Migdal et al, Equation (51)

Time bar (total: 6.5s)

start0.0ms (0%)

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

analyze129.0ms (2%)

Memory
31.9MiB live, 225.2MiB allocated; 22ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%51.5%0%7
52.5%25%22.6%0.1%0%52.3%0%8
53.8%25%21.5%0.1%0%53.5%0%9
54.5%25%20.9%0.1%0%54%0%10
55.3%25%20.2%0.1%0%54.7%0%11
55.7%25%19.9%0.1%0%55.1%0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.0s (46.9%)

Memory
120.1MiB live, 4 723.7MiB allocated; 1.2s collecting garbage
Samples
1.4s5 341×1invalid
973.0ms8 253×0valid
148.0ms480×2invalid
30.0ms327×0invalid
22.0ms232×0exit
1.0ms1valid
Precisions
Click to see histograms. Total time spent on operations: 1.9s
ival-pow: 641.0ms (34.3% of total)
adjust: 339.0ms (18.1% of total)
ival-mult!: 299.0ms (16% of total)
ival-sqrt: 271.0ms (14.5% of total)
ival-div!: 228.0ms (12.2% of total)
ival-sub!: 91.0ms (4.9% of total)
ival-pi: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

preprocess46.0ms (0.7%)

Memory
0.1MiB live, 45.7MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033102
112588
245388
3197588
Stop Event
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))))
Compiler

Compiled 30 to 26 computations (13.3% saved)

series70.0ms (1.1%)

Memory
7.1MiB live, 94.7MiB allocated; 12ms collecting garbage
Counts
13 → 37
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Calls

6 calls:

TimeVariablePointExpression
28.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
21.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
11.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
2.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
2.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))

rewrite243.0ms (3.7%)

Memory
22.4MiB live, 203.3MiB allocated; 28ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01671003
0181952
1830850
07625832
Stop Event
iter-limit
iter-limit
node-limit
iter-limit
Counts
50 → 239
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(+.f64 (/.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 2 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k)))
(/.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 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 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 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(pow.f64 k #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(sqrt.f64 k)
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
k
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(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k) #s(literal 1/8 binary64)) (fma.f64 (*.f64 k k) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) k))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k) #s(literal 1/8 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(neg.f64 (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))
(neg.f64 (/.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)))
(neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))
(neg.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (/.f64 (*.f64 (*.f64 k k) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal -1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(+.f64 (/.f64 (neg.f64 k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(+.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (/.f64 (neg.f64 k) #s(literal 2 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (/.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 (*.f64 k k) #s(literal 1 binary64)) (-.f64 (neg.f64 k) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k))) (neg.f64 (+.f64 k #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k))) (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 k #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) (fma.f64 k k (+.f64 k #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(neg.f64 (-.f64 k #s(literal 1 binary64)))
(fma.f64 (neg.f64 k) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
(fma.f64 k #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (neg.f64 k) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 k k) k) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(-.f64 (neg.f64 k) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 k k) (neg.f64 k)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(+.f64 (neg.f64 k) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (fma.f64 k (/.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/8 binary64)) (*.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/48 binary64))) (sqrt.f64 k)) (*.f64 (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (-.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/8 binary64)) (*.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/48 binary64))) k) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (-.f64 #s(literal 1 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 k) k) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k))
#s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (neg.f64 (/.f64 (sqrt.f64 k) k))))
#s(approx (/ 1 (sqrt k)) (neg.f64 (/.f64 (sqrt.f64 k) k)))
#s(approx (sqrt k) (/.f64 (neg.f64 k) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (* 2 (PI)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))

eval45.0ms (0.7%)

Memory
1.9MiB live, 62.0MiB allocated; 42ms collecting garbage
Compiler

Compiled 2 421 to 888 computations (63.3% saved)

prune14.0ms (0.2%)

Memory
-12.6MiB live, 35.7MiB allocated; 2ms collecting garbage
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New20716223
Fresh000
Picked101
Done000
Total20816224
Accuracy
100.0%
Counts
224 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.0%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
98.8%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
98.9%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
98.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
98.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
95.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
98.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
95.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
48.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.4%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
41.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
49.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
99.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 k) k) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
Compiler

Compiled 692 to 552 computations (20.2% saved)

series211.0ms (3.3%)

