Migdal et al, Equation (51)

Time bar (total: 7.0s)

start0.0ms (0%)

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

analyze111.0ms (1.6%)

Memory
35.9MiB live, 116.5MiB allocated; 28ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%51.5%0%7
52.5%25%22.6%0.1%0%52.3%0%8
53.8%25%21.5%0.1%0%53.5%0%9
54.5%25%20.9%0.1%0%54%0%10
55.3%25%20.2%0.1%0%54.7%0%11
55.7%25%19.9%0.1%0%55.1%0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.2s (46.3%)

Memory
28.3MiB live, 3 994.2MiB allocated; 1.6s collecting garbage
Samples
1.1s5 513×1invalid
925.0ms8 256×0valid
440.0ms228×0exit
194.0ms441×2invalid
22.0ms349×0invalid
Precisions
Click to see histograms. Total time spent on operations: 2.0s
ival-sub!: 534.0ms (27% of total)
ival-pow: 510.0ms (25.8% of total)
ival-mult!: 304.0ms (15.4% of total)
adjust: 252.0ms (12.8% of total)
ival-div!: 233.0ms (11.8% of total)
ival-sqrt: 144.0ms (7.3% of total)
ival-pi: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

preprocess54.0ms (0.8%)

Memory
-34.2MiB live, 52.2MiB allocated; 13ms 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
▶99.4%
(*.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)

series78.0ms (1.1%)

Memory
37.5MiB live, 185.2MiB allocated; 18ms collecting garbage
Counts
13 → 37
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Calls

6 calls:

TimeVariablePointExpression
40.0ms
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))
23.0ms
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))

rewrite212.0ms (3%)

Memory
21.9MiB live, 289.3MiB allocated; 79ms 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))))

eval49.0ms (0.7%)

Memory
14.4MiB live, 93.1MiB allocated; 32ms collecting garbage
Compiler

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

prune44.0ms (0.6%)

Memory
-56.5MiB live, 56.3MiB allocated; 34ms collecting garbage
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New22817245
Fresh000
Picked101
Done000
Total22917246
Accuracy
100.0%
Counts
246 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.4%
(/.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))
99.4%
(/.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)))))
▶99.4%
(*.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)))
99.3%
(*.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)))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.3%
(*.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))))
55.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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)))))
47.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
▶99.4%
(*.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))))
▶96.3%
(*.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.4%
(*.f64 #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))))
39.2%
#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))))
48.1%
#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)))
96.2%
#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)))
▶35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
Compiler

Compiled 798 to 620 computations (22.3% saved)

series151.0ms (2.2%)

Memory
45.3MiB live, 275.7MiB allocated; 68ms collecting garbage
Counts
36 → 88
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)
(*.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)))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k))))
#s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))
(/.f64 k (sqrt.f64 k))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #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 #s(literal 1 binary64) k)
(*.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))
(log.f64 (sqrt.f64 k))
#s(literal -1 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)))))
#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 (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (/ k (sqrt k)) #s(hole binary64 (/ k (sqrt k))))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (log (sqrt k)) -1) #s(hole binary64 (* -1 (log (sqrt k)))))
#s(approx (log (sqrt k)) #s(hole binary64 (log (sqrt 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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (/ 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 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (log (sqrt k)) -1) #s(hole binary64 (* -1 (+ (log (sqrt (/ 1 k))) (* -1 (log (/ 1 k)))))))
#s(approx (log (sqrt k)) #s(hole binary64 (+ (log (sqrt (/ 1 k))) (* -1 (log (/ 1 k))))))
#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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) #s(hole binary64 (* -1 (/ (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (/ 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) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (log (sqrt k)) -1) #s(hole binary64 (* -1 (+ (log (sqrt (/ 1 k))) (* -1 (log (/ -1 k)))))))
#s(approx (log (sqrt k)) #s(hole binary64 (+ (log (sqrt (/ 1 k))) (* -1 (log (/ -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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
#s(approx (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)) (/ (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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (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)) (/ (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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (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
41.0ms
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) (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (/ k (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (- 1 k) (* (exp (* (log (sqrt k)) -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (sqrt k)) -1)) (* (log (sqrt k)) -1) (log (sqrt k)) -1)
33.0ms
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) (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (/ k (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (- 1 k) (* (exp (* (log (sqrt k)) -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (sqrt k)) -1)) (* (log (sqrt k)) -1) (log (sqrt k)) -1)
29.0ms
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) (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (/ k (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (- 1 k) (* (exp (* (log (sqrt k)) -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (sqrt k)) -1)) (* (log (sqrt k)) -1) (log (sqrt k)) -1)
21.0ms
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) (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (/ k (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (- 1 k) (* (exp (* (log (sqrt k)) -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (sqrt k)) -1)) (* (log (sqrt k)) -1) (log (sqrt k)) -1)
13.0ms
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) (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (/ k (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (- 1 k) (* (exp (* (log (sqrt k)) -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (sqrt k)) -1)) (* (log (sqrt k)) -1) (log (sqrt k)) -1)

rewrite230.0ms (3.3%)

