Migdal et al, Equation (51)

Time bar (total: 6.1s)

start0.0ms (0%)

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

analyze104.0ms (1.7%)

Memory
-65.4MiB live, 89.9MiB allocated; 26ms 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)

sample2.5s (41.2%)

Memory
105.6MiB live, 2 740.8MiB allocated; 462ms collecting garbage
Samples
1.1s5 551×1invalid
672.0ms8 256×0valid
109.0ms476×2invalid
43.0ms249×0exit
22.0ms370×0invalid
Precisions
Click to see histograms. Total time spent on operations: 1.3s
ival-pow: 405.0ms (32.1% of total)
ival-mult!: 216.0ms (17.1% of total)
adjust: 215.0ms (17% of total)
ival-div!: 196.0ms (15.5% of total)
ival-sqrt: 161.0ms (12.8% of total)
ival-sub!: 69.0ms (5.5% of total)
ival-pi: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

preprocess66.0ms (1.1%)

Memory
-44.7MiB live, 26.6MiB allocated; 36ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

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

(abs k)

Compiler

Compiled 30 to 26 computations (13.3% saved)

series71.0ms (1.2%)

Memory
38.1MiB live, 81.2MiB allocated; 10ms collecting garbage
Counts
13 → 37
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Calls

6 calls:

TimeVariablePointExpression
29.0ms
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))
27.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
8.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
2.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
2.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))

rewrite158.0ms (2.6%)

Memory
-21.4MiB live, 309.6MiB allocated; 72ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01671003
0181944
1950877
08355841
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
50 → 262
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(fabs.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 k) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(neg.f64 (/.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(sqrt.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)))
(sqrt.f64 k)
(fabs.f64 (neg.f64 (sqrt.f64 k)))
(fabs.f64 (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
k
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(*.f64 (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
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(fma.f64 (/.f64 #s(literal 1 binary64) k) k (neg.f64 k))
(fma.f64 (neg.f64 k) #s(literal 1 binary64) (*.f64 (neg.f64 k) (/.f64 #s(literal -1 binary64) k)))
(fma.f64 (neg.f64 k) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) k) (neg.f64 k)))
(fma.f64 (neg.f64 k) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) k (*.f64 (neg.f64 k) (/.f64 #s(literal -1 binary64) k)))
(fma.f64 #s(literal -1 binary64) k (*.f64 (/.f64 #s(literal -1 binary64) k) (neg.f64 k)))
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 2 binary64) (*.f64 (neg.f64 k) (/.f64 #s(literal -1 binary64) k)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 2 binary64) (*.f64 (/.f64 #s(literal -1 binary64) k) (neg.f64 k)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 1/2 binary64)) (*.f64 (neg.f64 k) (/.f64 #s(literal -1 binary64) k)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 1/2 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) k) (neg.f64 k)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 k (/.f64 #s(literal 1 binary64) k) (neg.f64 k))
(fma.f64 k #s(literal -1 binary64) (*.f64 (neg.f64 k) (/.f64 #s(literal -1 binary64) k)))
(fma.f64 k #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) k) (neg.f64 k)))
(fma.f64 k #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (neg.f64 k) (*.f64 (neg.f64 k) (/.f64 #s(literal -1 binary64) k)))
(fma.f64 #s(literal 1 binary64) (neg.f64 k) (*.f64 (/.f64 #s(literal -1 binary64) k) (neg.f64 k)))
(fma.f64 #s(literal 1 binary64) (neg.f64 k) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k)) (/.f64 (*.f64 k k) (+.f64 #s(literal 1 binary64) k)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 k k k))) (/.f64 (*.f64 (*.f64 k k) k) (+.f64 #s(literal 1 binary64) (fma.f64 k k k))))
(-.f64 (neg.f64 k) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (*.f64 k (/.f64 #s(literal 1 binary64) k)) (neg.f64 k))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) k) (neg.f64 k))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 k k k))) (/.f64 (*.f64 (*.f64 k k) (neg.f64 k)) (+.f64 #s(literal 1 binary64) (fma.f64 k k k))))
(+.f64 (neg.f64 k) (*.f64 (neg.f64 k) (/.f64 #s(literal -1 binary64) k)))
(+.f64 (neg.f64 k) (*.f64 (/.f64 #s(literal -1 binary64) k) (neg.f64 k)))
(+.f64 (neg.f64 k) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (fma.f64 k (/.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/8 binary64))) (sqrt.f64 k)) (*.f64 (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/8 binary64))) k) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (-.f64 #s(literal 1 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) k) (sqrt.f64 k)))
#s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))
#s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (-.f64 #s(literal 1 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (*.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) k) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal -1 binary64) k) (sqrt.f64 k)))
#s(approx (sqrt k) (/.f64 (neg.f64 k) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (-.f64 #s(literal 1 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* 2 (PI)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (neg.f64 n) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (neg.f64 n) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))

eval28.0ms (0.5%)