Memory
1.3MiB live, 323.1MiB allocated; 51ms collecting garbage
Counts
37 → 119
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(/.f64 (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
(fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
Outputs
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (/ (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) #s(hole binary64 (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))) (sqrt k))) (/ (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 2) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))) (sqrt k))))) (/ (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 3) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 2) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)) (sqrt k))))))) (/ (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2) (sqrt k)))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))) (* 1/8 (* k (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 2) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)))))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 3) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)))) (* 1/8 (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 2) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))))))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k)))) (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (/ (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (- 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k)))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* k (+ (* -1 (/ (sqrt (* 2 (* n (PI)))) k)) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (+ 1 (* -1 k)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))))) (sqrt k))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) #s(hole binary64 (* -1 (log (sqrt (* 2 (* n (PI))))))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (log (sqrt (* 2 (* n (PI)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (- 1 k)))) (sqrt k))))
#s(approx (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) #s(hole binary64 (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))))
#s(approx (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) #s(hole binary64 (pow (sqrt (* n (PI))) 2)))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))) (sqrt k))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))))))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) #s(hole binary64 (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) #s(hole binary64 (* -1 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* (pow (sqrt 2) 2) (pow (sqrt (/ (PI) n)) 2))) (* -2 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* (pow (sqrt 2) 2) (pow (sqrt (/ (PI) n)) 2))) (* -2 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) #s(hole binary64 (* (pow n 2) (* (pow (sqrt 2) 2) (pow (sqrt (/ (PI) n)) 2)))))
#s(approx (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) #s(hole binary64 (* (pow n 2) (pow (sqrt (/ (PI) n)) 2))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* n (sqrt (/ (PI) n)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (* -1 (/ (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))) (sqrt k)))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))))))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) #s(hole binary64 (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) #s(hole binary64 (* -1 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* (pow (sqrt 2) 2) (pow (sqrt (/ (PI) n)) 2))) (* -2 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* (pow (sqrt 2) 2) (pow (sqrt (/ (PI) n)) 2))) (* -2 (log (/ -1 n)))) (- 1 k))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) n))))))
Calls

6 calls:

TimeVariablePointExpression
49.0ms
n
@-inf
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (neg (log (sqrt (* (+ (PI) (PI)) n)))) (log (sqrt (* (+ (PI) (PI)) n))) (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (* (sqrt 2) (sqrt 2)) (sqrt 2) (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) (sqrt (* (PI) n)) (* (PI) n))
46.0ms
n
@0
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (neg (log (sqrt (* (+ (PI) (PI)) n)))) (log (sqrt (* (+ (PI) (PI)) n))) (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (* (sqrt 2) (sqrt 2)) (sqrt 2) (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) (sqrt (* (PI) n)) (* (PI) n))
35.0ms
k
@inf
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (neg (log (sqrt (* (+ (PI) (PI)) n)))) (log (sqrt (* (+ (PI) (PI)) n))) (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (* (sqrt 2) (sqrt 2)) (sqrt 2) (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) (sqrt (* (PI) n)) (* (PI) n))
32.0ms
k
@0
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (neg (log (sqrt (* (+ (PI) (PI)) n)))) (log (sqrt (* (+ (PI) (PI)) n))) (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (* (sqrt 2) (sqrt 2)) (sqrt 2) (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) (sqrt (* (PI) n)) (* (PI) n))
28.0ms
n
@inf
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (neg (log (sqrt (* (+ (PI) (PI)) n)))) (log (sqrt (* (+ (PI) (PI)) n))) (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (* (sqrt 2) (sqrt 2)) (sqrt 2) (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) (sqrt (* (PI) n)) (* (PI) n))

rewrite176.0ms (2.7%)

