Migdal et al, Equation (51)

Time bar (total: 6.5s)

start0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze121.0ms (1.9%)

Memory
24.1MiB live, 311.3MiB allocated; 23ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%51.5%0%7
52.5%25%22.6%0.1%0%52.3%0%8
53.8%25%21.5%0.1%0%53.5%0%9
54.5%25%20.9%0.1%0%54%0%10
55.3%25%20.2%0.1%0%54.7%0%11
55.7%25%19.9%0.1%0%55.1%0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.0s (45.6%)

Memory
99.3MiB live, 4 086.9MiB allocated; 916ms collecting garbage
Samples
1.3s5 592×1invalid
952.0ms8 256×0valid
129.0ms498×2invalid
43.0ms234×0exit
20.0ms359×0invalid
Precisions
Click to see histograms. Total time spent on operations: 1.7s
ival-pow: 571.0ms (34% of total)
adjust: 322.0ms (19.2% of total)
ival-mult!: 309.0ms (18.4% of total)
ival-div!: 221.0ms (13.2% of total)
ival-sqrt: 197.0ms (11.7% of total)
ival-sub!: 60.0ms (3.6% of total)
ival-pi: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

preprocess69.0ms (1.1%)

Memory
-45.1MiB live, 51.2MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033104
110890
234588
3150388
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(*.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)

series87.0ms (1.3%)

Memory
39.6MiB live, 126.2MiB allocated; 18ms 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
46.0ms
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))
26.0ms
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))
8.0ms
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))

rewrite248.0ms (3.8%)

Memory
20.1MiB live, 297.4MiB allocated; 113ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01671003
0181956
1765852
06608834
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
50 → 216
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 4 binary64)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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 4 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (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) (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 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.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) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.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)))
(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
(*.f64 (*.f64 #s(literal 1 binary64) (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 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
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(+.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 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)))
(neg.f64 (+.f64 #s(literal -1 binary64) k))
(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) (*.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 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 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)) (/.f64 (neg.f64 k) (sqrt.f64 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 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k)) (neg.f64 k)))
#s(approx (- 1 k) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)) (neg.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 (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 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))))))

eval26.0ms (0.4%)

Memory
-32.3MiB live, 59.4MiB allocated; 9ms collecting garbage
Compiler

Compiled 2 273 to 825 computations (63.7% saved)

prune11.0ms (0.2%)

Memory
33.6MiB live, 33.6MiB allocated; 0ms collecting garbage
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New18814202
Fresh000
Picked101
Done000
Total18914203
Accuracy
100.0%
Counts
203 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.3%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
72.4%
(*.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))))
▶99.1%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
▶99.0%
(*.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))))
72.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
52.3%
(*.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))))
99.5%
(*.f64 (*.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))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶99.6%
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (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))))
44.7%
#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))))
52.6%
#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)))
▶99.2%
#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)) (/.f64 k (sqrt.f64 k))))
▶40.4%
#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 628 to 498 computations (20.7% saved)

series190.0ms (2.9%)

Memory
-20.1MiB live, 358.0MiB allocated; 47ms collecting garbage
Counts
38 → 124
Calls
Call 1
Inputs
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (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))))
#s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k))
(/.f64 (sqrt.f64 k) k)
(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(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
#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)) (/.f64 k (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 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 k (sqrt.f64 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 #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 (*.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)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.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 4 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))
#s(literal 4 binary64)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 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) k) #s(hole binary64 (/ (sqrt k) 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))))
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#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))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
Calls

6 calls:

TimeVariablePointExpression
71.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (/ k (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ (- 1 k) 4) 4 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))))
57.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (/ k (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ (- 1 k) 4) 4 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))))
34.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (/ k (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ (- 1 k) 4) 4 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))))
13.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (/ k (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ (- 1 k) 4) 4 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))))
7.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (/ k (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* (sqrt 2) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt (* (PI) n)))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ (- 1 k) 4) 4 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))))

rewrite215.0ms (3.3%)