Memory
34.0MiB live, 78.9MiB allocated; 7ms collecting garbage
Compiler

Compiled 2 220 to 1 020 computations (54.1% saved)

prune16.0ms (0.3%)

Memory
-10.0MiB live, 35.8MiB allocated; 7ms collecting garbage
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New23114245
Fresh000
Picked101
Done000
Total23214246
Accuracy
100.0%
Counts
246 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
99.5%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
▶99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
76.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
46.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶99.5%
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
41.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
47.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
▶96.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
▶36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
Compiler

Compiled 620 to 504 computations (18.7% saved)

series260.0ms (4.3%)

Memory
-41.0MiB live, 307.6MiB allocated; 151ms collecting garbage
Counts
37 → 130
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))
(log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(-.f64 #s(literal 1 binary64) k)
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
Outputs
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1/4 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (* 1/2 (/ (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
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#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt k))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))
#s(approx (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 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Calls

6 calls:

TimeVariablePointExpression
163.0ms
n
@-inf
((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (* (/ 1 k) (sqrt k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) (* (- 1 k) 1/4) 1/4)
29.0ms
n
@0
((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (* (/ 1 k) (sqrt k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) (* (- 1 k) 1/4) 1/4)
24.0ms
n
@inf
((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (* (/ 1 k) (sqrt k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) (* (- 1 k) 1/4) 1/4)
16.0ms
k
@-inf
((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (* (/ 1 k) (sqrt k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) (* (- 1 k) 1/4) 1/4)
15.0ms
k
@0
((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (* (/ 1 k) (sqrt k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) (* (- 1 k) 1/4) 1/4)

rewrite264.0ms (4.4%)

Memory
-24.2MiB live, 353.1MiB allocated; 53ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05964976
06534489
139274231
087544154
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
167 → 630
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))
(log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(-.f64 #s(literal 1 binary64) k)
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1/4 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (* 1/2 (/ (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/16 (/ (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/48 (/ (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1/4 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (* 1/2 (/ (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1/2 (* k (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* -1 (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI)))))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI)))))))))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 1))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (* 1/2 k) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (/ (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (log (sqrt (* 2 (* n (PI)))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (+ (log (sqrt (* 2 (* n (PI))))) (* -1 (* k (log (sqrt (* 2 (* n (PI))))))))))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 k) (sqrt k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* -1/64 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* -1/192 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))))))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (pow (pow (* 2 (* n (PI))) 1/4) 2)))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)))) (pow (pow (* 2 (* n (PI))) 1/4) 2))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2)))))) (pow (pow (* 2 (* n (PI))) 1/4) 2))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (* k (+ (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (* k (+ (* -1/64 (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (* -1/192 (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2))))))))) (pow (pow (* 2 (* n (PI))) 1/4) 2))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/4)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (+ (* -1/4 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/4)))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/4))) (* 1/32 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/4)))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/4))) (* k (+ (* -1/384 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/4)))) (* 1/32 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/4))))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (* (- 1 k) 1/4) #s(hole binary64 1/4))
#s(approx (* (- 1 k) 1/4) #s(hole binary64 (+ 1/4 (* -1/4 k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* k (+ (* -1 (log (sqrt (* 2 (* n (PI)))))) (/ (log (sqrt (* 2 (* n (PI))))) k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 k) (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2) (* k (sqrt (/ 1 k))))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (* (- 1 k) 1/4) #s(hole binary64 (* -1/4 k)))
#s(approx (* (- 1 k) 1/4) #s(hole binary64 (* k (- (* 1/4 (/ 1 k)) 1/4))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k))))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* -1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* -1 (/ (log (sqrt (* 2 (* n (PI))))) k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 k) (sqrt k)) #s(hole binary64 (* -1 (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (* -1 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (* (- 1 k) 1/4) #s(hole binary64 (* -1 (* k (- 1/4 (* 1/4 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))
#s(approx (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 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt k))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))
#s(approx (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 (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) k))
(*.f64 (/.f64 (sqrt.f64 k) k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1 binary64)) (*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal -1 binary64)) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 (sqrt.f64 k) #s(literal 1 binary64))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (/.f64 (sqrt.f64 k) #s(literal 1 binary64))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (*.f64 (/.f64 (sqrt.f64 k) #s(literal 1 binary64)) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (*.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (neg.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
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#s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
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#s(approx (/ 1 k) (/.f64 #s(literal 1 binary64) k))
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#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
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#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)) k))
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#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (- 1 k) 1/4) (*.f64 #s(literal -1/4 binary64) k))
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#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
#s(approx (sqrt k) (*.f64 (neg.f64 k) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
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#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k))))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (- 1 k) 1/4) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) k))))
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#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
#s(approx (* (+ (PI) (PI)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx n n)
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
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#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
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#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
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#s(approx (sqrt (* (+ (PI) (PI)) n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
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#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
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#s(approx (log (sqrt (* (+ (PI) (PI)) n))) (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (exp.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (exp.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))))