Memory
8.2MiB live, 233.4MiB allocated; 112ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04053037
04542731
124722512
092432484
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
124 → 645
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)
(*.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)))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k))))
#s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))
(/.f64 k (sqrt.f64 k))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #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 #s(literal 1 binary64) k)
(*.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))
(log.f64 (sqrt.f64 k))
#s(literal -1 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 (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (/ k (sqrt k)) #s(hole binary64 (/ k (sqrt k))))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (log (sqrt k)) -1) #s(hole binary64 (* -1 (log (sqrt k)))))
#s(approx (log (sqrt k)) #s(hole binary64 (log (sqrt 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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (/ 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 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (log (sqrt k)) -1) #s(hole binary64 (* -1 (+ (log (sqrt (/ 1 k))) (* -1 (log (/ 1 k)))))))
#s(approx (log (sqrt k)) #s(hole binary64 (+ (log (sqrt (/ 1 k))) (* -1 (log (/ 1 k))))))
#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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) #s(hole binary64 (* -1 (/ (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (/ 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) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (log (sqrt k)) -1) #s(hole binary64 (* -1 (+ (log (sqrt (/ 1 k))) (* -1 (log (/ -1 k)))))))
#s(approx (log (sqrt k)) #s(hole binary64 (+ (log (sqrt (/ 1 k))) (* -1 (log (/ -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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
#s(approx (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)) (/ (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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (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)) (/ (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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64)))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) 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 (/.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))))
(pow.f64 (/.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)))) #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))) (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))))
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#s(literal 1 binary64)
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k
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (fma.f64 k (/.f64 (fma.f64 (*.f64 #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 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)))) #s(literal -1/2 binary64))) k (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k))
#s(approx (/ (* (+ (PI) (PI)) n) k) (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (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 (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (fma.f64 k (fma.f64 (*.f64 #s(literal 1/8 binary64) 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 (PI.f64) (PI.f64)) n))) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (fma.f64 (fma.f64 k (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))) (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1/2 binary64))) k (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 (/ k (sqrt k)) (/.f64 k (sqrt.f64 k)))
#s(approx (- 1 k) (-.f64 #s(literal 1 binary64) k))
#s(approx (* (log (sqrt k)) -1) (neg.f64 (log.f64 (sqrt.f64 k))))
#s(approx (log (sqrt k)) (log.f64 (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 k (exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))) (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 (/ (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 (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)) (/.f64 k (sqrt.f64 k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 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 k (sqrt.f64 k))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (/ k (sqrt k)) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k))
#s(approx (* (log (sqrt k)) -1) (neg.f64 (-.f64 (neg.f64 (log.f64 (sqrt.f64 k))) (neg.f64 (log.f64 k)))))
#s(approx (log (sqrt k)) (-.f64 (neg.f64 (log.f64 (sqrt.f64 k))) (neg.f64 (log.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (neg.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 k (exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))) (sqrt.f64 k)))))
#s(approx (/ 1 (sqrt k)) (*.f64 (/.f64 #s(literal -1 binary64) k) (sqrt.f64 k)))
#s(approx (sqrt k) (neg.f64 (/.f64 k (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (neg.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 k (sqrt.f64 k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (/ k (sqrt k)) (*.f64 #s(literal -1 binary64) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (sqrt k)) -1) (neg.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 (neg.f64 k)))) (neg.f64 (log.f64 (sqrt.f64 k))))))
#s(approx (log (sqrt k)) (+.f64 (neg.f64 (neg.f64 (log.f64 (neg.f64 k)))) (neg.f64 (log.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k))))
#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)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 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 (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (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 (* (* 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)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 n (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) k) #s(literal 1/2 binary64))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (*.f64 n (/.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) k) #s(literal 1/2 binary64))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) k) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 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 (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (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 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (neg.f64 (*.f64 (/.f64 n (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)))) k) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (neg.f64 (*.f64 n (/.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (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)))) k) #s(literal 1/2 binary64)))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) k) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 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 (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (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 (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))))

eval131.0ms (1.9%)

Memory
7.4MiB live, 110.2MiB allocated; 13ms collecting garbage
Compiler

Compiled 8 432 to 2 428 computations (71.2% saved)

prune40.0ms (0.6%)