Memory
-5.7MiB live, 243.5MiB allocated; 54ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05814912
06444157
130683868
089333810
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
162 → 631
Calls
Call 1
Inputs
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (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))))
#s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k))
(/.f64 (sqrt.f64 k) k)
(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(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
#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)) (/.f64 k (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 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 k (sqrt.f64 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 #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 (*.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)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.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 4 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))
#s(literal 4 binary64)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 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) k) #s(hole binary64 (/ (sqrt k) 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 (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)) (/ k (sqrt k))) #s(hole binary64 (/ (* (sqrt k) (sqrt (* 2 (* n (PI))))) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (+ (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (* (sqrt k) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (* (sqrt k) (sqrt (* 2 (* n (PI))))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI))))))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) 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 (/ k (sqrt k)) #s(hole binary64 (/ k (sqrt k))))
#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))))
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#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 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) #s(hole binary64 (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* -1/64 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* -1/192 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))))))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/4)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) #s(hole binary64 (+ (* -1/4 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/4)))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/4))) (* 1/32 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/4)))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/4))) (* k (+ (* -1/384 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/4)))) (* 1/32 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/4))))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (/ (- 1 k) 4) #s(hole binary64 1/4))
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#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/4) (sqrt k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* -1/4 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/4))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/4) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1/4 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/4)) (sqrt k))) (* 1/32 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/4))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/4) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1/4 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/4)) (sqrt k))) (* k (+ (* -1/384 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/4))) (sqrt k))) (* 1/32 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/4)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/4) (sqrt 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) k) #s(hole binary64 (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 (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (* (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 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 (/ k (sqrt k)) #s(hole binary64 (/ 1 (sqrt (/ 1 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 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) #s(hole binary64 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 4) #s(hole binary64 (* -1/4 k)))
#s(approx (/ (- 1 k) 4) #s(hole binary64 (* k (- (* 1/4 (/ 1 k)) 1/4))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* 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 (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 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 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (* -1 (* (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 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 (/ k (sqrt k)) #s(hole binary64 (/ -1 (sqrt (/ 1 k)))))
#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 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) #s(hole binary64 (* -1 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 4) #s(hole binary64 (* -1 (* k (- 1/4 (* 1/4 (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) #s(hole binary64 (* -1 (/ (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (* (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k)) 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)))) (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 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt 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))))))
#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)) (/ k (sqrt k))) #s(hole binary64 (/ (* (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k)) 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 (* (/ 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 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt 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))))))
#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)) (/ k (sqrt k))) #s(hole binary64 (/ (* (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k)) 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 (* (/ 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))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
Outputs
(*.f64 (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)))
(*.f64 #s(approx (/ 1 (sqrt k)) (/.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))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (neg.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 k))
(/.f64 (sqrt.f64 k) k)
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 k) #s(literal 1 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
(/.f64 #s(literal 1 binary64) (pow.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)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 k)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
k
(*.f64 (fabs.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (fabs.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))) (fabs.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))))
(*.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 n) (-.f64 #s(literal 1 binary64) k)))
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(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
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(*.f64 (neg.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))) (neg.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))))
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#s(approx (/ k (sqrt k)) (/.f64 k (sqrt.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)))
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#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 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
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#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
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#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (*.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)))) k) #s(literal 1/8 binary64))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
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#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (fma.f64 (*.f64 #s(literal -1/4 binary64) k) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (fma.f64 k (fma.f64 (*.f64 (exp.f64 (fma.f64 (log.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) k) #s(literal 1/32 binary64) (*.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1/4 binary64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (exp.f64 (fma.f64 (log.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 3 binary64) (*.f64 #s(literal 1/4 binary64) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) k) #s(literal -1/384 binary64) (*.f64 (exp.f64 (fma.f64 (log.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) #s(literal 1/32 binary64))) k (*.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1/4 binary64))) k (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))))
#s(approx (/ (- 1 k) 4) #s(literal 1/4 binary64))
#s(approx (/ (- 1 k) 4) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) (/.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) k) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) (fma.f64 k (/.f64 (fma.f64 (*.f64 (exp.f64 (fma.f64 (log.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) k) #s(literal 1/32 binary64) (*.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1/4 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (sqrt.f64 k))))
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#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)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))
#s(approx (/ (sqrt k) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (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 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt 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))))
#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 (/ k (sqrt 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)) (*.f64 (/.f64 #s(literal 1 binary64) (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 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))))
#s(approx (/ (- 1 k) 4) (*.f64 #s(literal -1/4 binary64) k))
#s(approx (/ (- 1 k) 4) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))) k)))
#s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal -1 binary64) k) (sqrt.f64 k)))
#s(approx (/ (sqrt k) k) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (sqrt k) (*.f64 (neg.f64 k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))))
#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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (neg.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))))
#s(approx (/ k (sqrt k)) (*.f64 #s(literal -1 binary64) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))) k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (exp.f64 (*.f64 (*.f64 (+.f64 (neg.f64 k) #s(literal 1 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/4 binary64))))
#s(approx (/ (- 1 k) 4) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 (*.f64 (+.f64 (neg.f64 k) #s(literal 1 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/4 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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 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 (* (* 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 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (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 (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 (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)) (-.f64 #s(literal 1 binary64) k))) (/.f64 (sqrt.f64 k) 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 (* (/ 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 (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (sqrt.f64 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 #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 (sqrt (/ (* (+ (PI) (PI)) n) k)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.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))) (/.f64 (sqrt.f64 k) 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 (sqrt (* (+ (PI) (PI)) n)) (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 #s(literal 1/2 binary64) (fma.f64 (neg.f64 (log.f64 (neg.f64 n))) #s(literal -2 binary64) (log.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 (*.f64 #s(literal 1/2 binary64) (fma.f64 (neg.f64 (log.f64 (neg.f64 n))) #s(literal -2 binary64) (log.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (PI) n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) n)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k)))) (/.f64 (exp.f64 (*.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 1/4 binary64)) #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (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 1/4 binary64))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ 1 (sqrt k))) (/.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 1/4 binary64))) (sqrt.f64 k)))