eval110.0ms (1.8%)

Memory
43.6MiB live, 224.0MiB allocated; 25ms collecting garbage
Compiler

Compiled 9 535 to 2 738 computations (71.3% saved)

prune61.0ms (1%)

Memory
0.9MiB live, 122.6MiB allocated; 38ms collecting garbage
Pruning

26 alts after pruning (24 fresh and 2 done)

PrunedKeptTotal
New67324697
Fresh909
Picked325
Done000
Total68526711
Accuracy
100.0%
Counts
711 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
99.6%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)))
50.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)))))
46.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.5%
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
46.6%
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.6%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
99.6%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
▶36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
99.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k)))
▶99.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
46.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
✓96.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
43.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 k)))
37.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
36.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
▶22.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
▶36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
27.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)) (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))))
34.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
36.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k)))
49.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Compiler

Compiled 1 202 to 1 090 computations (9.3% saved)

series124.0ms (2%)

Memory
-46.5MiB live, 168.9MiB allocated; 61ms collecting garbage
Counts
32 → 100
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(neg.f64 k)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))
(/.f64 n k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
(sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))
(-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 1))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (+ 1 (* -1 (* k (log (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (+ 1 (* k (+ (* -1 (log (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (+ 1 (* k (+ (* -1 (log (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#s(approx (neg k) #s(hole binary64 (* -1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* -1/64 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* -1/192 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))))))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (+ (PI) (PI)) (/ n k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (/ (sqrt (* k (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))))) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) k)))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* -1/2 (/ (* k (log (* 2 (* n (PI))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (+ (* -1/16 (/ (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/48 (/ (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))))) (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* 1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* 1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) -1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* 1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2)))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) -1/2)))) (* 1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2))))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) -1/2))))))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (- (* 1/2 k) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/2 k) 1/2) #s(hole binary64 (- (* 1/2 k) 1/2)))
#s(approx (* 1/2 k) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* (exp (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))) (sqrt (* 2 (* n (PI))))) (* k (sqrt (/ 1 k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* (exp (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))) (sqrt (* 2 (* n (PI)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (exp (* -1 (* k (log (sqrt (* 2 (* n (PI))))))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (sqrt (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) k))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* k (* (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* k (* (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
#s(approx (- (* 1/2 k) 1/2) #s(hole binary64 (* k (- 1/2 (* 1/2 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (* -1 (/ (* (exp (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))) (sqrt (* 2 (* n (PI))))) (* k (sqrt (/ 1 k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (* -1 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ -1 (* k (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* -1 (* k (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (sqrt (/ 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
#s(approx (- (* 1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- (* 1/2 (/ 1 k)) 1/2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* (exp (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))) (sqrt (* 2 (* n (PI))))) (sqrt k))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (sqrt (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (sqrt (* 4 (pow (PI) 2))))))
#s(approx (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) #s(hole binary64 (* 4 (* (pow n 2) (pow (PI) 2)))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* n (* (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))) (sqrt (* 2 (/ (PI) n))))) (sqrt k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (* (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))) (sqrt (* 2 (/ (PI) n)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (* n (sqrt (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (* -1 (/ (* n (* (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))) (sqrt (* 2 (/ (PI) n))))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* n (* (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))) (sqrt (* 2 (/ (PI) n))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (* -1 (* n (sqrt (* -1 (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* n (sqrt (* 4 (pow (PI) 2)))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
Calls

6 calls:

TimeVariablePointExpression
38.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (neg k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (+ (PI) (PI)) n) (/ 1 k))) (* (* (+ (PI) (PI)) n) (/ 1 k)) (/ 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (- (* 1/2 k) 1/2) (* 1/2 k) 1/2)
25.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (neg k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (+ (PI) (PI)) n) (/ 1 k))) (* (* (+ (PI) (PI)) n) (/ 1 k)) (/ 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (- (* 1/2 k) 1/2) (* 1/2 k) 1/2)
23.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (neg k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (+ (PI) (PI)) n) (/ 1 k))) (* (* (+ (PI) (PI)) n) (/ 1 k)) (/ 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (- (* 1/2 k) 1/2) (* 1/2 k) 1/2)
20.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (neg k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (+ (PI) (PI)) n) (/ 1 k))) (* (* (+ (PI) (PI)) n) (/ 1 k)) (/ 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (- (* 1/2 k) 1/2) (* 1/2 k) 1/2)
6.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (neg k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (+ (PI) (PI)) n) (/ 1 k))) (* (* (+ (PI) (PI)) n) (/ 1 k)) (/ 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (- (* 1/2 k) 1/2) (* 1/2 k) 1/2)

rewrite160.0ms (2.6%)

Memory
46.0MiB live, 187.5MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05314164
05763613
132403434
083173338
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
132 → 647
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(neg.f64 k)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))
(/.f64 n k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
(sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))
(-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 1))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (+ 1 (* -1 (* k (log (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (+ 1 (* k (+ (* -1 (log (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (+ 1 (* k (+ (* -1 (log (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#s(approx (neg k) #s(hole binary64 (* -1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* -1/64 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* -1/192 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))))))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (+ (PI) (PI)) (/ n k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (/ (sqrt (* k (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))))) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) k)))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* -1/2 (/ (* k (log (* 2 (* n (PI))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (+ (* -1/16 (/ (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/48 (/ (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))))) (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* 1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* 1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) -1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* 1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2)))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) -1/2)))) (* 1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2))))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) -1/2))))))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (- (* 1/2 k) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/2 k) 1/2) #s(hole binary64 (- (* 1/2 k) 1/2)))
#s(approx (* 1/2 k) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* (exp (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))) (sqrt (* 2 (* n (PI))))) (* k (sqrt (/ 1 k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* (exp (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))) (sqrt (* 2 (* n (PI)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (exp (* -1 (* k (log (sqrt (* 2 (* n (PI))))))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (sqrt (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) k))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* k (* (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* k (* (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
#s(approx (- (* 1/2 k) 1/2) #s(hole binary64 (* k (- 1/2 (* 1/2 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (* -1 (/ (* (exp (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))) (sqrt (* 2 (* n (PI))))) (* k (sqrt (/ 1 k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (* -1 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ -1 (* k (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* -1 (* k (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (sqrt (/ 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
#s(approx (- (* 1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- (* 1/2 (/ 1 k)) 1/2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* (exp (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))) (sqrt (* 2 (* n (PI))))) (sqrt k))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (sqrt (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (sqrt (* 4 (pow (PI) 2))))))
#s(approx (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) #s(hole binary64 (* 4 (* (pow n 2) (pow (PI) 2)))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* n (* (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))) (sqrt (* 2 (/ (PI) n))))) (sqrt k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (* (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))) (sqrt (* 2 (/ (PI) n)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (* n (sqrt (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (* -1 (/ (* n (* (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))) (sqrt (* 2 (/ (PI) n))))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* n (* (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))) (sqrt (* 2 (/ (PI) n))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(hole binary64 (exp (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (* -1 (* n (sqrt (* -1 (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* n (sqrt (* 4 (pow (PI) 2)))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
Outputs
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