Memory
-23.9MiB live, 63.2MiB allocated; 14ms collecting garbage
Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New69221713
Fresh9312
Picked415
Done000
Total70525730
Accuracy
100.0%
Counts
730 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.4%
(/.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))
▶99.7%
(/.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)))
75.3%
(/.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)))
▶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))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
99.4%
(*.f64 (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 (sqrt k)) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k))))
51.2%
(*.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)))))
47.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
95.7%
(exp.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 (log.f64 (sqrt.f64 k)))))
99.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
99.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
96.2%
#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)))
35.3%
#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))))
35.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
35.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))))
✓35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
18.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
▶33.2%
#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))) k)))
35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
35.4%
#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))))
▶35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
33.3%
#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))))
33.5%
#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)))
▶44.8%
#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 1 052 to 967 computations (8.1% saved)

series63.0ms (0.9%)

Memory
-8.9MiB live, 134.1MiB allocated; 21ms collecting garbage
Counts
35 → 85
Calls
Call 1
Inputs
(/.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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.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))
(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)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
(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))) #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))
(*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)
(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 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
(sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k))
(/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)
(exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.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 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (sqrt k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* 1/2 (* k (* (log (* 2 (* n (PI)))) (sqrt k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt k))))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt k))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt k)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt k))))))))))
#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 k #s(hole 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 (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (+ (PI) (PI)) (/ n k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k)))
#s(approx (sqrt (/ (+ (PI) (PI)) (* n k))) #s(hole binary64 (/ (sqrt (* 2 (/ (* k (PI)) n))) k)))
#s(approx (/ (+ (PI) (PI)) (* n k)) #s(hole binary64 (* 2 (/ (PI) (* k n)))))
#s(approx (* n k) #s(hole binary64 (* k n)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (sqrt (/ (+ (PI) (PI)) (* n k))) #s(hole binary64 (sqrt (* 2 (/ (PI) (* k n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (exp (* (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 (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k))))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* -1 (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (exp (* (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 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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)) 1) #s(hole binary64 (sqrt (* 2 (* n (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)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt k))))
#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 (sqrt (/ (+ (PI) (PI)) (* n k))) #s(hole binary64 (/ (sqrt (* 2 (/ (* n (PI)) k))) n)))
#s(approx (log (* (+ (PI) (PI)) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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)) 1) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt k))))
#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 (log (* (+ (PI) (PI)) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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)) 1) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt k))))
#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 (log (* (+ (PI) (PI)) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
Calls

6 calls:

TimeVariablePointExpression
17.0ms
n
@inf
((/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n 1 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (exp (log (* (+ (PI) (PI)) n))) k)) (/ (exp (log (* (+ (PI) (PI)) n))) k) (exp (log (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 (sqrt (/ 1 k)) (/ 1 k))
15.0ms
n
@0
((/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n 1 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (exp (log (* (+ (PI) (PI)) n))) k)) (/ (exp (log (* (+ (PI) (PI)) n))) k) (exp (log (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 (sqrt (/ 1 k)) (/ 1 k))
13.0ms
n
@-inf
((/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n 1 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (exp (log (* (+ (PI) (PI)) n))) k)) (/ (exp (log (* (+ (PI) (PI)) n))) k) (exp (log (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 (sqrt (/ 1 k)) (/ 1 k))
5.0ms
k
@-inf
((/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n 1 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (exp (log (* (+ (PI) (PI)) n))) k)) (/ (exp (log (* (+ (PI) (PI)) n))) k) (exp (log (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 (sqrt (/ 1 k)) (/ 1 k))
5.0ms
k
@0
((/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n 1 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (exp (log (* (+ (PI) (PI)) n))) k)) (/ (exp (log (* (+ (PI) (PI)) n))) k) (exp (log (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 (sqrt (/ 1 k)) (/ 1 k))

rewrite188.0ms (2.7%)