Memory
53.2MiB live, 183.5MiB allocated; 18ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05224769
05853881
129283689
088643619
Stop Event
iter-limit
node-limit
iter-limit
Counts
156 → 851
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(/.f64 (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
(fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (/ (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) #s(hole binary64 (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))) (sqrt k))) (/ (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 2) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))) (sqrt k))))) (/ (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 3) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 2) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)) (sqrt k))))))) (/ (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2) (sqrt k)))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))) (* 1/8 (* k (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 2) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)))))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 3) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2)))) (* 1/8 (* (pow (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) 2) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))))))) (pow (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2)) 1/2))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k)))) (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (/ (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (- 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k)))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* k (+ (* -1 (/ (sqrt (* 2 (* n (PI)))) k)) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (+ 1 (* -1 k)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))))) (sqrt k))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) #s(hole binary64 (* -1 (log (sqrt (* 2 (* n (PI))))))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (log (sqrt (* 2 (* n (PI)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))) (- 1 k)))) (sqrt k))))
#s(approx (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) #s(hole binary64 (* (pow (sqrt 2) 2) (pow (sqrt (* n (PI))) 2))))
#s(approx (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) #s(hole binary64 (pow (sqrt (* n (PI))) 2)))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))) (sqrt k))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))))))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) #s(hole binary64 (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) #s(hole binary64 (* -1 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* (pow (sqrt 2) 2) (pow (sqrt (/ (PI) n)) 2))) (* -2 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* (pow (sqrt 2) 2) (pow (sqrt (/ (PI) n)) 2))) (* -2 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) #s(hole binary64 (* (pow n 2) (* (pow (sqrt 2) 2) (pow (sqrt (/ (PI) n)) 2)))))
#s(approx (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) #s(hole binary64 (* (pow n 2) (pow (sqrt (/ (PI) n)) 2))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* n (sqrt (/ (PI) n)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (* -1 (/ (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))) (sqrt k)))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))))))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) #s(hole binary64 (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) #s(hole binary64 (* -1 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* (pow (sqrt 2) 2) (pow (sqrt (/ (PI) n)) 2))) (* -2 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* (pow (sqrt 2) 2) (pow (sqrt (/ (PI) n)) 2))) (* -2 (log (/ -1 n)))) (- 1 k))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) n))))))
Outputs
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) k))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) k) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) k)) (/.f64 (pow.f64 n (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) k))
(*.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) k) (/.f64 (pow.f64 n (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) k))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) k) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 (sqrt.f64 k) k) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 k) k))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal -1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal -1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (*.f64 (neg.f64 k) (/.f64 (sqrt.f64 k) k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
(/.f64 (neg.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) k)) (neg.f64 (/.f64 (sqrt.f64 k) k)))
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(pow.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal 2 binary64))
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#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 k (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(literal 1/8 binary64))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))
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#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) 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))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))
#s(approx (sqrt k) (*.f64 (/.f64 (sqrt.f64 k) k) k))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (neg.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+.f64 (neg.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (*.f64 (neg.f64 k) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (*.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (sqrt (/ 1 k)) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) k)))
#s(approx (sqrt k) (*.f64 (neg.f64 k) (/.f64 (sqrt.f64 k) k)))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (fma.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (*.f64 (neg.f64 k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (* 2 (PI)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (fma.f64 (neg.f64 k) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (* (* 2 (PI)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) (*.f64 (PI.f64) n))
#s(approx (sqrt (* (PI) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
#s(approx (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) (*.f64 (PI.f64) n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (*.f64 n (/.f64 (fma.f64 (neg.f64 k) (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (*.f64 (fma.f64 (neg.f64 k) (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) n))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (*.f64 (neg.f64 k) (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) (neg.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (fma.f64 #s(literal -2 binary64) (neg.f64 (log.f64 n)) (log.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (*.f64 (fma.f64 #s(literal -2 binary64) (neg.f64 (log.f64 n)) (log.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (* (* 2 (PI)) n) (*.f64 (*.f64 n n) (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (* (sqrt (* (PI) n)) (sqrt (* (PI) n))) (*.f64 (*.f64 n n) (/.f64 (PI.f64) n)))
#s(approx (sqrt (* (PI) n)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (*.f64 #s(literal -1 binary64) n) (*.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 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (*.f64 #s(literal -1 binary64) n) (*.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 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (*.f64 #s(literal -1 binary64) n) (*.f64 #s(literal -2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
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#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (neg.f64 (*.f64 (fma.f64 (neg.f64 k) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) n)))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (*.f64 (neg.f64 k) (log.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) (neg.f64 (log.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) (log.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (fma.f64 #s(literal -2 binary64) (neg.f64 (log.f64 n)) (log.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (*.f64 (fma.f64 #s(literal -2 binary64) (neg.f64 (log.f64 n)) (log.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (sqrt (* (PI) n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) n)))

eval105.0ms (1.6%)

Memory
-20.1MiB live, 166.7MiB allocated; 40ms collecting garbage
Compiler

Compiled 10 871 to 2 725 computations (74.9% saved)

prune595.0ms (9.1%)

Memory
-165.8MiB live, 47.8MiB allocated; 1.0s collecting garbage
Pruning

39 alts after pruning (37 fresh and 2 done)

PrunedKeptTotal
New65731688
Fresh5611
Picked325
Done000
Total66539704
Accuracy
100.0%
Counts
704 → 39
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.9%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k))
99.0%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
98.9%
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
98.9%
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
98.8%
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
98.9%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
98.9%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 (/.f64 (sqrt.f64 k) k) k))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
98.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
95.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
48.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.4%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
99.0%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
98.8%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
43.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (/.f64 (sqrt.f64 k) k)))
49.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
48.7%
#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)))
37.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) #s(literal -1/2 binary64))))
43.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 n) k)))
48.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k))))
43.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
48.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k))))
49.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 (sqrt.f64 k) k)))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
48.6%
#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 k) k)))
36.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
24.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)) (*.f64 k k))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
27.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
3.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
3.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (neg.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (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))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Compiler

Compiled 1 683 to 1 483 computations (11.9% saved)

series227.0ms (3.5%)

Memory
-45.7MiB live, 275.3MiB allocated; 43ms collecting garbage
Counts
36 → 96
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))
(+.f64 (PI.f64) (PI.f64))
(/.f64 n k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64)))
(*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))
(log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))
(log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(-.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (+ (PI) (PI)) (/ n k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log (* 2 (* n (PI)))) (* -1 (log k)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (log (sqrt (* 2 (* n (PI)))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (+ (log (sqrt (* 2 (* n (PI))))) (* -1 (* k (log (sqrt (* 2 (* n (PI))))))))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log (* 2 (* n (PI)))) (log (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* k (+ (* -1 (log (sqrt (* 2 (* n (PI)))))) (/ (log (sqrt (* 2 (* n (PI))))) k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log (* -2 (* n (PI)))) (log (/ -1 k)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* -1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* -1 (/ (log (sqrt (* 2 (* n (PI))))) k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log n) (log (* 2 (/ (PI) k))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n)))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))
Calls