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#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (fma.f64 (fma.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) #s(literal 1/8 binary64) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal -1/2 binary64))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (fma.f64 (fma.f64 (fma.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) #s(literal -1/48 binary64) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal 1/8 binary64))) k (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal -1/2 binary64))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+.f64 (neg.f64 (*.f64 k (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (fma.f64 (fma.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) #s(literal 1/2 binary64) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (fma.f64 (fma.f64 (fma.f64 (*.f64 k (/.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))) #s(literal -1/6 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal 1/2 binary64))) k (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (fma.f64 (neg.f64 k) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (fma.f64 k (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (fma.f64 k (fma.f64 k (fma.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/6 binary64))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) #s(literal 1 binary64))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (fma.f64 (fma.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) k) #s(literal 1/2 binary64) (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) k #s(literal 1 binary64)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (fma.f64 k (fma.f64 k (fma.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 3 binary64)) k) #s(literal -1/6 binary64) (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) #s(literal 1 binary64)))
#s(approx (neg k) (neg.f64 k))
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (fma.f64 (*.f64 k (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (fma.f64 (fma.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) #s(literal 1/8 binary64) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal -1/2 binary64))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal -1/48 binary64)) k (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal 1/8 binary64))) k (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal -1/2 binary64))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) k))
#s(approx (* (+ (PI) (PI)) (/ n k)) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
#s(approx (/ n k) (/.f64 n k))
#s(approx (/ 1 k) (/.f64 #s(literal 1 binary64) k))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (+ (PI) (PI)) (/ n k)) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (fma.f64 (/.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (fma.f64 (-.f64 (*.f64 (neg.f64 k) (*.f64 (/.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))) #s(literal -1/8 binary64))) (/.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))) k (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (fma.f64 (-.f64 (*.f64 (-.f64 (*.f64 (neg.f64 k) (fma.f64 (/.f64 (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))) #s(literal -1/24 binary64) (*.f64 (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (*.f64 (/.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))) #s(literal -1/8 binary64))))) (*.f64 (/.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))) #s(literal -1/8 binary64))) k) (/.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))) k (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (fma.f64 k (fma.f64 (*.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)) (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k) #s(literal 1/8 binary64) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (fma.f64 (fma.f64 k (fma.f64 (*.f64 #s(literal 1/48 binary64) k) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)) (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64))) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)) (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(literal 1/8 binary64))) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))) k (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (fma.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) k (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (fma.f64 (fma.f64 k (fma.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64))) k) #s(literal 1/48 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(literal 1/8 binary64))) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) k (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (- (* 1/2 k) 1/2) #s(literal -1/2 binary64))
#s(approx (- (* 1/2 k) 1/2) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
#s(approx (* 1/2 k) (*.f64 #s(literal 1/2 binary64) k))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)))
#s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) k))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
#s(approx (- (* 1/2 k) 1/2) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k)) k))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (sqrt k) (*.f64 (neg.f64 k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 k (exp.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (*.f64 (neg.f64 k) (*.f64 (exp.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (exp.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
#s(approx (- (* 1/2 k) 1/2) (*.f64 (neg.f64 k) (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (* (+ (PI) (PI)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (+ (PI) (PI)) (/ n k)) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
#s(approx (* (+ (PI) (PI)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (*.f64 (*.f64 #s(literal 4 binary64) (*.f64 n n)) (*.f64 (PI.f64) (PI.f64))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (neg.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (*.f64 n (/.f64 (*.f64 (exp.f64 (*.f64 (neg.f64 k) (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (*.f64 (*.f64 (exp.f64 (*.f64 (neg.f64 k) (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) n))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (exp.f64 (*.f64 (neg.f64 k) (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (neg.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (*.f64 #s(literal -1 binary64) n) (*.f64 #s(literal -2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (neg.f64 (*.f64 (*.f64 (exp.f64 (*.f64 (neg.f64 k) (log.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) n)) (sqrt.f64 k)))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (neg.f64 (*.f64 (*.f64 (exp.f64 (*.f64 (neg.f64 k) (log.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) n)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (exp.f64 (*.f64 (neg.f64 k) (log.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 (*.f64 (*.f64 #s(literal -1 binary64) n) (*.f64 #s(literal -2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (neg.f64 (*.f64 (sqrt.f64 (neg.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k)))) n)))
#s(approx (* (+ (PI) (PI)) (/ n k)) (neg.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (+ (PI) (PI)) n) (neg.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (/.f64 (exp.f64 (neg.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal -1 binary64) n) (*.f64 #s(literal -2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal -1 binary64) n) (*.f64 #s(literal -2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal -1 binary64) n) (*.f64 #s(literal -2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))

