
99.3%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
▶99.3%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
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)) k) n)))
78.7%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
79.1%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
74.2%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
▶51.5%
#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)))
51.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
51.4%
#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))))
51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))))
51.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
51.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
✓51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
40.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
▶51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))))
51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
41.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
51.5%
#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))))
40.0%
#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)))))
51.5%
#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))))))
40.1%
#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)))))
40.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
51.5%
#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))))
40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
✓40.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
40.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
40.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
▶40.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
▶40.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
40.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)) (PI.f64))))
40.3%
#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))))
29.0%
#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)))))
51.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
51.5%
#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))))))
37.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
48.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
Compiler

Compiled 2 301 to 1 693 computations (26.4% saved)

series81.0ms (0.2%)

Memory
9.3MiB live, 100.7MiB allocated; 38ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02561631
Stop Event
1×iter-limit
Counts
30 → 68
Calls
Call 1
Inputs
(PI.f64)
(+.f64 (PI.f64) (PI.f64))
n
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
#s(literal 1 binary64)
k
(-.f64 #s(literal 1 binary64) k)
#s(literal 1/2 binary64)
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 n k)
(*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))
(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 n k) (+.f64 (PI.f64) (PI.f64)))))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
Outputs
#s(approx k 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 k) 1/2) #s(literal 1/2 binary64))
#s(approx (* (- 1 k) 1/2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (+.f64 (*.f64 k (+.f64 (*.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 (+.f64 (*.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 (sqrt k) (sqrt.f64 k))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (/ 1 (sqrt k))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (/ 1 (sqrt k))) (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (/ 1 (sqrt k))) (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) (sqrt.f64 k))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (/ 1 (sqrt k))) (+.f64 (*.f64 k (+.f64 (*.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 (+.f64 (*.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 (/ n k) (/.f64 n k))
#s(approx (* (/ n k) (+ (PI) (PI))) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
#s(approx (sqrt (* (/ n k) (+ (PI) (PI)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (sqrt k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt (* n (+ (PI) (PI))))) (sqrt k)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 2 binary64))))
#s(approx (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* n (+ (PI) (PI)))) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (sqrt.f64 k) #s(literal 2 binary64)))))
#s(approx (sqrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* n (+ (PI) (PI))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (sqrt.f64 k) #s(literal 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 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (* (- 1 k) 1/2) (*.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt 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 (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
#s(approx (sqrt (* (/ n k) (+ (PI) (PI)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (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 (* n (+ (PI) (PI))))) (sqrt k)) (/.f64 (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 k #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64)))))
#s(approx (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* n (+ (PI) (PI)))) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 (pow.f64 k #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))))))
#s(approx (sqrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* n (+ (PI) (PI))))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))))) k))
#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (- 1 k) 1/2) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
#s(approx (sqrt k) (*.f64 #s(literal -1 binary64) (*.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 (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (/ 1 (sqrt k))) (*.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt (* n (+ (PI) (PI))))) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (sqrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* n (+ (PI) (PI))))) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))))) k)))
#s(approx n n)
#s(approx (* (+ (PI) (PI)) n) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
#s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (* (/ n k) (+ (PI) (PI)))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))
#s(approx (/ (sqrt (* (+ (PI) (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 (* n (+ (PI) (PI))))) (/.f64 #s(literal 1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt (* n (+ (PI) (PI))))) (sqrt k)) (/.f64 (sqrt.f64 k) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (sqrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* n (+ (PI) (PI))))) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (pow.f64 (sqrt.f64 k) #s(literal 2 binary64))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/2)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
#s(approx (sqrt (* (/ n k) (+ (PI) (PI)))) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) (/.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt (* n (+ (PI) (PI))))) (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))))
#s(approx (sqrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (* n (+ (PI) (PI))))) (*.f64 #s(literal -1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 n (pow.f64 (sqrt.f64 k) #s(literal 2 binary64)))))))))
Calls

6 calls:

TimeVariablePoint
15.0ms
n
inf
11.0ms
n
-inf
11.0ms
n
0
4.0ms
k
-inf
4.0ms
k
0

rewrite221.0ms (0.4%)