6 calls:

TimeVariablePointExpression
93.0ms
k
@-inf
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (+ (PI) (PI)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2)) (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (log (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))
35.0ms
n
@0
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (+ (PI) (PI)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2)) (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (log (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))
32.0ms
n
@-inf
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (+ (PI) (PI)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2)) (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (log (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))
31.0ms
n
@inf
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (+ (PI) (PI)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2)) (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (log (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))
20.0ms
k
@0
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (+ (PI) (PI)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2)) (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (log (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))

rewrite208.0ms (3.2%)

Memory
39.1MiB live, 170.9MiB allocated; 23ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04073122
04522926
120632744
088972711
Stop Event
iter-limit
node-limit
iter-limit
Counts
132 → 577
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))
(+.f64 (PI.f64) (PI.f64))
(/.f64 n k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64)))
(*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))
(log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))
(log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (+ (PI) (PI)) (/ n k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log (* 2 (* n (PI)))) (* -1 (log k)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (log (sqrt (* 2 (* n (PI)))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (+ (log (sqrt (* 2 (* n (PI))))) (* -1 (* k (log (sqrt (* 2 (* n (PI))))))))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log (* 2 (* n (PI)))) (log (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* k (+ (* -1 (log (sqrt (* 2 (* n (PI)))))) (/ (log (sqrt (* 2 (* n (PI))))) k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log (* -2 (* n (PI)))) (log (/ -1 k)))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* -1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* -1 (/ (log (sqrt (* 2 (* n (PI))))) k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log n) (log (* 2 (/ (PI) k))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n)))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) #s(hole binary64 (* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))
Outputs
(*.f64 (/.f64 (sqrt.f64 k) k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 k) k))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 k) k) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) k))
(*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (/.f64 (sqrt.f64 k) k) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k))
(pow.f64 (*.f64 (/.f64 (sqrt.f64 k) k) k) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 k) k)))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (neg.f64 (neg.f64 k)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) k)) (neg.f64 (/.f64 (sqrt.f64 k) k)))
(/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 k))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 k) (/.f64 (sqrt.f64 k) k))))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 k) (/.f64 (sqrt.f64 k) k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 (sqrt.f64 k) k))
(/.f64 (sqrt.f64 k) k)
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 k) (/.f64 (sqrt.f64 k) k))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (/.f64 (sqrt.f64 k) k) k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 k) k) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (sqrt.f64 k) k) k)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 k))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) k))
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 k)))
(/.f64 #s(literal 1 binary64) k)
(exp.f64 (neg.f64 (log.f64 k)))
#s(literal 1 binary64)
k
(*.f64 (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (+.f64 (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sinh.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(*.f64 (fabs.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (fabs.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(pow.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1 binary64))
(/.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64))) (fma.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n) (-.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)))))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (fma.f64 (PI.f64) (PI.f64) (*.f64 (PI.f64) (neg.f64 (PI.f64))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))) (neg.f64 (-.f64 (PI.f64) (PI.f64))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)))) (neg.f64 (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (fma.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (PI.f64) (PI.f64))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))) (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))))
(+.f64 (PI.f64) (PI.f64))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)))
(log.f64 (*.f64 (exp.f64 (PI.f64)) (exp.f64 (PI.f64))))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 #s(literal 1/2 binary64) k) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) k)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal -1/2 binary64) k))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k) #s(literal 1/8 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (/.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal -1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(-.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal -1/2 binary64) k)))
(+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k)) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 k)))))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(pow.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) #s(literal 1/2 binary64))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) (-.f64 (*.f64 (sinh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) (sinh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))) (*.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) (sinh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (neg.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) (sinh.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
(*.f64 (fabs.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (fabs.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
(*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) k))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))
(*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
(pow.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 2 binary64))
(pow.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) #s(literal 1 binary64))
(/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 (*.f64 (PI.f64) n) k) (-.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 (*.f64 (PI.f64) n) k)))))
(/.f64 (+.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 (*.f64 (PI.f64) n))) (neg.f64 k))
(/.f64 (fma.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 k) (*.f64 (neg.f64 k) (neg.f64 (*.f64 (PI.f64) n)))) (*.f64 k k))
(/.f64 (fma.f64 (neg.f64 (*.f64 (PI.f64) n)) k (*.f64 (neg.f64 k) (*.f64 (PI.f64) n))) (*.f64 (neg.f64 k) k))
(/.f64 (fma.f64 (*.f64 (PI.f64) n) (neg.f64 k) (*.f64 k (neg.f64 (*.f64 (PI.f64) n)))) (*.f64 k (neg.f64 k)))
(/.f64 (*.f64 (neg.f64 n) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))) (*.f64 (neg.f64 k) (-.f64 (PI.f64) (PI.f64))))
(/.f64 (*.f64 (neg.f64 n) (fma.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)))) (*.f64 (neg.f64 k) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))))
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(/.f64 (*.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) n) (*.f64 (-.f64 (PI.f64) (PI.f64)) k))
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(fma.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k) (/.f64 (*.f64 (PI.f64) n) k))
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(exp.f64 (+.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
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(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (fma.f64 k (/.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/6 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (neg.f64 k) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 k (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/6 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/2 binary64))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (-.f64 #s(literal 1 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k))
#s(approx (sqrt k) (*.f64 (/.f64 (sqrt.f64 k) k) k))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (*.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)) k))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt k)) (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) k)))
#s(approx (sqrt k) (*.f64 (neg.f64 k) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 (log.f64 (*.f64 (/.f64 #s(literal -1 binary64) k) (*.f64 #s(literal -2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (log.f64 (*.f64 (/.f64 #s(literal -1 binary64) k) (*.f64 #s(literal -2 binary64) (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (*.f64 (neg.f64 k) (-.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k))))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (* 2 (PI)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 (log.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)) #s(literal 1/2 binary64)))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (log.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (/.f64 (+.f64 (PI.f64) (PI.f64)) k))) #s(literal 1/2 binary64)))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (/.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 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 (log.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)))) #s(literal 1/2 binary64)))
#s(approx (log (/ (* (+ (PI) (PI)) n) k)) (log.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))))