Memory
37.1MiB live, 308.4MiB allocated; 40ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04143041
04562804
124322637
091512601
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
120 → 645
Calls
Call 1
Inputs
(/.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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.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))
(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)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
(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))) #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))
(*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)
(sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k)))
(/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))
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(sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k))
(/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)
(exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.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 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
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#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
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#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt k))))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt k))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt k)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt k))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 1))
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#s(approx (* 1/2 k) #s(hole binary64 (* 1/2 k)))
#s(approx k #s(hole 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 (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (+ (PI) (PI)) (/ n k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k)))
#s(approx (sqrt (/ (+ (PI) (PI)) (* n k))) #s(hole binary64 (/ (sqrt (* 2 (/ (* k (PI)) n))) k)))
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#s(approx (* n k) #s(hole binary64 (* k n)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (sqrt (/ (+ (PI) (PI)) (* n k))) #s(hole binary64 (sqrt (* 2 (/ (PI) (* k n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (exp (* (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 (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k))))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* -1 (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (exp (* (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 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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)) 1) #s(hole binary64 (sqrt (* 2 (* n (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)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt k))))
#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 (sqrt (/ (+ (PI) (PI)) (* n k))) #s(hole binary64 (/ (sqrt (* 2 (/ (* n (PI)) k))) n)))
#s(approx (log (* (+ (PI) (PI)) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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)) 1) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt k))))
#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 (log (* (+ (PI) (PI)) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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)) 1) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt k))))
#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 (log (* (+ (PI) (PI)) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
Outputs
(*.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 n k)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 k) k) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) k))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1 binary64))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal -1 binary64)) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (neg.f64 (neg.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))))
(/.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k))))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(fabs.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(pow.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal -1/2 binary64)))
(sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64)))
(sqrt.f64 (*.f64 #s(literal 1 binary64) (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(fabs.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(fabs.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(exp.f64 (/.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sinh.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(*.f64 (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(pow.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal -1/2 binary64)))
(sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64)))
(sqrt.f64 (*.f64 #s(literal 1 binary64) (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(fabs.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(fabs.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(exp.f64 (/.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sinh.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(*.f64 (fabs.f64 (*.f64 #s(literal 2 binary64) n)) (PI.f64))
(*.f64 (fabs.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64))
(*.f64 (fabs.f64 n) (fabs.f64 (+.f64 (PI.f64) (PI.f64))))
(*.f64 (fabs.f64 (+.f64 (PI.f64) (PI.f64))) (fabs.f64 n))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (exp.f64 (log.f64 (+.f64 (PI.f64) (PI.f64)))) (exp.f64 (log.f64 n)))
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) (/.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (log.f64 n)))) (log.f64 n))
(pow.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64))
(/.f64 (exp.f64 (log.f64 n)) (exp.f64 (neg.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))))))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(fabs.f64 (neg.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(fabs.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(+.f64 (cosh.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sinh.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (fma.f64 (PI.f64) (PI.f64) (*.f64 (PI.f64) (neg.f64 (PI.f64))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))) (neg.f64 (-.f64 (PI.f64) (PI.f64))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)))) (neg.f64 (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (fma.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (PI.f64) (PI.f64))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
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(+.f64 (PI.f64) (PI.f64))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)))
(log.f64 (*.f64 (exp.f64 (PI.f64)) (exp.f64 (PI.f64))))
(PI.f64)
n
#s(literal 1 binary64)
(*.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k))
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#s(approx (/ n k) (/.f64 n k))
#s(approx (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (/.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n) k))
#s(approx (sqrt (/ (+ (PI) (PI)) (* n k))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k))
#s(approx (/ (+ (PI) (PI)) (* n k)) (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n)))
#s(approx (* n k) (*.f64 k n))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) k))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) k))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (fma.f64 k (fma.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) #s(literal 1/8 binary64))) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) k))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (fma.f64 (fma.f64 k (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 3 binary64)) k) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) #s(literal -1/48 binary64) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/8 binary64)) (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1/2 binary64))) k (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) k))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (fma.f64 k (fma.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (fma.f64 (fma.f64 k (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 3 binary64))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/8 binary64))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1/2 binary64))) k (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#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 (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))
#s(approx (/ 1 k) (/.f64 #s(literal 1 binary64) k))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))) (sqrt.f64 k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (*.f64 (*.f64 (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (/.f64 (sqrt.f64 k) k)) k))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (sqrt k) (*.f64 (/.f64 (sqrt.f64 k) k) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) n))
#s(approx (sqrt (/ (+ (PI) (PI)) (* n k))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))) (sqrt.f64 k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (*.f64 (neg.f64 k) (*.f64 (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (/.f64 (sqrt.f64 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 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (+ (PI) (PI)) n) (*.f64 n (+.f64 (PI.f64) (PI.f64))))
#s(approx n n)
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (*.f64 (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (sqrt (/ (+ (PI) (PI)) (* n k))) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) n))
#s(approx (log (* (+ (PI) (PI)) n)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (*.f64 (/.f64 n (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) k) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n)))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (*.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) k) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (log (* (+ (PI) (PI)) n)) (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 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)))) (/.f64 (sqrt.f64 k) 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 (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (neg.f64 (*.f64 (/.f64 n (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)))) k) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (*.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) k) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) n)))
#s(approx (log (* (+ (PI) (PI)) n)) (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 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)))) (/.f64 (sqrt.f64 k) 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)))))

eval136.0ms (1.9%)

Memory
-18.0MiB live, 146.6MiB allocated; 131ms collecting garbage
Compiler

Compiled 8 286 to 2 562 computations (69.1% saved)

prune56.0ms (0.8%)

Memory
-28.0MiB live, 73.7MiB allocated; 15ms collecting garbage
Pruning

39 alts after pruning (34 fresh and 5 done)