eval62.0ms (0.9%)

Memory
23.5MiB live, 158.5MiB allocated; 13ms collecting garbage
Compiler

Compiled 7 050 to 2 052 computations (70.9% saved)

prune20.0ms (0.3%)

Memory
-9.5MiB live, 45.8MiB allocated; 5ms collecting garbage
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New49114505
Fresh729
Picked415
Done000
Total50217519
Accuracy
100.0%
Counts
519 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.3%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
▶99.3%
(/.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)))
▶99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
99.5%
(*.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 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.3%
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
52.3%
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
52.4%
#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)))
40.2%
#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))))
▶40.3%
#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))))
✓40.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
▶24.7%
#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))))
▶40.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
40.4%
#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))))
27.0%
#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)))))
37.7%
#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))))
42.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
49.9%
#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 700 to 627 computations (10.4% saved)

series97.0ms (1.5%)

Memory
15.5MiB live, 199.6MiB allocated; 26ms collecting garbage
Counts
36 → 84
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(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 n k)
#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))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#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))))
(sqrt.f64 (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)) (*.f64 k k)))
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)) (*.f64 k k))
(*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))
(*.f64 #s(literal 2 binary64) k)
(*.f64 (PI.f64) n)
(*.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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #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) (+ (* -1/2 k) 1/2)) #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) (+ (* -1/2 k) 1/2)) #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 (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 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 (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (/ (* (sqrt 2) (sqrt (* k (* n (PI))))) k)))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (/ (sqrt (* k (* 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 (* (* 2 k) (* (PI) n)) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* 2 k) #s(hole binary64 (* 2 k)))
#s(approx (* k k) #s(hole binary64 (pow k 2)))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) 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 (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/6 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt 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)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k)))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* k (+ (* 1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt k)))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 1))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* k (+ (* 1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #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 (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (sqrt (/ (* n (PI)) k)))))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (pow (sqrt (* 2 (* n (PI)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* -1 (/ (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #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 (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* -1 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
#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) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 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 (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* n (* (sqrt 2) (sqrt (/ (PI) (* k n)))))))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (* n (sqrt (/ (PI) (* k n))))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k)))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 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 (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* -1 (* n (* (sqrt 2) (sqrt (/ (PI) (* k n))))))))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) (* k n)))))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
Calls

6 calls:

TimeVariablePointExpression
27.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (+ (* -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)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (/ (PI) k))) (sqrt 2)) (sqrt (* n (/ (PI) k))) (* n (/ (PI) k)) (/ (PI) k) (sqrt 2) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* 2 k) (* (PI) n)) (* k k))) (/ (* (* 2 k) (* (PI) n)) (* k k)) (* (* 2 k) (* (PI) n)) (* 2 k) (* (PI) n) (* k k) (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k))
25.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (+ (* -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)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (/ (PI) k))) (sqrt 2)) (sqrt (* n (/ (PI) k))) (* n (/ (PI) k)) (/ (PI) k) (sqrt 2) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* 2 k) (* (PI) n)) (* k k))) (/ (* (* 2 k) (* (PI) n)) (* k k)) (* (* 2 k) (* (PI) n)) (* 2 k) (* (PI) n) (* k k) (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k))
24.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (+ (* -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)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (/ (PI) k))) (sqrt 2)) (sqrt (* n (/ (PI) k))) (* n (/ (PI) k)) (/ (PI) k) (sqrt 2) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* 2 k) (* (PI) n)) (* k k))) (/ (* (* 2 k) (* (PI) n)) (* k k)) (* (* 2 k) (* (PI) n)) (* 2 k) (* (PI) n) (* k k) (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k))
7.0ms
k
@inf
((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (+ (* -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)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (/ (PI) k))) (sqrt 2)) (sqrt (* n (/ (PI) k))) (* n (/ (PI) k)) (/ (PI) k) (sqrt 2) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* 2 k) (* (PI) n)) (* k k))) (/ (* (* 2 k) (* (PI) n)) (* k k)) (* (* 2 k) (* (PI) n)) (* 2 k) (* (PI) n) (* k k) (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k))
6.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (+ (* -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)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (/ (PI) k))) (sqrt 2)) (sqrt (* n (/ (PI) k))) (* n (/ (PI) k)) (/ (PI) k) (sqrt 2) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* 2 k) (* (PI) n)) (* k k))) (/ (* (* 2 k) (* (PI) n)) (* k k)) (* (* 2 k) (* (PI) n)) (* 2 k) (* (PI) n) (* k k) (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k))