eval53.0ms (0.8%)

Memory
32.0MiB live, 115.2MiB allocated; 16ms collecting garbage
Compiler

Compiled 6 221 to 1 832 computations (70.6% saved)

prune37.0ms (0.6%)

Memory
-15.9MiB live, 90.4MiB allocated; 16ms collecting garbage
Pruning

41 alts after pruning (36 fresh and 5 done)

PrunedKeptTotal
New41113424
Fresh92332
Picked235
Done022
Total42241463
Accuracy
100.0%
Counts
463 → 41
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.9%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k))
99.0%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
98.9%
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
98.9%
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
99.4%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 k) k))
98.8%
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
98.9%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
98.9%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 (/.f64 (sqrt.f64 k) k) k))))
48.6%
(*.f64 (/.f64 (sqrt.f64 k) k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
48.6%
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
98.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
95.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
48.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))))
48.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
48.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))))
48.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.0%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
43.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (/.f64 (sqrt.f64 k) k)))
49.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
48.7%
#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)))
37.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
43.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 n) k)))
48.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k))))
48.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k))))
49.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 (sqrt.f64 k) k)))
36.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
36.8%
#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)))))
45.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 k))))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
24.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
27.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
3.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
3.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (neg.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (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))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Compiler

Compiled 1 726 to 1 533 computations (11.2% saved)

series97.0ms (1.5%)

Memory
-11.8MiB live, 181.5MiB allocated; 49ms collecting garbage
Counts
37 → 90
Calls
Call 1
Inputs
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 k) k))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(/.f64 (sqrt.f64 k) k)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
(sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k)))
(/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))
(*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(*.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(*.f64 k k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) k)
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k))
(sqrt.f64 (*.f64 (PI.f64) n))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
Outputs
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx k #s(hole binary64 k))
#s(approx (/ (sqrt k) k) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (* n (/ (PI) k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* n (/ (PI) k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ (PI) k) #s(hole binary64 (/ (PI) k)))
#s(approx (* (* (* (PI) n) k) 2) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* (* (PI) n) k) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* k k) #s(hole binary64 (pow k 2)))
#s(approx (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) #s(hole binary64 (/ (* (sqrt 2) (sqrt (* n (PI)))) (sqrt k))))
#s(approx (/ (sqrt 2) k) #s(hole binary64 (/ (sqrt 2) k)))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) #s(hole binary64 (/ (* k (sqrt (* n (PI)))) (sqrt k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (/ (sqrt k) k) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) #s(hole binary64 (/ (* (sqrt 2) (sqrt (* n (PI)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) #s(hole binary64 (/ (sqrt (* n (PI))) (sqrt (/ 1 k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (* -1 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (/ (sqrt k) k) #s(hole binary64 (* -1 (sqrt (/ 1 k)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) #s(hole binary64 (* -1 (/ (* (sqrt 2) (sqrt (* n (PI)))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) #s(hole binary64 (* -1 (/ (sqrt (* n (PI))) (sqrt (/ 1 k))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k)) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k)) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) #s(hole binary64 (/ (* n (* (sqrt 2) (sqrt (/ (PI) n)))) (sqrt k))))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) #s(hole binary64 (/ (* k (* n (sqrt (/ (PI) n)))) (sqrt k))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* n (sqrt (/ (PI) n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k)) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) #s(hole binary64 (* -1 (/ (* n (* (sqrt 2) (sqrt (/ (PI) n)))) (sqrt k)))))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) #s(hole binary64 (* -1 (/ (* k (* n (sqrt (/ (PI) n)))) (sqrt k)))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) n))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
Calls