PrunedKeptTotal
New56421585
Fresh61319
Picked145
Done011
Total57139610
Accuracy
100.0%
Counts
610 → 39
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.4%
(/.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))
55.0%
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))) (sqrt.f64 k)))
▶99.7%
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
99.4%
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) k) (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))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
74.6%
(*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 n k)))
51.2%
(*.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)))))
47.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
95.7%
(exp.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 (log.f64 (sqrt.f64 k)))))
33.5%
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) k))
99.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
▶99.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
96.2%
#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)))
35.3%
#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))))
35.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (sqrt.f64 k) k)))
35.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))))
✓35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
18.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
✓33.2%
#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))) k)))
35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
▶35.4%
#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))))
✓35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
▶35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
33.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
47.4%
#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)) n)))
45.1%
#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 k n))) n)))
▶45.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64))))) n)))
44.8%
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) n)))
36.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (*.f64 k n) (*.f64 (PI.f64) n)) (*.f64 n (*.f64 k n)))) n)))
33.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
33.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (PI.f64) (*.f64 k n) (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 (*.f64 k n) (*.f64 k n)))) n)))
43.7%
#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)) n)))
✓44.8%
#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)))
44.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (PI.f64)))) n)))
42.9%
#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 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) n)))
49.8%
#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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
Compiler

Compiled 1 750 to 1 599 computations (8.6% saved)

series111.0ms (1.6%)

Memory
28.4MiB live, 163.9MiB allocated; 11ms collecting garbage
Counts
37 → 89
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
k
(sqrt.f64 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))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n))))
(*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))
(/.f64 #s(literal 1 binary64) (/.f64 k n))
#s(literal 1 binary64)
(/.f64 k n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64))))) n)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64))))) n))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64))))) n)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64))))
(/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64)))
(*.f64 k n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(-.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (sqrt k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* 1/2 (* k (* (log (* 2 (* n (PI)))) (sqrt k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt k))))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt k))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt k)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt k))))))))))
#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 k #s(hole 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 (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (/ (* (PI) n) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ 1 (/ k n)) #s(hole binary64 (/ n k)))
#s(approx (/ k n) #s(hole binary64 (/ k n)))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) #s(hole binary64 (/ n (sqrt (* 1/2 (/ (* k n) (PI)))))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) #s(hole binary64 (/ 1 (sqrt (* 1/2 (/ (* k n) (PI)))))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) #s(hole binary64 (sqrt (* 1/2 (/ (* k n) (PI))))))
#s(approx (/ (* k n) (+ (PI) (PI))) #s(hole binary64 (* 1/2 (/ (* k n) (PI)))))
#s(approx (* k n) #s(hole binary64 (* k n)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) #s(hole binary64 (/ n (* k (sqrt (* 1/2 (/ n (* k (PI)))))))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) #s(hole binary64 (/ 1 (* k (sqrt (* 1/2 (/ n (* k (PI)))))))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) #s(hole binary64 (* k (sqrt (* 1/2 (/ n (* k (PI))))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k))))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* -1 (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (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 (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) #s(hole binary64 (* -1 (/ n (* k (sqrt (* 1/2 (/ n (* k (PI))))))))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) #s(hole binary64 (/ -1 (* k (sqrt (* 1/2 (/ n (* k (PI)))))))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) #s(hole binary64 (* -1 (* k (sqrt (* 1/2 (/ n (* k (PI)))))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt k)))))
#s(approx (* n (+ (PI) (PI))) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt k))))
#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 (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (* n (+ (PI) (PI)))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt k))))
#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) n) k) 2)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) #s(hole binary64 (/ 1 (sqrt (* 1/2 (/ k (* n (PI))))))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) #s(hole binary64 (/ 1 (* n (sqrt (* 1/2 (/ k (* n (PI)))))))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) #s(hole binary64 (* n (sqrt (* 1/2 (/ k (* n (PI))))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (* n (+ (PI) (PI)))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt k))))
#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) n) k) 2)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) #s(hole binary64 (/ -1 (sqrt (* 1/2 (/ k (* n (PI))))))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) #s(hole binary64 (/ -1 (* n (sqrt (* 1/2 (/ k (* n (PI)))))))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) #s(hole binary64 (* -1 (* n (sqrt (* 1/2 (/ k (* n (PI)))))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
Calls

6 calls:

TimeVariablePointExpression
41.0ms
n
@0
((/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* (+ (PI) (PI)) n) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ 1 (/ k n)))) (* (+ (PI) (PI)) (/ 1 (/ k n))) (/ 1 (/ k n)) 1 (/ k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) (sqrt (/ (* k n) (+ (PI) (PI)))) (/ (* k n) (+ (PI) (PI))) (* k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (- 1 k))
30.0ms
n
@-inf
((/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* (+ (PI) (PI)) n) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ 1 (/ k n)))) (* (+ (PI) (PI)) (/ 1 (/ k n))) (/ 1 (/ k n)) 1 (/ k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) (sqrt (/ (* k n) (+ (PI) (PI)))) (/ (* k n) (+ (PI) (PI))) (* k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (- 1 k))
21.0ms
n
@inf
((/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* (+ (PI) (PI)) n) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ 1 (/ k n)))) (* (+ (PI) (PI)) (/ 1 (/ k n))) (/ 1 (/ k n)) 1 (/ k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) (sqrt (/ (* k n) (+ (PI) (PI)))) (/ (* k n) (+ (PI) (PI))) (* k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (- 1 k))
6.0ms
k
@-inf
((/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* (+ (PI) (PI)) n) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ 1 (/ k n)))) (* (+ (PI) (PI)) (/ 1 (/ k n))) (/ 1 (/ k n)) 1 (/ k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) (sqrt (/ (* k n) (+ (PI) (PI)))) (/ (* k n) (+ (PI) (PI))) (* k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (- 1 k))
5.0ms
k
@0
((/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* (+ (PI) (PI)) n) (* 1/2 k) 1/2 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ 1 (/ k n)))) (* (+ (PI) (PI)) (/ 1 (/ k n))) (/ 1 (/ k n)) 1 (/ k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) (sqrt (/ (* k n) (+ (PI) (PI)))) (/ (* k n) (+ (PI) (PI))) (* k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (- 1 k))

rewrite223.0ms (3.2%)

Memory
7.1MiB live, 247.0MiB allocated; 29ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04403150
04862904
125712793
094342757
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
126 → 641
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
k
(sqrt.f64 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))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n))))
(*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))
(/.f64 #s(literal 1 binary64) (/.f64 k n))
#s(literal 1 binary64)
(/.f64 k n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64))))) n)))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64))))) n))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64))))) n)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64))))
(/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64)))
(*.f64 k n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(-.f64 #s(literal 1 binary64) k)
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (sqrt k)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* 1/2 (* k (* (log (* 2 (* n (PI)))) (sqrt k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt k)))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt k))))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt k))) (* k (+ (* 1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt k)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt k))))))))))
#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 k #s(hole 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 (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (/ (* (PI) n) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ 1 (/ k n)) #s(hole binary64 (/ n k)))
#s(approx (/ k n) #s(hole binary64 (/ k n)))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) #s(hole binary64 (/ n (sqrt (* 1/2 (/ (* k n) (PI)))))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) #s(hole binary64 (/ 1 (sqrt (* 1/2 (/ (* k n) (PI)))))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) #s(hole binary64 (sqrt (* 1/2 (/ (* k n) (PI))))))
#s(approx (/ (* k n) (+ (PI) (PI))) #s(hole binary64 (* 1/2 (/ (* k n) (PI)))))
#s(approx (* k n) #s(hole binary64 (* k n)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) #s(hole binary64 (/ n (* k (sqrt (* 1/2 (/ n (* k (PI)))))))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) #s(hole binary64 (/ 1 (* k (sqrt (* 1/2 (/ n (* k (PI)))))))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) #s(hole binary64 (* k (sqrt (* 1/2 (/ n (* k (PI))))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k))))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* -1 (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (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 (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) #s(hole binary64 (* -1 (/ n (* k (sqrt (* 1/2 (/ n (* k (PI))))))))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) #s(hole binary64 (/ -1 (* k (sqrt (* 1/2 (/ n (* k (PI)))))))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) #s(hole binary64 (* -1 (* k (sqrt (* 1/2 (/ n (* k (PI)))))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt k)))))
#s(approx (* n (+ (PI) (PI))) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt k))))
#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 (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (* n (+ (PI) (PI)))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt k))))
#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) n) k) 2)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) #s(hole binary64 (/ 1 (sqrt (* 1/2 (/ k (* n (PI))))))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) #s(hole binary64 (/ 1 (* n (sqrt (* 1/2 (/ k (* n (PI)))))))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) #s(hole binary64 (* n (sqrt (* 1/2 (/ k (* n (PI))))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt 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 (* n (+ (PI) (PI)))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) #s(hole binary64 (* (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt k))))
#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) n) k) 2)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) #s(hole binary64 (/ -1 (sqrt (* 1/2 (/ k (* n (PI))))))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) #s(hole binary64 (/ -1 (* n (sqrt (* 1/2 (/ k (* n (PI)))))))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) #s(hole binary64 (* -1 (* n (sqrt (* 1/2 (/ k (* n (PI)))))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
Outputs
(*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 n k)))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 n k)) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k))))
(pow.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)) (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) (*.f64 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 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))))
(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 n) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 n) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(pow.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal -1 binary64)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(fabs.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(fabs.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sinh.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(pow.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1 binary64))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(fabs.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (fma.f64 (PI.f64) (PI.f64) (*.f64 (PI.f64) (neg.f64 (PI.f64))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))) (neg.f64 (-.f64 (PI.f64) (PI.f64))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)))) (neg.f64 (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (fma.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (PI.f64) (PI.f64))))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))) (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))))
(+.f64 (PI.f64) (PI.f64))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)))
(log.f64 (*.f64 (exp.f64 (PI.f64)) (exp.f64 (PI.f64))))
(PI.f64)
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (*.f64 k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 n (*.f64 k #s(literal 1/2 binary64))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k #s(literal 1/2 binary64))) (pow.f64 n (*.f64 k #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 k #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (+.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))
(fabs.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 k #s(literal 1/2 binary64))))
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(-.f64 #s(literal 1 binary64) k)
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#s(approx (/ (* k n) (+ (PI) (PI))) (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* k n) (*.f64 k n))
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#s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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 (sqrt (* (/ (* (PI) n) k) 2)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) (/.f64 n (*.f64 (sqrt.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) k)) #s(literal 1/2 binary64))) k)))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) k)) #s(literal 1/2 binary64))) k)))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) k)) #s(literal 1/2 binary64))) k))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (neg.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) k))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (*.f64 (neg.f64 k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))))
#s(approx (sqrt k) (*.f64 (neg.f64 k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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 (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) (neg.f64 (/.f64 n (*.f64 (sqrt.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) k)) #s(literal 1/2 binary64))) k))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) k)) #s(literal 1/2 binary64))) k)))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) (*.f64 (neg.f64 k) (sqrt.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) k)) #s(literal 1/2 binary64)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k))))
#s(approx (* n (+ (PI) (PI))) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx n n)
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (*.f64 (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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) n) (*.f64 (PI.f64) n))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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 (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 n (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) k) #s(literal 1/2 binary64))))))
#s(approx (sqrt (* n (+ (PI) (PI)))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (*.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) k) #s(literal 1/2 binary64))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) n))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) (*.f64 (/.f64 #s(literal 1 binary64) n) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) n))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k))) (neg.f64 (*.f64 (/.f64 n (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)))) k) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (sqrt (* n (+ (PI) (PI)))) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (*.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) k) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) k) #s(literal 1/2 binary64))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) n) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ 1 (sqrt (/ (* k n) (+ (PI) (PI))))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) n)))
#s(approx (sqrt (/ (* k n) (+ (PI) (PI)))) (neg.f64 (*.f64 (sqrt.f64 (/.f64 k (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) n)))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k))))

