Migdal et al, Equation (51)

Time bar (total: 9.8s)

start0.0ms (0%)

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

analyze133.0ms (1.4%)

Memory
-31.1MiB live, 208.1MiB allocated; 71ms 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)

sample3.9s (39.6%)

Memory
176.0MiB live, 4 246.4MiB allocated; 3.0s collecting garbage
Samples
1.4s5 485×1invalid
1.2s8 255×0valid
152.0ms497×2invalid
58.0ms246×0exit
19.0ms349×0invalid
0.0ms1×1valid
Precisions
Click to see histograms. Total time spent on operations: 2.0s
ival-pow: 623.0ms (30.7% of total)
ival-mult!: 404.0ms (19.9% of total)
adjust: 287.0ms (14.2% of total)
ival-sub!: 285.0ms (14.1% of total)
ival-div!: 279.0ms (13.8% of total)
ival-sqrt: 148.0ms (7.3% of total)
ival-pi: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

preprocess145.0ms (1.5%)

Memory
-19.2MiB live, 30.3MiB allocated; 180ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033104
110890
234488
3148888
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 30 to 26 computations (13.3% saved)

series217.0ms (2.2%)

Memory
63.5MiB live, 286.1MiB allocated; 158ms collecting garbage
Counts
13 → 35
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 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 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 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 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 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 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 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt -1)) (sqrt -1)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1))))))
#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 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Calls

6 calls:

TimeVariablePointExpression
106.0ms
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))
54.0ms
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))
39.0ms
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))
9.0ms
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))
4.0ms
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))

rewrite45.0ms (0.5%)

Memory
-36.9MiB live, 53.2MiB allocated; 35ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0186987
0200975
Stop Event
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
48 → 48
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 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 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 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 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 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 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 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt -1)) (sqrt -1)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1))))))
#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 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.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))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) k))
#s(approx (- 1 k) (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (/ 1 (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt k) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (* 2 (PI)) n) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))

eval4.0ms (0%)

Memory
10.4MiB live, 10.4MiB allocated; 0ms collecting garbage
Compiler

Compiled 627 to 228 computations (63.6% saved)

prune7.0ms (0.1%)

Memory
15.6MiB live, 15.6MiB allocated; 0ms collecting garbage
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New26935
Fresh000
Picked101
Done000
Total27936
Accuracy
99.9%
Counts
36 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
54.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
▶48.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
58.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
49.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
48.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
▶99.5%
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶55.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
▶40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
Compiler

Compiled 470 to 416 computations (11.5% saved)

series1.4s (14%)

Memory
-8.8MiB live, 783.3MiB allocated; 1.8s collecting garbage
Counts
46 → 92
Calls
Call 1
Inputs
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (PI.f64))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
#s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64))))
(*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))
(pow.f64 k #s(literal 3 binary64))
#s(literal 3 binary64)
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))
(*.f64 k (*.f64 n (PI.f64)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 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 (/ (* n (PI)) k)) (sqrt 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt (/ (* n (PI)) k)) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (/ (* n (PI)) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (+ 1/2 (* -1/2 k)) #s(hole binary64 1/2))
#s(approx (+ 1/2 (* -1/2 k)) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (sqrt (* (pow k 3) (* n (PI)))) #s(hole binary64 (sqrt (* (pow k 3) (* n (PI))))))
#s(approx (* (pow k 3) (* n (PI))) #s(hole binary64 (* (pow k 3) (* n (PI)))))
#s(approx (pow k 3) #s(hole binary64 (pow k 3)))
#s(approx (* (sqrt (* k (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (sqrt (* k (* n (PI)))) #s(hole binary64 (sqrt (* k (* n (PI))))))
#s(approx (* k (* n (PI))) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 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 (+ 1/2 (* -1/2 k)) #s(hole binary64 (* -1/2 k)))
#s(approx (+ 1/2 (* -1/2 k)) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt -1)) (sqrt -1)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (* (sqrt -1) (sqrt -1)))))
#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 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))
#s(approx (sqrt (/ (* n (PI)) k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -1) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1))))))
#s(approx (+ 1/2 (* -1/2 k)) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1 (* k (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))
#s(approx (sqrt (* (pow k 3) (* n (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt -1) (sqrt -1)))))
#s(approx (* (sqrt (* k (* n (PI)))) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))
#s(approx (sqrt (* k (* n (PI)))) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -1) (sqrt -1))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* n (PI)) #s(hole binary64 (* n (PI))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* 2 (* n (PI))) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) k)))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))
#s(approx (sqrt (/ (* n (PI)) k)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -1) (sqrt -1))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))) k))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
#s(approx (sqrt (* (pow k 3) (* n (PI)))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt -1) (sqrt -1))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
Calls