rewrite177.0ms (2.7%)

Memory
2.5MiB live, 284.6MiB allocated; 36ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03912740
04372490
118662383
083572355
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
120 → 498
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(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 n k)
#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))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#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))))
(sqrt.f64 (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)) (*.f64 k k)))
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)) (*.f64 k k))
(*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))
(*.f64 #s(literal 2 binary64) k)
(*.f64 (PI.f64) n)
(*.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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #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) (+ (* -1/2 k) 1/2)) #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) (+ (* -1/2 k) 1/2)) #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 (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 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 (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (/ (* (sqrt 2) (sqrt (* k (* n (PI))))) k)))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (/ (sqrt (* k (* 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 (* (* 2 k) (* (PI) n)) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* 2 k) #s(hole binary64 (* 2 k)))
#s(approx (* k k) #s(hole binary64 (pow k 2)))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) 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 (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/6 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt 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)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k)))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* k (+ (* 1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt k)))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 1))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* k (+ (* 1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #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 (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (sqrt (/ (* n (PI)) k)))))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (pow (sqrt (* 2 (* n (PI)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* -1 (/ (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #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 (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* -1 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
#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) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 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 (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* n (* (sqrt 2) (sqrt (/ (PI) (* k n)))))))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (* n (sqrt (/ (PI) (* k n))))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k)))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 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 (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* -1 (* n (* (sqrt 2) (sqrt (/ (PI) (* k n))))))))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) (* k n)))))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
Outputs
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (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 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.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))
(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)
(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
(*.f64 (fabs.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (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 (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 (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 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (exp.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 n))) (exp.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 n)) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 n)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (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 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (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 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)))
(pow.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (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 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (+.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (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))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (cosh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (-.f64 (*.f64 (sinh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sinh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (*.f64 (cosh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sinh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))))))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(exp.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(+.f64 (cosh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sinh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(*.f64 (fabs.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (fabs.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (exp.f64 (log.f64 (+.f64 (PI.f64) (PI.f64)))) (exp.f64 (log.f64 n)))
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (+.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))
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#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(literal 1 binary64))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k #s(literal 1 binary64)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (fma.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)) k) #s(literal 1/2 binary64) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k #s(literal 1 binary64)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 k (fma.f64 k (fma.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 3 binary64)) k) #s(literal 1/6 binary64) (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))
#s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (sqrt (* n (/ (PI) k))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (*.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (neg.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal -1 binary64) k) (sqrt.f64 k)))
#s(approx (sqrt k) (*.f64 (neg.f64 k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (+.f64 (neg.f64 k) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) k) (sqrt.f64 k)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (*.f64 (neg.f64 k) (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (* (+ (PI) (PI)) n) (*.f64 n (+.f64 (PI.f64) (PI.f64))))
#s(approx n n)
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (* (PI) n) (*.f64 (PI.f64) n))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (/.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 k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n))
#s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (*.f64 (/.f64 n (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)))) k))) (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (*.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)))) k)) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (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)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (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)))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (/.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 k))) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (sqrt (* n (/ (PI) k))) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 n (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)))) k))))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (*.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)))) k)) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) 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)))) k)))

eval779.0ms (12%)

Memory
-119.6MiB live, 193.5MiB allocated; 1.3s collecting garbage
Compiler

Compiled 5 821 to 1 675 computations (71.2% saved)

prune23.0ms (0.4%)