eval59.0ms (0.8%)

Memory
-16.6MiB live, 116.4MiB allocated; 14ms collecting garbage
Compiler

Compiled 7 192 to 2 293 computations (68.1% saved)

prune54.0ms (0.8%)

Memory
-1.9MiB live, 106.1MiB allocated; 21ms collecting garbage
Pruning

49 alts after pruning (41 fresh and 8 done)

PrunedKeptTotal
New48721508
Fresh92029
Picked145
Done145
Total49849547
Accuracy
100.0%
Counts
547 → 49
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.4%
(/.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))
✓99.7%
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
55.0%
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64))) (sqrt.f64 k)))
47.4%
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
74.6%
(*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 n k)))
51.2%
(*.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)))))
47.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.3%
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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)))
45.2%
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
33.5%
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) k))
99.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
✓99.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
54.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k)))
99.6%
#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)))
99.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 k #s(literal 1 binary64)))) (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)))
35.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
96.2%
#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)))
99.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
35.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
35.3%
#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))))
35.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
35.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (sqrt.f64 k) k)))
35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
35.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))))
✓35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
18.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
✓33.2%
#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))) k)))
35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
✓35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
✓35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
33.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (exp.f64 (*.f64 (log.f64 (/.f64 k n)) #s(literal -1 binary64))))))
35.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
33.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
47.4%
#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)) n)))
45.1%
#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 k n))) n)))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) n)))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k n))) (sqrt.f64 (PI.f64)))) n)))
45.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) n)))
47.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 n (+.f64 (PI.f64) (PI.f64)))))) n)))
✓45.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.f64 (PI.f64) (PI.f64))))) n)))
44.8%
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) n)))
36.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (*.f64 k n) (*.f64 (PI.f64) n)) (*.f64 n (*.f64 k n)))) n)))
33.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
43.7%
#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)) n)))
✓44.8%
#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)))
42.9%
#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 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) n)))
49.8%
#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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
Compiler