6 calls:

TimeVariablePointExpression
854.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (+ 1/2 (* -1/2 k)) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* (pow k 3) (* n (PI)))) (* (pow k 3) (* n (PI))) (pow k 3) 3 (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))))
150.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (+ 1/2 (* -1/2 k)) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* (pow k 3) (* n (PI)))) (* (pow k 3) (* n (PI))) (pow k 3) 3 (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))))
116.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (+ 1/2 (* -1/2 k)) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* (pow k 3) (* n (PI)))) (* (pow k 3) (* n (PI))) (pow k 3) 3 (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))))
100.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (+ 1/2 (* -1/2 k)) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* (pow k 3) (* n (PI)))) (* (pow k 3) (* n (PI))) (pow k 3) 3 (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))))
82.0ms
k
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (sqrt (/ (* n (PI)) k)) (/ (* n (PI)) k) (* n (PI)) (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (+ 1/2 (* -1/2 k)) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* (pow k 3) (* n (PI)))) (* (pow k 3) (* n (PI))) (pow k 3) 3 (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))))

rewrite63.0ms (0.6%)

Memory
-19.2MiB live, 75.4MiB allocated; 51ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03413225
04063204
Stop Event
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
138 → 139
Calls
Call 1
Inputs
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (PI.f64))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
#s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64))))
(*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))
(pow.f64 k #s(literal 3 binary64))
#s(literal 3 binary64)
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))
(*.f64 k (*.f64 n (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 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 (/ (* n (PI)) k)) (sqrt 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt (/ (* n (PI)) k)) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (/ (* n (PI)) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (+ 1/2 (* -1/2 k)) #s(hole binary64 1/2))
#s(approx (+ 1/2 (* -1/2 k)) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (sqrt (* (pow k 3) (* n (PI)))) #s(hole binary64 (sqrt (* (pow k 3) (* n (PI))))))
#s(approx (* (pow k 3) (* n (PI))) #s(hole binary64 (* (pow k 3) (* n (PI)))))
#s(approx (pow k 3) #s(hole binary64 (pow k 3)))
#s(approx (* (sqrt (* k (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (sqrt (* k (* n (PI)))) #s(hole binary64 (sqrt (* k (* n (PI))))))
#s(approx (* k (* n (PI))) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 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 (+ 1/2 (* -1/2 k)) #s(hole binary64 (* -1/2 k)))
#s(approx (+ 1/2 (* -1/2 k)) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt -1)) (sqrt -1)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (* (sqrt -1) (sqrt -1)))))
#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 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))
#s(approx (sqrt (/ (* n (PI)) k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -1) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1))))))
#s(approx (+ 1/2 (* -1/2 k)) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1 (* k (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))
#s(approx (sqrt (* (pow k 3) (* n (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt -1) (sqrt -1)))))
#s(approx (* (sqrt (* k (* n (PI)))) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))
#s(approx (sqrt (* k (* n (PI)))) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -1) (sqrt -1))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* n (PI)) #s(hole binary64 (* n (PI))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* 2 (* n (PI))) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) k)))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))
#s(approx (sqrt (/ (* n (PI)) k)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -1) (sqrt -1))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))) k))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
#s(approx (sqrt (* (pow k 3) (* n (PI)))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt -1) (sqrt -1))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
Outputs
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (PI.f64))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
#s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64))))
(*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))
(pow.f64 k #s(literal 3 binary64))
#s(literal 3 binary64)
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))
(*.f64 k (*.f64 n (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (sqrt (/ 1 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (/ 1 k) (/.f64 #s(literal 1 binary64) k))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
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#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
#s(approx (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (* n (PI)) k)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
#s(approx (/ (* n (PI)) k) (/.f64 (*.f64 n (PI.f64)) k))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (+ 1/2 (* -1/2 k)) #s(literal 1/2 binary64))
#s(approx (+ 1/2 (* -1/2 k)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (* -1/2 k) (*.f64 #s(literal -1/2 binary64) k))
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#s(approx (pow k 3) (pow.f64 k #s(literal 3 binary64)))
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#s(approx (sqrt (* k (* n (PI)))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))
#s(approx (* k (* n (PI))) (*.f64 k (*.f64 n (PI.f64))))
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#s(approx (/ (- 1 k) 2) (*.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
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#s(approx (+ 1/2 (* -1/2 k)) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ 1/2 (* -1/2 k)) (*.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
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#s(approx (sqrt (/ 1 k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
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#s(approx (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (* n (PI)) k)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
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#s(approx (+ 1/2 (* -1/2 k)) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k))))))
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#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))
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#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (sqrt (* (pow k 3) (* n (PI)))) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
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#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (* 2 (PI)) n) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
#s(approx n n)
#s(approx (* n (PI)) (*.f64 n (PI.f64)))
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#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
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#s(approx (log (* 2 (* n (PI)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
#s(approx (* 2 (* n (PI))) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
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#s(approx (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (sqrt (/ (* n (PI)) k)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) k)))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 #s(literal -1 binary64) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
#s(approx (sqrt (* (pow k 3) (* n (PI)))) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))
#s(approx (log (* 2 (* n (PI)))) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))