6 calls:

TimeVariablePointExpression
33.0ms
n
@inf
((* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (/ (sqrt k) k) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* (* (PI) n) k) 2) (* k k))) (/ (* (* (* (PI) n) k) 2) (* k k)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) (* k k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) (/ (sqrt 2) k) (sqrt 2) (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (sqrt (* (PI) n)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (- 1 k) 1)
22.0ms
n
@-inf
((* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (/ (sqrt k) k) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* (* (PI) n) k) 2) (* k k))) (/ (* (* (* (PI) n) k) 2) (* k k)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) (* k k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) (/ (sqrt 2) k) (sqrt 2) (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (sqrt (* (PI) n)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (- 1 k) 1)
21.0ms
n
@0
((* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (/ (sqrt k) k) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* (* (PI) n) k) 2) (* k k))) (/ (* (* (* (PI) n) k) 2) (* k k)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) (* k k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) (/ (sqrt 2) k) (sqrt 2) (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (sqrt (* (PI) n)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (- 1 k) 1)
7.0ms
k
@0
((* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (/ (sqrt k) k) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* (* (PI) n) k) 2) (* k k))) (/ (* (* (* (PI) n) k) 2) (* k k)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) (* k k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) (/ (sqrt 2) k) (sqrt 2) (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (sqrt (* (PI) n)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (- 1 k) 1)
7.0ms
k
@-inf
((* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (/ (sqrt k) k) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* (* (PI) n) k) 2) (* k k))) (/ (* (* (* (PI) n) k) 2) (* k k)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) (* k k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) (/ (sqrt 2) k) (sqrt 2) (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (sqrt (* (PI) n)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (- 1 k) 1)

rewrite197.0ms (3%)

Memory
20.2MiB live, 244.6MiB allocated; 44ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03962837
04452632
119782465
083042435
Stop Event
iter-limit
node-limit
iter-limit
Counts
127 → 625
Calls
Call 1
Inputs
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 k) k))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(/.f64 (sqrt.f64 k) k)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
(sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k)))
(/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))
(*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(*.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(*.f64 k k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) k)
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k))
(sqrt.f64 (*.f64 (PI.f64) n))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx k #s(hole binary64 k))
#s(approx (/ (sqrt k) k) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (* n (/ (PI) k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* n (/ (PI) k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ (PI) k) #s(hole binary64 (/ (PI) k)))
#s(approx (* (* (* (PI) n) k) 2) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* (* (PI) n) k) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* k k) #s(hole binary64 (pow k 2)))
#s(approx (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) #s(hole binary64 (/ (* (sqrt 2) (sqrt (* n (PI)))) (sqrt k))))
#s(approx (/ (sqrt 2) k) #s(hole binary64 (/ (sqrt 2) k)))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) #s(hole binary64 (/ (* k (sqrt (* n (PI)))) (sqrt k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (/ (sqrt k) k) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) #s(hole binary64 (/ (* (sqrt 2) (sqrt (* n (PI)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) #s(hole binary64 (/ (sqrt (* n (PI))) (sqrt (/ 1 k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (* -1 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (/ (sqrt k) k) #s(hole binary64 (* -1 (sqrt (/ 1 k)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) #s(hole binary64 (* -1 (/ (* (sqrt 2) (sqrt (* n (PI)))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) #s(hole binary64 (* -1 (/ (sqrt (* n (PI))) (sqrt (/ 1 k))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k)) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k)) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) #s(hole binary64 (/ (* n (* (sqrt 2) (sqrt (/ (PI) n)))) (sqrt k))))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) #s(hole binary64 (/ (* k (* n (sqrt (/ (PI) n)))) (sqrt k))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* n (sqrt (/ (PI) n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (sqrt k) k)) #s(hole binary64 (/ (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k)) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (/ (sqrt 2) k) (/ (sqrt (* (PI) n)) (/ (sqrt k) k))) #s(hole binary64 (* -1 (/ (* n (* (sqrt 2) (sqrt (/ (PI) n)))) (sqrt k)))))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) #s(hole binary64 (* -1 (/ (* k (* n (sqrt (/ (PI) n)))) (sqrt k)))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) n))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
Outputs
(*.f64 (/.f64 (sqrt.f64 k) k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 k) k))
(/.f64 (neg.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))) (neg.f64 k))
(/.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) k)
(*.f64 (fabs.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(*.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (+.f64 (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sinh.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(*.f64 (fabs.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (fabs.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(pow.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64))
(/.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64))) (fma.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n) (-.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)))))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (fma.f64 (PI.f64) (PI.f64) (*.f64 (PI.f64) (neg.f64 (PI.f64))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))) (neg.f64 (-.f64 (PI.f64) (PI.f64))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)))) (neg.f64 (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.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 (fma.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (PI.f64) (PI.f64))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))) (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))))
(+.f64 (PI.f64) (PI.f64))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)))
(log.f64 (*.f64 (exp.f64 (PI.f64)) (exp.f64 (PI.f64))))
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 #s(literal 1/2 binary64) k))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (-.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 #s(literal 1/2 binary64) k) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) k)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal -1/2 binary64) k))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k))) (+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal -1/2 binary64) k))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal -1/2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k) #s(literal 1/8 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (/.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(-.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal -1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(-.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal -1/2 binary64) k)))
(+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k)) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))))
(+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k k) k)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (neg.f64 (neg.f64 k)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 k))
(/.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 (sqrt.f64 k) k)
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))
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(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 k) (*.f64 k k))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 k k) (*.f64 #s(literal 1 binary64) (neg.f64 k)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(neg.f64 (-.f64 k #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
(fma.f64 k #s(literal -1 binary64) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 k))) (/.f64 (*.f64 k k) (-.f64 #s(literal 1 binary64) (neg.f64 k))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k)) (/.f64 (*.f64 k k) (+.f64 #s(literal 1 binary64) k)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k)))) (/.f64 (*.f64 (*.f64 k k) k) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k)))))
(-.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 k)))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 k k) (*.f64 #s(literal 1 binary64) (neg.f64 k))))) (/.f64 (*.f64 (neg.f64 k) (*.f64 k k)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 k k) (*.f64 #s(literal 1 binary64) (neg.f64 k))))))
(+.f64 (neg.f64 k) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 k))
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) k))
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#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (fma.f64 k (fma.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k) #s(literal 1/8 binary64))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
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#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx k k)
#s(approx (/ (sqrt k) k) (/.f64 (sqrt.f64 k) k))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
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#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (* n (/ (PI) k)) 2) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))
#s(approx (* n (/ (PI) k)) (*.f64 (/.f64 (PI.f64) k) n))
#s(approx (/ (PI) k) (/.f64 (PI.f64) k))
#s(approx (* (* (* (PI) n) k) 2) (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
#s(approx (* (* (PI) n) k) (*.f64 (*.f64 k n) (PI.f64)))
#s(approx (* k k) (*.f64 k k))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (/ (sqrt 2) k) (/.f64 (sqrt.f64 #s(literal 2 binary64)) k))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
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#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (fma.f64 (neg.f64 k) (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (fma.f64 k (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (fma.f64 k (fma.f64 k (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k) #s(literal -1/6 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/2 binary64))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (-.f64 #s(literal 1 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (/ (sqrt k) k) (/.f64 (sqrt.f64 k) k))
#s(approx (sqrt k) (sqrt.f64 k))
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#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64))))
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#s(approx (- 1 k) (neg.f64 k))
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#s(approx (* (+ (PI) (PI)) n) (*.f64 n (+.f64 (PI.f64) (PI.f64))))
#s(approx n n)
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#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) n)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (neg.f64 (*.f64 n (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (neg.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) n) k) (sqrt.f64 k))))
#s(approx (sqrt (* (PI) n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))