eval111.0ms (1.8%)

Memory
-7.8MiB live, 84.4MiB allocated; 21ms collecting garbage
Compiler

Compiled 10 147 to 2 875 computations (71.7% saved)

prune47.0ms (0.8%)

Memory
8.2MiB live, 54.4MiB allocated; 4ms collecting garbage
Pruning

31 alts after pruning (28 fresh and 3 done)

PrunedKeptTotal
New62821649
Fresh12719
Picked415
Done022
Total64431675
Accuracy
100.0%
Counts
675 → 31
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
▶46.5%
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
99.6%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)))
46.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
46.6%
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.6%
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
99.6%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
46.7%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
37.5%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
36.9%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
36.6%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) (/.f64 n k))))
▶36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
27.0%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
34.4%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
49.8%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
▶99.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k)))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
✓96.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
43.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 k)))
81.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
22.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
▶34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64))))))
22.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) k))))
34.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) k))))
▶36.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
Compiler

Compiled 1 507 to 1 341 computations (11% saved)

series176.0ms (2.9%)

Memory
-0.7MiB live, 229.3MiB allocated; 33ms collecting garbage
Counts
32 → 99
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
(sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k)))
(*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))
(/.f64 (+.f64 (PI.f64) (PI.f64)) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
#s(literal 1 binary64)
(*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64))))))
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64))))
(exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))
(*.f64 (log.f64 k) #s(literal -1 binary64))
(log.f64 k)
#s(literal -1 binary64)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/6 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* -1 (* k (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (+ (* -1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (* 1/6 (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))))))) (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 1))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* k (+ (* 1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* -1/64 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* -1/192 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))))))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* n (/ (+ (PI) (PI)) k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (+ (PI) (PI)) k) #s(hole binary64 (* 2 (/ (PI) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (* k (* n (PI)))))))
#s(approx (* (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* -1/2 (/ (* k (log (* 2 (* n (PI))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (+ (* -1/16 (/ (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/48 (/ (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))))) (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* 1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* 1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) -1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* 1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2)))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) -1/2)))) (* 1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2))))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) -1/2))))))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (exp (* (log k) -1)) #s(hole binary64 (/ 1 k)))
#s(approx (* (log k) -1) #s(hole binary64 (* -1 (log k))))
#s(approx (log k) #s(hole binary64 (log k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (pow (sqrt (* 2 (* n (PI)))) k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (pow (sqrt (* 2 (* n (PI)))) k)))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* k (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* k (* (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* k (* (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
#s(approx (* (log k) -1) #s(hole binary64 (log (/ 1 k))))
#s(approx (log k) #s(hole binary64 (* -1 (log (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (* -1 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* k (sqrt (* 2 (/ (* n (PI)) k)))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ -1 (* k (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* -1 (* k (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (sqrt (/ 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
#s(approx (/ 1 (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (/ 1 (sqrt (* 2 (* n (PI)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* n (sqrt (* 2 (/ (* k (PI)) n))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
#s(approx (/ 1 (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (/ 1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (* k (PI)) n)))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
#s(approx (/ 1 (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (/ -1 (* n (sqrt (* 2 (/ (PI) n)))))))
Calls

6 calls:

TimeVariablePointExpression
59.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/ 1 (sqrt (* (+ (PI) (PI)) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (+ (PI) (PI)) n) (exp (* (log k) -1)))) (* (* (+ (PI) (PI)) n) (exp (* (log k) -1))) (exp (* (log k) -1)) (* (log k) -1) (log k) -1)
43.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/ 1 (sqrt (* (+ (PI) (PI)) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (+ (PI) (PI)) n) (exp (* (log k) -1)))) (* (* (+ (PI) (PI)) n) (exp (* (log k) -1))) (exp (* (log k) -1)) (* (log k) -1) (log k) -1)
25.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/ 1 (sqrt (* (+ (PI) (PI)) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (+ (PI) (PI)) n) (exp (* (log k) -1)))) (* (* (+ (PI) (PI)) n) (exp (* (log k) -1))) (exp (* (log k) -1)) (* (log k) -1) (log k) -1)
19.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/ 1 (sqrt (* (+ (PI) (PI)) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (+ (PI) (PI)) n) (exp (* (log k) -1)))) (* (* (+ (PI) (PI)) n) (exp (* (log k) -1))) (exp (* (log k) -1)) (* (log k) -1) (log k) -1)
15.0ms
k
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/ 1 (sqrt (* (+ (PI) (PI)) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (+ (PI) (PI)) n) (exp (* (log k) -1)))) (* (* (+ (PI) (PI)) n) (exp (* (log k) -1))) (exp (* (log k) -1)) (* (log k) -1) (log k) -1)

rewrite203.0ms (3.4%)