eval14.0ms (0.1%)

Memory
-20.8MiB live, 24.5MiB allocated; 6ms collecting garbage
Compiler

Compiled 2 160 to 594 computations (72.5% saved)

prune11.0ms (0.1%)

Memory
25.0MiB live, 25.0MiB allocated; 0ms collecting garbage
Pruning

14 alts after pruning (9 fresh and 5 done)

PrunedKeptTotal
New965101
Fresh044
Picked055
Done000
Total9614110
Accuracy
99.9%
Counts
110 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
▶54.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
✓48.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
58.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
▶49.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
▶48.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
✓99.5%
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
49.0%
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(approx (- 1 k) #s(literal 1 binary64)) #s(literal 2 binary64))))
48.8%
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
✓55.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
▶38.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
▶60.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
✓40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
3.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
Compiler

Compiled 768 to 673 computations (12.4% saved)

series1.4s (14.4%)

Memory
95.2MiB live, 1 700.2MiB allocated; 1.2s collecting garbage
Counts
56 → 129
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k)
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))
n
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(literal -1/2 binary64)
(*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
(/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)
(*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64))
(pow.f64 k #s(literal 3 binary64))
k
#s(literal 3 binary64)
(PI.f64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))
(log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))
#s(literal -1 binary64)
(log.f64 (/.f64 #s(literal 1 binary64) n))
(/.f64 #s(literal 1 binary64) n)
#s(literal 1 binary64)
(*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n))
(/.f64 (*.f64 k (PI.f64)) n)
(*.f64 k (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))
(*.f64 k (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) #s(hole binary64 (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))))
#s(approx (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) #s(hole binary64 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (sqrt (/ (* (pow k 3) (PI)) n)) #s(hole binary64 (sqrt (/ (* (pow k 3) (PI)) n))))
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#s(approx (sqrt (* k (* n (PI)))) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -1) (sqrt -1))))))
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#s(approx (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) #s(hole binary64 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
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#s(approx (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
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#s(approx (/ 1 n) #s(hole binary64 (/ 1 n)))
#s(approx (* n (PI)) #s(hole binary64 (* n (PI))))
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#s(approx (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))))
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#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))))
#s(approx (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
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#s(approx (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* k (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
Calls

6 calls:

TimeVariablePointExpression
365.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (* (pow k 3) (PI)) n)) (/ (* (pow k 3) (PI)) n) (* (pow k 3) (PI)) (pow k 3) k 3 (PI) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))) (sqrt 2) 2 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (log (* 2 (PI))) (* 2 (PI)) (* -1 (log (/ 1 n))) -1 (log (/ 1 n)) (/ 1 n) 1 (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (sqrt (/ (* k (PI)) n)) (/ (* k (PI)) n) (* k (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (/ (- 1 k) 2) (* -1/2 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))))
246.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (* (pow k 3) (PI)) n)) (/ (* (pow k 3) (PI)) n) (* (pow k 3) (PI)) (pow k 3) k 3 (PI) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))) (sqrt 2) 2 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (log (* 2 (PI))) (* 2 (PI)) (* -1 (log (/ 1 n))) -1 (log (/ 1 n)) (/ 1 n) 1 (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (sqrt (/ (* k (PI)) n)) (/ (* k (PI)) n) (* k (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (/ (- 1 k) 2) (* -1/2 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))))
222.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (* (pow k 3) (PI)) n)) (/ (* (pow k 3) (PI)) n) (* (pow k 3) (PI)) (pow k 3) k 3 (PI) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))) (sqrt 2) 2 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (log (* 2 (PI))) (* 2 (PI)) (* -1 (log (/ 1 n))) -1 (log (/ 1 n)) (/ 1 n) 1 (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (sqrt (/ (* k (PI)) n)) (/ (* k (PI)) n) (* k (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (/ (- 1 k) 2) (* -1/2 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))))
211.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (* (pow k 3) (PI)) n)) (/ (* (pow k 3) (PI)) n) (* (pow k 3) (PI)) (pow k 3) k 3 (PI) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))) (sqrt 2) 2 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (log (* 2 (PI))) (* 2 (PI)) (* -1 (log (/ 1 n))) -1 (log (/ 1 n)) (/ 1 n) 1 (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (sqrt (/ (* k (PI)) n)) (/ (* k (PI)) n) (* k (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (/ (- 1 k) 2) (* -1/2 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))))
204.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (* (pow k 3) (PI)) n)) (/ (* (pow k 3) (PI)) n) (* (pow k 3) (PI)) (pow k 3) k 3 (PI) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))) (sqrt 2) 2 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (log (* 2 (PI))) (* 2 (PI)) (* -1 (log (/ 1 n))) -1 (log (/ 1 n)) (/ 1 n) 1 (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (sqrt (/ (* k (PI)) n)) (/ (* k (PI)) n) (* k (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* (sqrt (* k (* n (PI)))) (sqrt 2)) (sqrt (* k (* n (PI)))) (* k (* n (PI))) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (/ (- 1 k) 2) (* -1/2 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))))

rewrite135.0ms (1.4%)