Memory
11.9MiB live, 58.6MiB allocated; 2ms collecting garbage
Pruning

25 alts after pruning (22 fresh and 3 done)

PrunedKeptTotal
New40014414
Fresh3811
Picked325
Done011
Total40625431
Accuracy
100.0%
Counts
431 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.3%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
58.1%
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k #s(literal 1 binary64))) (sqrt.f64 k)))
75.2%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k))
52.3%
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
▶99.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
52.4%
#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)))
42.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 k k) (PI.f64)) n)) k))
52.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
52.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
40.2%
#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))))
40.2%
#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 k k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k k)))))
✓40.3%
#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))))
40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
41.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) k)))
37.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
▶49.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64))))
✓40.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
✓40.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
28.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 k k) (/.f64 (*.f64 (PI.f64) n) (*.f64 k k)))))
▶40.4%
#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))))
27.0%
#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)))))
▶37.7%
#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))))
▶42.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
49.9%
#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 1 059 to 991 computations (6.4% saved)

series261.0ms (4%)

Memory
5.4MiB live, 384.5MiB allocated; 22ms collecting garbage
Counts
37 → 85
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) 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)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)
(sqrt.f64 (/.f64 (PI.f64) (*.f64 n k)))
(/.f64 (PI.f64) (*.f64 n k))
(*.f64 n k)
(sqrt.f64 #s(literal 2 binary64))
#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)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #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 (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #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 (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #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 (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (* (sqrt k) (sqrt (* 2 (* n (PI))))) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (+ (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (* (sqrt k) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (* (sqrt k) (sqrt (* 2 (* n (PI))))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI))))))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (* k (* n (PI)))))))
#s(approx (* (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (/ (* (sqrt 2) (sqrt (* k (* n (PI))))) k)))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (/ (sqrt (* k (* n (PI)))) k)))
#s(approx (* (sqrt (/ (PI) (* n k))) n) #s(hole binary64 (/ (* n (sqrt (/ (* k (PI)) n))) k)))
#s(approx (sqrt (/ (PI) (* n k))) #s(hole binary64 (/ (sqrt (/ (* k (PI)) n)) k)))
#s(approx (/ (PI) (* n k)) #s(hole binary64 (/ (PI) (* k n))))
#s(approx (* n k) #s(hole binary64 (* k n)))
#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)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (* (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt (/ 1 k)))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* k (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (sqrt (/ (* n (PI)) k)))))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (* (sqrt (/ (PI) (* n k))) n) #s(hole binary64 (* n (sqrt (/ (PI) (* k n))))))
#s(approx (sqrt (/ (PI) (* n k))) #s(hole binary64 (sqrt (/ (PI) (* k n)))))
#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)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* -1 (/ (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (* -1 (* (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (sqrt (/ 1 k))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* k (sqrt (* 2 (/ (* n (PI)) 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)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (sqrt k))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* n (+ (PI) (PI))) #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)) (/ k (sqrt k))) #s(hole binary64 (/ (* (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k)) k)))
#s(approx (sqrt (/ (PI) (* n k))) #s(hole binary64 (/ (sqrt (/ (* n (PI)) k)) n)))
#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)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 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 (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (* (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k)) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* n (sqrt (* 2 (/ (* k (PI)) n))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* n (* (sqrt 2) (sqrt (/ (PI) (* k 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)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 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 (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (* (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k)) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (* k (PI)) n)))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* -1 (* n (* (sqrt 2) (sqrt (/ (PI) (* k n))))))))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) (* k 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))))))
Calls

6 calls:

TimeVariablePointExpression
82.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (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))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (/ (PI) k))) (sqrt 2)) (sqrt (* n (/ (PI) k))) (* (sqrt (/ (PI) (* n k))) n) (sqrt (/ (PI) (* n k))) (/ (PI) (* n k)) (* n k) (sqrt 2) (* (/ 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))
54.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (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))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (/ (PI) k))) (sqrt 2)) (sqrt (* n (/ (PI) k))) (* (sqrt (/ (PI) (* n k))) n) (sqrt (/ (PI) (* n k))) (/ (PI) (* n k)) (* n k) (sqrt 2) (* (/ 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))
52.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (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))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (/ (PI) k))) (sqrt 2)) (sqrt (* n (/ (PI) k))) (* (sqrt (/ (PI) (* n k))) n) (sqrt (/ (PI) (* n k))) (/ (PI) (* n k)) (* n k) (sqrt 2) (* (/ 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))
36.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (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))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (/ (PI) k))) (sqrt 2)) (sqrt (* n (/ (PI) k))) (* (sqrt (/ (PI) (* n k))) n) (sqrt (/ (PI) (* n k))) (/ (PI) (* n k)) (* n k) (sqrt 2) (* (/ 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))
20.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (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))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (* (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* n (/ (PI) k))) (sqrt 2)) (sqrt (* n (/ (PI) k))) (* (sqrt (/ (PI) (* n k))) n) (sqrt (/ (PI) (* n k))) (/ (PI) (* n k)) (* n k) (sqrt 2) (* (/ 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))

rewrite184.0ms (2.8%)