Memory
12.7MiB live, 240.3MiB allocated; 94ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05374279
05803825
133883661
084853575
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
131 → 489
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
(sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k)))
(*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))
(/.f64 (+.f64 (PI.f64) (PI.f64)) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
#s(literal 1 binary64)
(*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64))))))
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64))))
(exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))
(*.f64 (log.f64 k) #s(literal -1 binary64))
(log.f64 k)
#s(literal -1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/6 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* -1 (* k (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (+ (* -1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (* 1/6 (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))))))) (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 1))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* k (+ (* 1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2))) (sqrt k))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* k (+ (* -1/64 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))) (* -1/192 (/ (* (pow (log (* 2 (* n (PI)))) 3) (pow (pow (* 2 (* n (PI))) 1/4) 2)) (sqrt k))))))))) (/ (pow (pow (* 2 (* n (PI))) 1/4) 2) (sqrt k)))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* n (/ (+ (PI) (PI)) k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (+ (PI) (PI)) k) #s(hole binary64 (* 2 (/ (PI) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (* k (* n (PI)))))))
#s(approx (* (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* -1/2 (/ (* k (log (* 2 (* n (PI))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (+ (* -1/16 (/ (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/48 (/ (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))))) (+ (* -1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (/ (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (/ 1 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* 1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* 1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) -1/2)))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) -1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* 1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2)))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) -1/2)))) (* 1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2))))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) -1/2))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) -1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) -1/2))))))) (pow (* 2 (* n (PI))) -1/2))))
#s(approx (exp (* (log k) -1)) #s(hole binary64 (/ 1 k)))
#s(approx (* (log k) -1) #s(hole binary64 (* -1 (log k))))
#s(approx (log k) #s(hole binary64 (log k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (pow (sqrt (* 2 (* n (PI)))) k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (pow (sqrt (* 2 (* n (PI)))) k)))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* k (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* k (* (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* k (* (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
#s(approx (* (log k) -1) #s(hole binary64 (log (/ 1 k))))
#s(approx (log k) #s(hole binary64 (* -1 (log (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (* -1 (/ (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* k (sqrt (* 2 (/ (* n (PI)) k)))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ -1 (* k (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* -1 (* k (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (sqrt (/ 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
#s(approx (/ 1 (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (/ 1 (sqrt (* 2 (* n (PI)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* n (sqrt (* 2 (/ (* k (PI)) n))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
#s(approx (/ 1 (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (/ 1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(hole binary64 (/ (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2) (sqrt k))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (* k (PI)) n)))))))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) #s(hole binary64 (/ 1 (* (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) (sqrt k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) #s(hole binary64 (* (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) #s(hole binary64 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
#s(approx (/ 1 (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (/ -1 (* n (sqrt (* 2 (/ (PI) n)))))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1 binary64))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1 binary64)) (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal -1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (/.f64 (sqrt.f64 k) #s(literal 1 binary64))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (/.f64 (sqrt.f64 k) #s(literal 1 binary64))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (neg.f64 (neg.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n))) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
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#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (/.f64 (exp.f64 (neg.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
#s(approx (/ 1 (sqrt (* (+ (PI) (PI)) n))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (*.f64 (/.f64 n (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k))) (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (neg.f64 (*.f64 n (/.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (exp.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (neg.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (neg.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)))
#s(approx (/ 1 (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k))) (/.f64 (exp.f64 (neg.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt k)) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
#s(approx (/ 1 (sqrt (* (+ (PI) (PI)) n))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))

eval68.0ms (1.1%)

Memory
-9.8MiB live, 139.2MiB allocated; 22ms collecting garbage
Compiler

Compiled 8 535 to 2 469 computations (71.1% saved)

prune56.0ms (0.9%)

Memory
-16.2MiB live, 127.8MiB allocated; 16ms collecting garbage
Pruning

43 alts after pruning (38 fresh and 5 done)

PrunedKeptTotal
New52320543
Fresh51823
Picked325
Done033
Total53143574
Accuracy
100.0%
Counts
574 → 43
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
46.4%
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))) (sqrt.f64 k)))
46.5%
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
46.5%
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
46.5%
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
46.5%
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
46.6%
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
99.6%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)))
46.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
46.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.6%
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
99.6%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
46.7%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
37.5%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
36.9%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
34.4%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
49.8%
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
51.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64)))) (sqrt.f64 k)))
81.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
99.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))))
✓96.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
43.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 k)))
81.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
22.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
34.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))))
34.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (neg.f64 (log.f64 k))))))
22.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) k))))
34.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) k))))
35.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
35.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
✓36.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
33.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)) k)))
33.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))) k)))
46.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))
35.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 #s(literal 1 binary64) k))))
Compiler

Compiled 2 092 to 1 369 computations (34.6% saved)

regimes88.0ms (1.4%)

Memory
3.7MiB live, 192.1MiB allocated; 13ms collecting garbage
Counts
80 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 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))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)) (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (neg.f64 (log.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) (/.f64 n k))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)))))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
Calls

4 calls:

22.0ms
n
22.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
21.0ms
k
19.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1k
99.7%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes114.0ms (1.9%)

Memory
13.2MiB live, 158.0MiB allocated; 26ms collecting garbage
Counts
73 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 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))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)) (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (neg.f64 (log.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) (/.f64 n k))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)))))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k)))
Calls

4 calls:

55.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
20.0ms
n
19.0ms
k
15.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1k
99.7%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes99.0ms (1.6%)

Memory
0.0MiB live, 181.7MiB allocated; 17ms collecting garbage
Counts
72 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 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))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)) (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (neg.f64 (log.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) (/.f64 n k))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)))))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))))
Calls

4 calls:

35.0ms
n
22.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
21.0ms
k
17.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1k
99.7%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes308.0ms (5.1%)

Memory
106.0MiB live, 243.3MiB allocated; 150ms collecting garbage
Counts
70 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 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))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)) (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (neg.f64 (log.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (/ (* (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) (/.f64 n k))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (neg k)) (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (*.f64 (/.f64 (sqrt.f64 k) k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)))))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
Calls

4 calls:

187.0ms
k
74.0ms
(*.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))))
27.0ms
n
17.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%1k
99.6%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes57.0ms (0.9%)

Memory
-8.2MiB live, 87.5MiB allocated; 7ms collecting garbage
Counts
51 → 3
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 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))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)) (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (neg.f64 (log.f64 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))) k)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Calls

4 calls:

13.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms
k
13.0ms
n
12.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
71.8%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
69.9%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
64.4%3k
71.8%3n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes25.0ms (0.4%)

Memory
-10.1MiB live, 34.5MiB allocated; 4ms collecting garbage
Counts
35 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 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))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))
(*.f64 #s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (- (* 1/2 k) 1/2)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Calls

2 calls:

13.0ms
n
9.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
69.9%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
69.9%2n
Compiler

Compiled 6 to 8 computations (-33.3% saved)

regimes36.0ms (0.6%)

Memory
-12.1MiB live, 35.8MiB allocated; 10ms collecting garbage
Counts
27 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 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))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n k))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 k) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 #s(literal 1 binary64) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Calls

4 calls:

12.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
7.0ms
k
7.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms
n
Results
AccuracySegmentsBranch
60.7%2k
60.7%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))))
60.8%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
60.8%2n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes18.0ms (0.3%)

Memory
23.4MiB live, 23.4MiB allocated; 0ms collecting garbage
Counts
15 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 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))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) k)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
Calls

4 calls:

4.0ms
k
4.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms
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
46.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
46.7%1k
46.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
46.7%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes10.0ms (0.2%)

Memory
-32.8MiB live, 13.8MiB allocated; 2ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
Calls

4 calls:

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

Compiled 22 to 23 computations (-4.5% saved)

regimes8.0ms (0.1%)

Memory
12.7MiB live, 12.7MiB allocated; 0ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #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
36.7%1k
36.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
36.7%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes6.0ms (0.1%)

Memory
10.6MiB live, 10.6MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (* (- 1 k) 1/4)) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
Calls

4 calls:

2.0ms
n
1.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
k
1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
36.7%1k
36.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
36.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.7%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch29.0ms (0.5%)

Memory
-19.6MiB live, 26.4MiB allocated; 3ms collecting garbage
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
13.0ms
7.605605667198788e+84
3.9898089349060366e+89
12.0ms
106128639328.6627
3626371463757.522
Samples
16.0ms240×0valid
Compiler

Compiled 870 to 810 computations (6.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-pow: 4.0ms (38.3% of total)
ival-sqrt: 2.0ms (19.1% of total)
ival-div!: 2.0ms (19.1% of total)
ival-mult!: 2.0ms (19.1% of total)
ival-sub!: 1.0ms (9.6% of total)
adjust: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory
2.2MiB live, 2.2MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
2.0ms
1.9399271827067823e-16
1.5761717278508498e-14
Samples
1.0ms16×0valid
Compiler

Compiled 83 to 76 computations (8.4% saved)

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

bsearch11.0ms (0.2%)

Memory
13.3MiB live, 13.3MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
10.0ms
3.655658346691168e-11
1.5459626680077064e-10
Samples
7.0ms96×0valid
Compiler

Compiled 325 to 306 computations (5.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-pow: 2.0ms (44.5% of total)
ival-sqrt: 1.0ms (22.3% of total)
ival-div!: 1.0ms (22.3% of total)
ival-mult!: 1.0ms (22.3% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

derivations583.0ms (9.6%)

Memory
-6.8MiB live, 372.3MiB allocated; 248ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 199 to 101 computations (49.2% saved)

preprocess91.0ms (1.5%)

Memory
14.6MiB live, 208.9MiB allocated; 15ms collecting garbage
Remove

(abs k)

Compiler

Compiled 948 to 724 computations (23.6% saved)

end0.0ms (0%)

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

Profiling

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