Memory
16.6MiB live, 435.4MiB allocated; 61ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040284
062235
1244228
2924227
04206227
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
30 → 1 809
Calls
Call 1
Inputs
(PI.f64)
(+.f64 (PI.f64) (PI.f64))
n
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
#s(literal 1 binary64)
k
(-.f64 #s(literal 1 binary64) k)
#s(literal 1/2 binary64)
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 n k)
(*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))
(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 n k) (+.f64 (PI.f64) (PI.f64)))))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
Outputs
(PI.f64)
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 1 binary64)))) (*.f64 (PI.f64) #s(literal 1 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 #s(literal 1 binary64) (PI.f64)))) (*.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (neg.f64 (PI.f64))) (PI.f64))) (PI.f64))
(*.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (PI.f64)) (PI.f64))) (PI.f64))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (PI.f64)) (+.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 #s(literal 2 binary64) (log.f64 (exp.f64 (PI.f64))))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (neg.f64 (neg.f64 (PI.f64)))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (neg.f64 (PI.f64))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 1 binary64))) (*.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 1 binary64)))) (-.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 1 binary64))) (-.f64 (*.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 1 binary64))) (*.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 1 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 #s(literal 1 binary64) (PI.f64))) (*.f64 (*.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 #s(literal 1 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 #s(literal 1 binary64) (PI.f64))))
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(/.f64 (+.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (pow.f64 (neg.f64 (neg.f64 (PI.f64))) #s(literal 3 binary64))) (+.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (neg.f64 (neg.f64 (PI.f64)))))))
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(fabs.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))
(+.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 n (PI.f64))) (sqrt.f64 k)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 n (PI.f64))) (sqrt.f64 k)))
(+.f64 (/.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64))) (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64))))
(+.f64 (*.f64 (/.f64 n k) (PI.f64)) (*.f64 (neg.f64 (neg.f64 (PI.f64))) (/.f64 n k)))
(+.f64 (*.f64 (/.f64 n k) (PI.f64)) (*.f64 (/.f64 n k) (PI.f64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 (/.f64 n k) #s(literal 2 binary64))))
(log.f64 (pow.f64 (exp.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(log.f64 (pow.f64 (exp.f64 (+.f64 (PI.f64) (PI.f64))) (/.f64 n k)))
(log.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64))) #s(literal 2 binary64)))
(log.f64 (*.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64))) (exp.f64 (*.f64 (/.f64 n k) (PI.f64)))))
(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 k)) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (sqrt.f64 k)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (sqrt.f64 k)))))
(*.f64 (sqrt.f64 #s(literal 1 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (pow.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (sqrt.f64 k))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (sqrt.f64 k))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 n #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (+.f64 n n) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (pow.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))) (pow.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal -1 binary64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (pow.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1 binary64)) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (neg.f64 (sqrt.f64 k)))) (sqrt.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 (neg.f64 n) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
(/.f64 #s(literal -2 binary64) (*.f64 (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))
(/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))) #s(literal 1 binary64)))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))) #s(literal -1 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))))
(sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))
(fabs.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))) #s(literal 1 binary64)))
(fabs.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))) #s(literal -1 binary64)))
(fabs.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))) #s(literal -1 binary64)))
(fabs.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))))
(fabs.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(+.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))

eval10.0s (18.6%)

Memory
-543.4MiB live, 9 956.5MiB allocated; 11.1s collecting garbage
Samples
4.3s64 588×0valid
270.0ms3 250×0invalid
0.0ms2×1valid
Compiler

Compiled 52 026 to 5 956 computations (88.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.5s
ival-mult!: 1.2s (78.0% of total)
ival-sub!: 208.0ms (13.9% of total)
adjust: 120.0ms (8.0% of total)

prune218.0ms (0.4%)

Memory
-34.6MiB live, 725.0MiB allocated; 140ms collecting garbage
Pruning

50 alts after pruning (44 fresh and 6 done)

PrunedKeptTotal
New1 573211 594
Fresh112334
Picked505
Done-363
Total1 586501 636
Accuracy
100.0%
Counts
1 636 → 50
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.3%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
79.1%
(/.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)))
99.3%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
99.4%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)) k) n)))
78.7%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (/.f64 (+.f64 n n) k) (PI.f64))))
79.1%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
74.2%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
51.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k)))
51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
51.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
46.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
51.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))))
✓51.5%
#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)))
51.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
51.4%
#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))))
51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))))
51.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
51.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
✓51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
40.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))))
51.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
✓51.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))))
51.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))))
51.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 #s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) (/.f64 #s(literal 1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))) (sqrt.f64 k))))
41.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
51.5%
#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))))
46.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
40.0%
#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)))))
51.5%
#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))))))
40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
51.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n)))
40.1%
#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)))))
40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))))
40.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
51.5%
#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))))
24.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (*.f64 (*.f64 n (PI.f64)) k) (*.f64 (*.f64 n (PI.f64)) k)) (*.f64 k k))))
✓40.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
40.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
✓40.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
40.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)) (PI.f64))))
40.3%
#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))))
35.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k)) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
29.0%
#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)))))
37.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
48.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
Compiler