Memory
-19.6MiB live, 116.3MiB allocated; 155ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04625694
05505635
Stop Event
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
185 → 187
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k)
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))
n
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(literal -1/2 binary64)
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(sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
(/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)
(*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64))
(pow.f64 k #s(literal 3 binary64))
k
#s(literal 3 binary64)
(PI.f64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))
(log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))
#s(literal -1 binary64)
(log.f64 (/.f64 #s(literal 1 binary64) n))
(/.f64 #s(literal 1 binary64) n)
#s(literal 1 binary64)
(*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n))
(/.f64 (*.f64 k (PI.f64)) n)
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#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
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#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
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#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
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#s(approx (/ 1 n) #s(hole binary64 (/ 1 n)))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))) k))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (+ (log -1) (log (/ -1 n)))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (+ (log -1) (log (/ -1 n)))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))
#s(approx (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) #s(hole binary64 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (+ (log -1) (log (/ -1 n)))))))))))
#s(approx (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (+ (log -1) (log (/ -1 n))))))))
#s(approx (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (+ (log -1) (log (/ -1 n)))))))
#s(approx (* -1 (log (/ 1 n))) #s(hole binary64 (* -1 (+ (log -1) (log (/ -1 n))))))
#s(approx (log (/ 1 n)) #s(hole binary64 (+ (log -1) (log (/ -1 n)))))
#s(approx (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) #s(hole binary64 (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))
#s(approx (sqrt (/ (* k (PI)) n)) #s(hole binary64 (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (sqrt -1)))))
#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 (* n (PI))) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))
#s(approx (sqrt (* n (PI))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -1) (sqrt -1))))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) #s(hole binary64 (* -1 (* (* k (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (sqrt (* n (PI)))))))
#s(approx (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* k (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k)
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))
n
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(literal -1/2 binary64)
(*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
(/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)
(*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64))
(pow.f64 k #s(literal 3 binary64))
k
#s(literal 3 binary64)
(PI.f64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))
(log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))
#s(literal -1 binary64)
(log.f64 (/.f64 #s(literal 1 binary64) n))
(/.f64 #s(literal 1 binary64) n)
#s(literal 1 binary64)
(*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n))
(/.f64 (*.f64 k (PI.f64)) n)
(*.f64 k (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))
(*.f64 k (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
#s(approx (sqrt (/ (* (pow k 3) (PI)) n)) (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)))
#s(approx (/ (* (pow k 3) (PI)) n) (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
#s(approx (* (pow k 3) (PI)) (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)))
#s(approx (pow k 3) (pow.f64 k #s(literal 3 binary64)))
#s(approx k k)
#s(approx (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (* k (PI)) n)) (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)))
#s(approx (/ (* k (PI)) n) (/.f64 (*.f64 k (PI.f64)) n))
#s(approx (* k (PI)) (*.f64 k (PI.f64)))
#s(approx (* (sqrt (* k (* n (PI)))) (sqrt 2)) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (* k (* n (PI)))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))
#s(approx (* k (* n (PI))) (*.f64 k (*.f64 n (PI.f64))))
#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
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#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (* -1/2 k) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))
#s(approx (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (pow.f64 k #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (pow.f64 k #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (pow.f64 k #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
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#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 (pow.f64 k #s(literal 3 binary64)) n))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 k (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 (pow.f64 k #s(literal 3 binary64)) n))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))))))
#s(approx (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
#s(approx (sqrt (/ (* (pow k 3) (PI)) n)) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (sqrt (/ (* k (PI)) n)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (* (sqrt (* k (* n (PI)))) (sqrt 2)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (sqrt (* k (* n (PI)))) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (/ 1 (sqrt k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt k) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (*.f64 #s(literal -1 binary64) (*.f64 k (fma.f64 #s(literal -1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx n n)
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) n))
#s(approx (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
#s(approx (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
#s(approx (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
#s(approx (* -1 (log (/ 1 n))) (log.f64 n))
#s(approx (log (/ 1 n)) (*.f64 #s(literal -1 binary64) (log.f64 n)))
#s(approx (/ 1 n) (/.f64 #s(literal 1 binary64) n))
#s(approx (* n (PI)) (*.f64 n (PI.f64)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (sqrt (* n (PI))) (sqrt 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (* n (PI))) (sqrt.f64 (*.f64 n (PI.f64))))
#s(approx (* (* 2 (PI)) n) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64)))))
#s(approx (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
#s(approx (log (* 2 (* n (PI)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
#s(approx (* 2 (* n (PI))) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (/.f64 (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))
#s(approx (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))
#s(approx (* -1 (log (/ 1 n))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))
#s(approx (log (/ 1 n)) (log.f64 (/.f64 #s(literal 1 binary64) n)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (sqrt.f64 (/.f64 (PI.f64) n))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (sqrt.f64 (*.f64 n (PI.f64)))))
#s(approx (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))
#s(approx (log (* 2 (* n (PI)))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) k)))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 #s(literal -1 binary64) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
#s(approx (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
#s(approx (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))))))
#s(approx (* -1 (log (/ 1 n))) (*.f64 #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
#s(approx (log (/ 1 n)) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))))
#s(approx (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (* k (PI)) n)) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (sqrt (* n (PI))) (sqrt 2)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (sqrt (* n (PI))) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (*.f64 #s(literal -1 binary64) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (sqrt.f64 (/.f64 (PI.f64) n))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))
#s(approx (log (* 2 (* n (PI)))) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))

eval25.0ms (0.3%)

Memory
-17.3MiB live, 32.3MiB allocated; 23ms collecting garbage
Compiler

Compiled 3 793 to 965 computations (74.6% saved)

prune8.0ms (0.1%)

Memory
17.7MiB live, 17.7MiB allocated; 0ms collecting garbage
Pruning

13 alts after pruning (4 fresh and 9 done)

PrunedKeptTotal
New1401141
Fresh134
Picked145
Done055
Total14213155
Accuracy
99.9%
Counts
155 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
✓54.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
✓48.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
▶58.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
✓49.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
✓48.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
✓99.5%
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶48.8%
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
✓55.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
✓38.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
▶52.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
✓40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
▶3.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
Compiler

Compiled 427 to 373 computations (12.6% saved)

series1.9s (19.7%)