eval84.0ms (1.3%)

Memory
-22.8MiB live, 130.3MiB allocated; 23ms collecting garbage
Compiler

Compiled 6 065 to 2 005 computations (66.9% saved)

prune51.0ms (0.8%)

Memory
16.9MiB live, 108.4MiB allocated; 7ms collecting garbage
Pruning

54 alts after pruning (46 fresh and 8 done)

PrunedKeptTotal
New49824522
Fresh92231
Picked145
Done145
Total50954563
Accuracy
100.0%
Counts
563 → 54
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.8%
(/.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
99.4%
(/.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))
99.0%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
51.9%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
98.9%
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 k))
99.0%
(/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) k)
98.9%
(/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (neg.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
98.9%
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
72.0%
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) k))
95.7%
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
99.4%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 k) k))
48.6%
(*.f64 (/.f64 (sqrt.f64 k) k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
48.6%
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
95.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
48.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))))
48.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))))
48.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.0%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
43.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (/.f64 (sqrt.f64 k) k)))
49.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
43.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (sqrt.f64 k) k)))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
48.7%
#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)))
37.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
34.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) k))))
43.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 n) k)))
48.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (/.f64 (sqrt.f64 k) k))))
48.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k)) k))))
48.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))))
43.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) k)))))
48.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k)))))
48.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 k) k)))))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
37.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k)))))
37.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64)))))
43.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) #s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) n) k) (sqrt.f64 k)))))
49.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 (sqrt.f64 k) k)))
37.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 k n) (PI.f64)) k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
36.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
36.8%
#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)))))
28.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 k k)))))
48.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
24.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
27.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
3.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
3.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (neg.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (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))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Compiler

Compiled 2 207 to 1 470 computations (33.4% saved)

regimes143.0ms (2.2%)