Memory
-31.3MiB live, 208.3MiB allocated; 30ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03942618
04372486
117262429
081272411
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
122 → 405
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) 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)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)
(sqrt.f64 (/.f64 (PI.f64) (*.f64 n k)))
(/.f64 (PI.f64) (*.f64 n k))
(*.f64 n k)
(sqrt.f64 #s(literal 2 binary64))
#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)
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #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 (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #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 (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #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 (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #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 (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (* (sqrt k) (sqrt (* 2 (* n (PI))))) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (+ (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (* (sqrt k) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (* (sqrt k) (sqrt (* 2 (* n (PI))))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI))))))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (* k (* n (PI)))))))
#s(approx (* (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (/ (* (sqrt 2) (sqrt (* k (* n (PI))))) k)))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (/ (sqrt (* k (* n (PI)))) k)))
#s(approx (* (sqrt (/ (PI) (* n k))) n) #s(hole binary64 (/ (* n (sqrt (/ (* k (PI)) n))) k)))
#s(approx (sqrt (/ (PI) (* n k))) #s(hole binary64 (/ (sqrt (/ (* k (PI)) n)) k)))
#s(approx (/ (PI) (* n k)) #s(hole binary64 (/ (PI) (* k n))))
#s(approx (* n k) #s(hole binary64 (* k n)))
#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)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (* (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt (/ 1 k)))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* k (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (sqrt (/ (* n (PI)) k)))))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (* (sqrt (/ (PI) (* n k))) n) #s(hole binary64 (* n (sqrt (/ (PI) (* k n))))))
#s(approx (sqrt (/ (PI) (* n k))) #s(hole binary64 (sqrt (/ (PI) (* k n)))))
#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)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* -1 (/ (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (* -1 (* (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (sqrt (/ 1 k))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* k (sqrt (* 2 (/ (* n (PI)) 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)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (sqrt k))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* n (+ (PI) (PI))) #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)) (/ k (sqrt k))) #s(hole binary64 (/ (* (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k)) k)))
#s(approx (sqrt (/ (PI) (* n k))) #s(hole binary64 (/ (sqrt (/ (* n (PI)) k)) n)))
#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)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 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 (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (* (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k)) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* n (sqrt (* 2 (/ (* k (PI)) n))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* n (* (sqrt 2) (sqrt (/ (PI) (* k 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)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 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 (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) #s(hole binary64 (/ (* (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k)) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (* k (PI)) n)))))))
#s(approx (* (sqrt (* n (/ (PI) k))) (sqrt 2)) #s(hole binary64 (* -1 (* n (* (sqrt 2) (sqrt (/ (PI) (* k n))))))))
#s(approx (sqrt (* n (/ (PI) k))) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) (* k 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))))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(+.f64 (/.f64 (cosh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) (/.f64 (sinh.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 2 binary64))) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 2 binary64))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (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 (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 (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 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (exp.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 n))) (exp.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (*.f64 n (PI.f64)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 n)) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 n)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (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 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (pow.f64 (+.f64 (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 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(*.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)))
(pow.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))
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#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (sqrt.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (* (+ (PI) (PI)) n) k) (*.f64 (*.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) k))
#s(approx (sqrt (* n (/ (PI) k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) k))
#s(approx (* (sqrt (/ (PI) (* n k))) n) (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) n) k))
#s(approx (sqrt (/ (PI) (* n k))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) k))
#s(approx (/ (PI) (* n k)) (/.f64 (PI.f64) (*.f64 n k)))
#s(approx (* n k) (*.f64 n k))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (+.f64 (PI.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 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 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)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt 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))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (sqrt (* n (/ (PI) k))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)))
#s(approx (* (sqrt (/ (PI) (* n k))) n) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n))
#s(approx (sqrt (/ (PI) (* n k))) (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (+.f64 (PI.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 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (neg.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (sqrt k) (*.f64 (neg.f64 k) (/.f64 #s(literal 1 binary64) (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 (neg.f64 k) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (neg.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (neg.f64 k) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) 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 n (PI.f64))))) #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 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (* n (+ (PI) (PI))) (*.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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 k) k)))
#s(approx (sqrt (/ (PI) (* n k))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) n))
#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)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
#s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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 (* (* n (/ (PI) k)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.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))) (/.f64 (sqrt.f64 k) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (/.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n) k))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) 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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.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 (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (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)))))
#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 n k))) n)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.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))) (/.f64 (sqrt.f64 k) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (neg.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (neg.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (sqrt (* n (/ (PI) k))) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)))
#s(approx (* (log (/ (* (+ (PI) (PI)) n) k)) 1/2) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k)) (/.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 #s(literal -2 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)))))