Memory
-29.9MiB live, 1 648.5MiB allocated; 2.6s collecting garbage
Counts
46 → 134
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
#s(literal -1/2 binary64)
(*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))
(*.f64 k (*.f64 n (PI.f64)))
k
(*.f64 n (PI.f64))
n
(PI.f64)
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k)
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n))
(/.f64 (*.f64 k (PI.f64)) n)
(*.f64 k (PI.f64))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))
#s(literal 1/8 binary64)
(*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (sqrt (* k (* n (PI)))) #s(hole binary64 (sqrt (* k (* n (PI))))))
#s(approx (* k (* n (PI))) #s(hole binary64 (* k (* n (PI)))))
#s(approx k #s(hole binary64 k))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) #s(hole binary64 (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))))
#s(approx (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) #s(hole binary64 (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))
#s(approx (sqrt (/ (* k (PI)) n)) #s(hole binary64 (sqrt (/ (* k (PI)) n))))
#s(approx (/ (* k (PI)) n) #s(hole binary64 (/ (* k (PI)) n)))
#s(approx (* k (PI)) #s(hole binary64 (* k (PI))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) #s(hole binary64 (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))))
#s(approx (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) #s(hole binary64 (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) #s(hole binary64 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))
#s(approx (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) #s(hole binary64 (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) #s(hole binary64 (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (PI) (* k n))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (PI) (* (pow k 3) n))) (sqrt 2))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (* 1/8 (* (* (pow k 2) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (/ (* (log (* 2 (* n (PI)))) (sqrt 2)) k) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))
#s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (/ (* (log (* 2 (* n (PI)))) (sqrt 2)) k) (sqrt (* n (PI))))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* (/ (sqrt 2) (pow k 2)) (sqrt (* n (PI)))))))))
#s(approx (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) #s(hole binary64 (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))))
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#s(approx (* n (PI)) #s(hole binary64 (* n (PI))))
#s(approx n #s(hole binary64 n))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
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#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (sqrt (* n (PI))) (sqrt 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
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#s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* 1/8 (* (* k (* (sqrt 2) (pow (+ (log n) (log (* 2 (PI)))) 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
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#s(approx (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) #s(hole binary64 (* (* k (* (sqrt 2) (pow (+ (log n) (log (* 2 (PI)))) 2))) (sqrt (* n (PI))))))
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Calls

6 calls:

TimeVariablePointExpression
948.0ms
n
@inf
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280.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* k (* n (PI)))) (* k (* n (PI))) k (* n (PI)) n (PI) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (sqrt (/ (* k (PI)) n)) (/ (* k (PI)) n) (* k (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (pow (log (* 2 (* n (PI)))) 2))
268.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* k (* n (PI)))) (* k (* n (PI))) k (* n (PI)) n (PI) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (sqrt (/ (* k (PI)) n)) (/ (* k (PI)) n) (* k (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (pow (log (* 2 (* n (PI)))) 2))
156.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* k (* n (PI)))) (* k (* n (PI))) k (* n (PI)) n (PI) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (sqrt (/ (* k (PI)) n)) (/ (* k (PI)) n) (* k (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (pow (log (* 2 (* n (PI)))) 2))
150.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* k (* n (PI)))) (* k (* n (PI))) k (* n (PI)) n (PI) (* (log (* 2 (* n (PI)))) (sqrt 2)) (log (* 2 (* n (PI)))) (* 2 (* n (PI))) 2 (sqrt 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (sqrt (/ (* k (PI)) n)) (/ (* k (PI)) n) (* k (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (pow (log (* 2 (* n (PI)))) 2))

rewrite66.0ms (0.7%)