Memory
11.0MiB live, 109.8MiB allocated; 10ms collecting garbage
Counts
85 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.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(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 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 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 (sqrt.f64 k) k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.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 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 k n) (PI.f64)) k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) #s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) n) k) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 k) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) #s(literal -1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (neg.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 k))))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 k) k) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) k)
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 k) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (neg.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) k))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (*.f64 (/.f64 (sqrt.f64 k) k) k))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (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 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
Outputs
(/.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))
Calls

4 calls:

48.0ms
(*.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))))
48.0ms
n
21.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
21.0ms
k
Results
AccuracySegmentsBranch
99.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
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%1k
99.4%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes99.0ms (1.5%)

Memory
-39.2MiB live, 122.2MiB allocated; 66ms collecting garbage
Counts
52 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.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(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 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 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 (sqrt.f64 k) k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.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 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 k n) (PI.f64)) k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) #s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) n) k) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 k) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) #s(literal -1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (neg.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 k))))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
Outputs
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
Calls

4 calls:

42.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
16.0ms
k
13.0ms
n
12.0ms
(*.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
99.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.0%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.0%1k
99.0%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes61.0ms (0.9%)

Memory
5.0MiB live, 140.7MiB allocated; 11ms collecting garbage
Counts
51 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.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(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 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 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 (sqrt.f64 k) k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.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 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 k n) (PI.f64)) k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) #s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) n) k) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 k) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) #s(literal -1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (neg.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 k))))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
Calls

4 calls:

16.0ms
k
16.0ms
n
14.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms
(*.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
71.7%4(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
95.8%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))))
95.8%2k
71.7%4n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes54.0ms (0.8%)

Memory
13.6MiB live, 115.1MiB allocated; 6ms collecting garbage
Counts
48 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.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(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 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 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 (sqrt.f64 k) k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.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 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 k n) (PI.f64)) k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (/.f64 (sqrt.f64 k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) #s(approx (/ (sqrt (* (PI) n)) (/ (sqrt k) k)) (/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) n) k) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 k) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 k) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (exp.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) k)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) #s(literal -1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (neg.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.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)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Calls

4 calls:

15.0ms
k
13.0ms
n
12.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms
(*.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
64.3%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
64.3%2n
64.2%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))))
64.2%2k
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes14.0ms (0.2%)

Memory
-19.7MiB live, 26.9MiB allocated; 1ms collecting garbage
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.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(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 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 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 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) k) #s(literal 2 binary64)))))
Calls

4 calls:

4.0ms
n
3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms
k
3.0ms
(*.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
48.7%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))))
48.7%1k
48.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
48.7%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes10.0ms (0.1%)

Memory
21.7MiB live, 21.6MiB allocated; 0ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.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(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 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)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
Calls

4 calls:

2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
k
2.0ms
n
2.0ms
(*.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
48.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
48.7%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))))
48.7%1k
48.7%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes10.0ms (0.2%)

Memory
-26.4MiB live, 19.3MiB allocated; 3ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.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(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 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)))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
Calls

4 calls:

3.0ms
k
2.0ms
n
2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
(*.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
36.8%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.8%1n
36.8%1k
36.8%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes7.0ms (0.1%)

Memory
11.5MiB live, 11.5MiB allocated; 0ms collecting garbage
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.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(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
Calls

4 calls:

2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
n
1.0ms
k
1.0ms
(*.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
36.7%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))))
36.7%1k
36.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.7%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes4.0ms (0.1%)

Memory
12.4MiB live, 12.4MiB allocated; 0ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
Calls

4 calls:

1.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
(*.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))))
1.0ms
k
1.0ms
n
Results
AccuracySegmentsBranch
36.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
36.6%1k
36.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.6%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch8.0ms (0.1%)

Memory
8.1MiB live, 8.1MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
7.0ms
0.6945737974343417
1.2860138573419142
Samples
4.0ms64×0valid
0.0ms0invalid
Compiler

Compiled 159 to 158 computations (0.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-div!: 1.0ms (34.4% of total)
ival-pow: 1.0ms (34.4% of total)
ival-mult!: 1.0ms (34.4% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)

bsearch35.0ms (0.5%)

Memory
-24.4MiB live, 26.7MiB allocated; 6ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
33.0ms
7.459160780822727e-61
4.481520440670534e-47
Samples
27.0ms160×0valid
Compiler

Compiled 499 to 478 computations (4.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-pow: 18.0ms (78.3% of total)
ival-div!: 2.0ms (8.7% of total)
ival-sqrt: 1.0ms (4.3% of total)
ival-mult!: 1.0ms (4.3% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

derivations286.0ms (4.4%)

Memory
12.6MiB live, 201.0MiB allocated; 14ms collecting garbage
Stop Event
fuel
Compiler

Compiled 96 to 66 computations (31.3% saved)

preprocess133.0ms (2.1%)

Memory
1.0MiB live, 141.5MiB allocated; 9ms collecting garbage
Compiler

Compiled 111 to 79 computations (28.8% saved)

end0.0ms (0%)

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

Profiling

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