eval38.0ms (0.6%)

Memory
39.4MiB live, 85.1MiB allocated; 5ms collecting garbage
Compiler

Compiled 5 134 to 1 695 computations (67% saved)

prune35.0ms (0.5%)

Memory
-18.5MiB live, 73.9MiB allocated; 7ms collecting garbage
Pruning

36 alts after pruning (29 fresh and 7 done)

PrunedKeptTotal
New30517322
Fresh51217
Picked145
Done033
Total31136347
Accuracy
100.0%
Counts
347 → 36
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.3%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
58.1%
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k #s(literal 1 binary64))) (sqrt.f64 k)))
75.2%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k))
✓99.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
51.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
52.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 #s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
52.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
52.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
40.2%
#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))))
40.2%
#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 k k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k k)))))
✓40.3%
#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))))
52.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
41.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) k)))
52.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 k)) n)) (sqrt.f64 #s(literal 2 binary64))))
48.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) n)) n)) (sqrt.f64 #s(literal 2 binary64))))
✓49.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64))))
54.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 #s(approx (sqrt (/ (PI) (* n k))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) k)) n)) (sqrt.f64 #s(literal 2 binary64))))
54.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) #s(approx (* (sqrt (/ (PI) (* n k))) n) (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) n) k))) (sqrt.f64 #s(literal 2 binary64))))
37.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (log.f64 k)))))
✓40.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
✓40.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
28.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 k k) (/.f64 (*.f64 (PI.f64) n) (*.f64 k k)))))
✓40.4%
#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))))
40.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
27.0%
#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)))))
37.7%
#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)) k) n)))))
37.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
41.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
52.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
42.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
✓42.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
27.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k)))
54.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n)) k)))
45.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))))
49.9%
#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 1 625 to 1 153 computations (29% saved)

regimes72.0ms (1.1%)

Memory
12.0MiB live, 149.2MiB allocated; 15ms collecting garbage
Counts
60 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (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 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 #s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 k k) (PI.f64)) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) n)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 k k) (/.f64 (*.f64 (PI.f64) n) (*.f64 k 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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 k)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 k k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) #s(approx (* (sqrt (/ (PI) (* n k))) n) (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) n) k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 #s(approx (sqrt (/ (PI) (* n k))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) k)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.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))) (sqrt.f64 (exp.f64 (log.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (log.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64))) (sqrt.f64 #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))) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(/.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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
#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)) (/.f64 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 #s(approx (/ 1 (sqrt k)) (/.f64 (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 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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k #s(literal 1 binary64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.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 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) 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)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.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 (*.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 (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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#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
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
Calls

4 calls:

20.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms
n
17.0ms
k
13.0ms
(*.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
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1k
99.7%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes78.0ms (1.2%)

Memory
15.3MiB live, 107.3MiB allocated; 43ms collecting garbage
Counts
42 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (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 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 #s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 k k) (PI.f64)) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) n)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 k k) (/.f64 (*.f64 (PI.f64) n) (*.f64 k 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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 k)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 k k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) #s(approx (* (sqrt (/ (PI) (* n k))) n) (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) n) k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 #s(approx (sqrt (/ (PI) (* n k))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) k)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.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))) (sqrt.f64 (exp.f64 (log.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (log.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64))) (sqrt.f64 #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))) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(/.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:

30.0ms
n
24.0ms
(*.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))))
11.0ms
k
11.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
99.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.3%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.3%1k
99.3%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes68.0ms (1%)

Memory
16.2MiB live, 145.8MiB allocated; 29ms collecting garbage
Counts
41 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (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 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 #s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 k k) (PI.f64)) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) n)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 k k) (/.f64 (*.f64 (PI.f64) n) (*.f64 k 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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 k)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 k k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) #s(approx (* (sqrt (/ (PI) (* n k))) n) (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) n) k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 #s(approx (sqrt (/ (PI) (* n k))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) k)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.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))) (sqrt.f64 (exp.f64 (log.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (log.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64))) (sqrt.f64 #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))) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
Calls