Memory
-12.7MiB live, 81.8MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05037140
05747045
Stop Event
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
180 → 182
Calls
Call 1
Inputs
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k
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n
(PI.f64)
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#s(approx (pow (log (* 2 (* n (PI)))) 2) #s(hole binary64 (pow (+ (log n) (log (* 2 (PI)))) 2)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) k)))
#s(approx (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))))
#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 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (* n (+ (* k (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* 1/8 (* (* k (* (sqrt 2) (pow (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) 2))) (sqrt (/ (PI) n)))))) (* (sqrt (/ (PI) n)) (sqrt 2))))))
#s(approx (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* 1/8 (* (* k (* (sqrt 2) (pow (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) 2))) (sqrt (/ (PI) n))))))))
#s(approx (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) #s(hole binary64 (* 1/8 (* (* k (* (sqrt 2) (pow (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) 2))) (sqrt (* n (PI)))))))
#s(approx (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) #s(hole binary64 (* (* k (* (sqrt 2) (pow (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) 2))) (sqrt (* n (PI))))))
#s(approx (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) #s(hole binary64 (* k (* (sqrt 2) (pow (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) 2)))))
#s(approx (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (pow (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) 2))))
#s(approx (pow (log (* 2 (* n (PI)))) 2) #s(hole binary64 (pow (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) 2)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))) k))))
#s(approx (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) #s(hole binary64 (* 1/2 (* (sqrt (* k (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
#s(approx (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* 2 (* n (PI)))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (+ (log -1) (log (/ -1 n)))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (+ (log -1) (log (/ -1 n)))))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))
#s(approx (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) #s(hole binary64 (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2))))))
#s(approx (sqrt (/ (* k (PI)) n)) #s(hole binary64 (* (sqrt (/ (* k (PI)) n)) (* (sqrt -1) (sqrt -1)))))
#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 (* n (PI))) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))
#s(approx (sqrt (* n (PI))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -1) (sqrt -1))))))
#s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) #s(hole binary64 (* -1 (* n (+ (* k (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* 1/8 (* (* k (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2))))) (sqrt (/ (PI) n)))))) (* (sqrt (/ (PI) n)) (* (sqrt -1) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* 1/8 (* (* k (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2))))) (sqrt (/ (PI) n)))))))))
#s(approx (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
#s(approx (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) #s(hole binary64 (* -1/8 (* (* k (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2))))) (sqrt (* n (PI)))))))
#s(approx (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) #s(hole binary64 (* -1 (* (* k (* (sqrt -1) (* (sqrt -1) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2))))) (sqrt (* n (PI)))))))
#s(approx (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) #s(hole binary64 (* k (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))))
#s(approx (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2))))
#s(approx (pow (log (* 2 (* n (PI)))) 2) #s(hole binary64 (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
#s(literal -1/2 binary64)
(*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))
(*.f64 k (*.f64 n (PI.f64)))
k
(*.f64 n (PI.f64))
n
(PI.f64)
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k)
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n))
(/.f64 (*.f64 k (PI.f64)) n)
(*.f64 k (PI.f64))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))
#s(literal 1/8 binary64)
(*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
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#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) (*.f64 n (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (PI.f64) n)))))))
#s(approx (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
#s(approx (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))
#s(approx (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64)))))
#s(approx (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64))))
#s(approx (pow (log (* 2 (* n (PI)))) 2) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) #s(literal 2 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) k)))
#s(approx (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
#s(approx (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
#s(approx (* (log (* 2 (* n (PI)))) (sqrt 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))
#s(approx (log (* 2 (* n (PI)))) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
#s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 #s(literal -1 binary64) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (* (sqrt (/ (* k (PI)) n)) (sqrt 2)) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (* k (PI)) n)) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (sqrt (* n (PI))) (sqrt 2)) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (sqrt (* n (PI))) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) (*.f64 #s(literal -1 binary64) (*.f64 n (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))) (*.f64 #s(literal -1 binary64) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 (PI.f64) n))))))))
#s(approx (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
#s(approx (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 k (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 n (PI.f64))))))
#s(approx (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))))
#s(approx (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64))))
#s(approx (pow (log (* 2 (* n (PI)))) 2) (pow.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) #s(literal 2 binary64)))

eval18.0ms (0.2%)

Memory
-11.0MiB live, 34.1MiB allocated; 5ms collecting garbage
Compiler

Compiled 4 944 to 1 045 computations (78.9% saved)

prune13.0ms (0.1%)

Memory
32.6MiB live, 32.6MiB allocated; 0ms collecting garbage
Pruning

14 alts after pruning (1 fresh and 13 done)

PrunedKeptTotal
New1461147
Fresh000
Picked044
Done099
Total14614160
Accuracy
99.9%
Counts
160 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
✓54.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
✓48.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
✓58.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
✓49.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
✓48.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
36.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))) k) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))))
✓99.5%
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓48.8%
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
✓55.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
✓38.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
✓52.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
✓40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
✓3.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
Compiler

Compiled 920 to 610 computations (33.7% saved)

regimes22.0ms (0.2%)

Memory
-5.2MiB live, 41.5MiB allocated; 2ms collecting garbage
Counts
17 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(approx (- 1 k) #s(literal 1 binary64)) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #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)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))) k) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))))
Outputs
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Calls

4 calls:

6.0ms
n
5.0ms
k
5.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms
(*.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
99.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%1k
99.5%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes19.0ms (0.2%)

Memory
-19.8MiB live, 29.0MiB allocated; 9ms collecting garbage
Counts
10 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(approx (- 1 k) #s(literal 1 binary64)) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
Calls

4 calls:

8.0ms
(*.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))))
3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms
n
3.0ms
k
Results
AccuracySegmentsBranch
99.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%1k
99.5%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes13.0ms (0.1%)