Compiled 1 433 to 1 049 computations (26.8% saved)

regimes784.0ms (1.5%)

Memory
79.9MiB live, 3 118.4MiB allocated; 460ms collecting garbage
Counts
1 → 1
5 → 1
30 → 2
56 → 3
59 → 1
71 → 1
89 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
Call 2
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 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 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)) (PI.f64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
Call 3
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 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 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#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 (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 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n)))
#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))) (sqrt.f64 (/.f64 (+.f64 (*.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))) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.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))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (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 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
Call 4
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 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 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#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 (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 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n)))
#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))) (sqrt.f64 (/.f64 (+.f64 (*.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))) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.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))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (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 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k)) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (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 (+.f64 (PI.f64) (PI.f64)))) (sqrt.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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 #s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) (/.f64 #s(literal 1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #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 (*.f64 (+.f64 (PI.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))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))))
#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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k)) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
Call 5
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 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 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#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 (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 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n)))
#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))) (sqrt.f64 (/.f64 (+.f64 (*.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))) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.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))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (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 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k)) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (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 (+.f64 (PI.f64) (PI.f64)))) (sqrt.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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 #s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) (/.f64 #s(literal 1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #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 (*.f64 (+.f64 (PI.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))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))))
#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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
Outputs
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
Call 6
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 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 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
#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 (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 (PI.f64)) (sqrt.f64 (/.f64 (+.f64 n n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n)))
#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))) (sqrt.f64 (/.f64 (+.f64 (*.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))) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.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))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (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 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k)) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (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 (+.f64 (PI.f64) (PI.f64)))) (sqrt.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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 #s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) (/.f64 #s(literal 1 binary64) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) n)))))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #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 (*.f64 (+.f64 (PI.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))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))))
#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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #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 n n) k) (PI.f64))))
(*.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)) k) n)))
(*.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 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 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
Outputs
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
Call 7
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 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 (/.f64 #s(literal 1 binary64) k) (+.f64 n n)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k n)))))))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))))
#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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #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 n n) k) (PI.f64))))
(*.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)) k) n)))
(*.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
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(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 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 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (PI.f64))))) k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
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(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) n) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
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(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal -1/2 binary64))))
(*.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 (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 (*.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 (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 (*.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 (+.f64 n n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
Outputs
(/.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)))
Calls

27 calls:

101.0ms
n
73.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
72.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
68.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
59.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
40.3%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
40.3%1k
40.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
40.3%1n
40.3%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
40.3%1k
40.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
40.3%1n
62.9%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
62.9%2n
62.9%2k
62.9%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
62.9%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))))
64.7%3k
62.9%2n
99.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.3%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.3%1k
99.3%1n
99.4%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))))
99.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.4%1k
99.4%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 2 511 to 505 computations (79.9% saved)

bsearch20.0ms (0.0%)

Memory
12.0MiB live, 111.2MiB allocated; 6ms collecting garbage
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×predicate-same
Steps
TimeLeftRight
16.0ms
1.93436357632582e+177
6.144706535735522e+177
2.0ms
8.290471059097932e-36
3.68272725238434e-33
Samples
12.0ms96×0valid
Compiler

Compiled 411 to 321 computations (21.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-sqrt: 3.0ms (37.3% of total)
ival-pow: 3.0ms (37.3% of total)
adjust: 1.0ms (12.4% of total)
ival-div!: 1.0ms (12.4% of total)
ival-mult!: 1.0ms (12.4% of total)
ival-sub!: 0.0ms (0.0% of total)

bsearch16.0ms (0.0%)

Memory
-17.6MiB live, 75.2MiB allocated; 6ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
15.0ms
2.4534333876986544e+32
2.3056922854147268e+34
Samples
8.0ms64×0valid
Compiler

Compiled 263 to 206 computations (21.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-pow: 2.0ms (46.9% of total)
adjust: 1.0ms (23.5% of total)
ival-sqrt: 1.0ms (23.5% of total)
ival-div!: 1.0ms (23.5% of total)
ival-mult!: 1.0ms (23.5% of total)
ival-sub!: 0.0ms (0.0% of total)

derivations196.0ms (0.4%)

Memory
16.7MiB live, 553.0MiB allocated; 29ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 264 to 72 computations (72.7% saved)

preprocess97.0ms (0.2%)

Memory
21.5MiB live, 556.3MiB allocated; 29ms collecting garbage
Compiler

Compiled 808 to 395 computations (51.1% saved)

end0.0ms (0.0%)

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

Profiling

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