4 calls:

21.0ms
n
17.0ms
k
17.0ms
(*.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))))
11.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
77.6%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.2%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.2%2k
77.6%3n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes91.0ms (1.4%)

Memory
-14.2MiB live, 178.1MiB allocated; 67ms collecting garbage
Counts
38 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (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 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 #s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 k k) (PI.f64)) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) n)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 k k) (/.f64 (*.f64 (PI.f64) n) (*.f64 k 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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 k)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 k k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) #s(approx (* (sqrt (/ (PI) (* n k))) n) (/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) n) k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 #s(approx (sqrt (/ (PI) (* n k))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) k)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.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))) (sqrt.f64 (exp.f64 (log.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (log.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (log.f64 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) 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:

58.0ms
k
11.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms
n
9.0ms
(*.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
74.9%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
74.9%2n
74.9%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))))
65.8%2k
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes37.0ms (0.6%)

Memory
-23.3MiB live, 74.1MiB allocated; 12ms collecting garbage
Counts
27 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (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 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 #s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 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))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 k k) (PI.f64)) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ k (sqrt k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (sqrt (* n (/ (PI) k))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) n)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 k k) (/.f64 (*.f64 (PI.f64) n) (*.f64 k 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))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Calls

4 calls:

12.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
9.0ms
k
7.0ms
n
6.0ms
(*.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
61.5%2k
61.5%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
61.6%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
61.6%2n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes16.0ms (0.3%)

Memory
3.3MiB live, 49.7MiB allocated; 3ms collecting garbage
Counts
11 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (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 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.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 (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 #s(approx (pow (* n (+ (PI) (PI))) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 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 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
Calls

4 calls:

5.0ms
(*.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))))
4.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms
n
3.0ms
k
Results
AccuracySegmentsBranch
52.4%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))))
52.4%1k
52.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
52.4%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes11.0ms (0.2%)

Memory
36.8MiB live, 36.8MiB allocated; 0ms collecting garbage
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (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 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.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 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
Calls

4 calls:

3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
n
2.0ms
k
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
52.4%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))))
52.4%1k
52.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
52.4%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes9.0ms (0.1%)

Memory
-16.4MiB live, 30.1MiB allocated; 2ms collecting garbage
Accuracy

Total -0.1b remaining (-0.1%)

Threshold costs -0.1b (-0.1%)

Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (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 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
Calls

4 calls:

3.0ms
n
2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
k
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
40.4%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))))
40.4%1k
40.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
40.4%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch24.0ms (0.4%)

Memory
-16.0MiB live, 35.5MiB allocated; 7ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
22.0ms
1.5943189621616666e-12
133.19865180217755
Samples
16.0ms160×0valid
0.0ms1×0invalid
Compiler

Compiled 509 to 478 computations (6.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-pow: 3.0ms (41.3% of total)
ival-sqrt: 1.0ms (13.8% of total)
ival-div!: 1.0ms (13.8% of total)
ival-mult!: 1.0ms (13.8% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch12.0ms (0.2%)

Memory
22.1MiB live, 22.1MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
11.0ms
1.7778466570380274e-5
8.506934040606096e-5
Samples
7.0ms96×0valid
Compiler

Compiled 427 to 372 computations (12.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-pow: 2.0ms (42.6% of total)
ival-sqrt: 1.0ms (21.3% of total)
ival-div!: 1.0ms (21.3% of total)
ival-mult!: 1.0ms (21.3% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch13.0ms (0.2%)

Memory
-30.7MiB live, 14.2MiB allocated; 6ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
12.0ms
3.387915720311114e+49
4.921002620934117e+49
Samples
4.0ms64×0valid
Compiler

Compiled 211 to 202 computations (4.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-div!: 1.0ms (35.7% of total)
ival-pow: 1.0ms (35.7% of total)
ival-mult!: 1.0ms (35.7% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)

derivations387.0ms (5.9%)

Memory
62.6MiB live, 377.3MiB allocated; 155ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 136 to 84 computations (38.2% saved)

preprocess79.0ms (1.2%)

Memory
2.0MiB live, 139.4MiB allocated; 26ms collecting garbage
Compiler

Compiled 151 to 97 computations (35.8% saved)

end0.0ms (0%)

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

Profiling

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