Memory
26.7MiB live, 26.7MiB allocated; 0ms collecting garbage
Counts
9 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(approx (- 1 k) #s(literal 1 binary64)) #s(literal 2 binary64))))
Outputs
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(approx (- 1 k) #s(literal 1 binary64)) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
Calls

4 calls:

3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms
k
3.0ms
n
3.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
69.7%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
98.4%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))))
98.4%2k
69.7%3n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes7.0ms (0.1%)

Memory
-36.8MiB live, 9.2MiB allocated; 4ms collecting garbage
Counts
8 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
Calls

1 calls:

6.0ms
k
Results
AccuracySegmentsBranch
98.3%2k
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes11.0ms (0.1%)

Memory
29.1MiB live, 29.1MiB allocated; 0ms collecting garbage
Counts
7 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
Calls

4 calls:

3.0ms
k
3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms
n
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
61.1%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
61.1%2n
61.2%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
61.2%2k
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes11.0ms (0.1%)

Memory
-26.8MiB live, 19.8MiB allocated; 3ms collecting garbage
Counts
5 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 n #s(approx (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
Calls

4 calls:

4.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
k
2.0ms
n
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
61.1%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
61.1%2n
61.1%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))))
61.1%2k
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes8.0ms (0.1%)

Memory
18.9MiB live, 18.9MiB allocated; 0ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
Calls

4 calls:

2.0ms
(*.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
48.8%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
48.8%1k
48.8%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
48.8%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes7.0ms (0.1%)

Memory
16.9MiB live, 16.9MiB allocated; 0ms collecting garbage
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
Outputs
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
Calls

4 calls:

2.0ms
k
2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
n
1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
48.8%1k
48.8%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
48.8%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
48.8%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes7.0ms (0.1%)

Memory
-33.6MiB live, 13.4MiB allocated; 2ms collecting garbage
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k))
Calls

4 calls:

3.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
1.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
k
1.0ms
n
Results
AccuracySegmentsBranch
40.1%1k
48.9%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
48.8%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
48.8%2n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes3.0ms (0%)

Memory
8.9MiB live, 8.9MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) 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 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
Calls

3 calls:

1.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
n
1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
40.1%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
40.1%1n
40.1%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 21 to 21 computations (0% saved)

bsearch13.0ms (0.1%)

Memory
24.4MiB live, 24.4MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
12.0ms
0.030530262757410515
7.783522001973496
Samples
7.0ms112×0valid
Compiler

Compiled 278 to 284 computations (-2.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-pow: 2.0ms (39.8% of total)
ival-sqrt: 1.0ms (19.9% of total)
ival-div!: 1.0ms (19.9% of total)
ival-mult!: 1.0ms (19.9% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
2.4MiB live, 2.4MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
1.0ms
0.030530262757410515
7.783522001973496
Compiler

Compiled 264 to 277 computations (-4.9% saved)

bsearch19.0ms (0.2%)

Memory
-20.6MiB live, 30.4MiB allocated; 3ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
17.0ms
2.2876578685865702e-18
4.165599609362434e-11
Samples
10.0ms144×0valid
Compiler

Compiled 811 to 711 computations (12.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-pow: 3.0ms (45.4% of total)
ival-sqrt: 1.0ms (15.1% of total)
ival-div!: 1.0ms (15.1% of total)
ival-mult!: 1.0ms (15.1% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch12.0ms (0.1%)

Memory
19.2MiB live, 19.2MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
10.0ms
1.364511390963466e-19
1.1752808653777473e-18
Samples
7.0ms96×0valid
Compiler

Compiled 571 to 504 computations (11.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-pow: 2.0ms (45.1% of total)
ival-sqrt: 1.0ms (22.5% of total)
ival-div!: 1.0ms (22.5% of total)
ival-mult!: 1.0ms (22.5% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
7.631792925953922e+141
5.683743984366331e+142
Compiler

Compiled 18 to 18 computations (0% saved)

derivations17.0ms (0.2%)

Memory
-23.5MiB live, 21.8MiB allocated; 4ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 200 to 116 computations (42% saved)

preprocess139.0ms (1.4%)

Memory
33.0MiB live, 221.8MiB allocated; 80ms collecting garbage
Compiler

Compiled 215 to 129 computations (40% saved)

end0.0ms (0%)

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

Profiling

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