Compiled 2 187 to 1 510 computations (31% saved)

regimes116.0ms (1.7%)

Memory
-1.6MiB live, 142.9MiB allocated; 9ms collecting garbage
Counts
81 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.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) (*.f64 (sqrt.f64 k) (sqrt.f64 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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 n (+.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k n)) (sqrt.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k n))) (sqrt.f64 (PI.f64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#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))) 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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (*.f64 k n) (*.f64 (PI.f64) n)) (*.f64 n (*.f64 k n)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (exp.f64 (*.f64 (log.f64 (/.f64 k n)) #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 (fma.f64 (PI.f64) (*.f64 k n) (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 (*.f64 k n) (*.f64 k n)))) n)))
#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 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) 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)))
(/.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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 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 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 k #s(literal 1 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 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 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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)))
(*.f64 (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 (sqrt k)) (*.f64 (/.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))) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))) (sqrt.f64 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))))
(*.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)))
(exp.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 (log.f64 (sqrt.f64 k)))))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.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 (PI.f64) (PI.f64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 n k)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 n 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)))
#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 (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) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (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 (exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (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)) #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 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
Outputs
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 k)))
Calls

4 calls:

54.0ms
k
21.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
19.0ms
n
18.0ms
(*.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)

regimes74.0ms (1.1%)

Memory
5.1MiB live, 143.6MiB allocated; 7ms collecting garbage
Counts
68 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.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) (*.f64 (sqrt.f64 k) (sqrt.f64 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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 n (+.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k n)) (sqrt.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k n))) (sqrt.f64 (PI.f64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#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))) 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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (*.f64 k n) (*.f64 (PI.f64) n)) (*.f64 n (*.f64 k n)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (exp.f64 (*.f64 (log.f64 (/.f64 k n)) #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 (fma.f64 (PI.f64) (*.f64 k n) (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 (*.f64 k n) (*.f64 k n)))) n)))
#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 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) 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)))
(/.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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 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 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 k #s(literal 1 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 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 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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)))
(*.f64 (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 (sqrt k)) (*.f64 (/.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))) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))) (sqrt.f64 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))))
(*.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)))
(exp.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 (log.f64 (sqrt.f64 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:

21.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
19.0ms
n
16.0ms
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)

regimes71.0ms (1%)

Memory
-5.1MiB live, 141.5MiB allocated; 7ms collecting garbage
Counts
66 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.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) (*.f64 (sqrt.f64 k) (sqrt.f64 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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 n (+.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k n)) (sqrt.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k n))) (sqrt.f64 (PI.f64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#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))) 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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (*.f64 k n) (*.f64 (PI.f64) n)) (*.f64 n (*.f64 k n)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (exp.f64 (*.f64 (log.f64 (/.f64 k n)) #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 (fma.f64 (PI.f64) (*.f64 k n) (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 (*.f64 k n) (*.f64 k n)))) n)))
#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 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) 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)))
(/.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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 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 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 k #s(literal 1 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 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 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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)))
(*.f64 (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 (sqrt k)) (*.f64 (/.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))) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))) (sqrt.f64 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))))
(*.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:

20.0ms
k
18.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
16.0ms
n
13.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%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)

regimes71.0ms (1%)

Memory
41.9MiB live, 136.9MiB allocated; 11ms collecting garbage
Counts
65 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.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) (*.f64 (sqrt.f64 k) (sqrt.f64 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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 n (+.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k n)) (sqrt.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k n))) (sqrt.f64 (PI.f64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#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))) 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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (*.f64 k n) (*.f64 (PI.f64) n)) (*.f64 n (*.f64 k n)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (exp.f64 (*.f64 (log.f64 (/.f64 k n)) #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 (fma.f64 (PI.f64) (*.f64 k n) (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 (*.f64 k n) (*.f64 k n)))) n)))
#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 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) 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)))
(/.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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 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 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 k #s(literal 1 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 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 (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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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)))
(*.f64 (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 (sqrt k)) (*.f64 (/.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))) (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))) (sqrt.f64 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))))
(*.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
(*.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 (/.f64 #s(literal 1 binary64) k)))
Calls

4 calls:

19.0ms
k
18.0ms
(*.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))))
15.0ms
n
15.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
99.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%1k
99.5%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes69.0ms (1%)

Memory
-9.7MiB live, 129.7MiB allocated; 10ms collecting garbage
Counts
52 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.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) (*.f64 (sqrt.f64 k) (sqrt.f64 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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 n (+.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k n)) (sqrt.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k n))) (sqrt.f64 (PI.f64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#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))) 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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (*.f64 k n) (*.f64 (PI.f64) n)) (*.f64 n (*.f64 k n)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (exp.f64 (*.f64 (log.f64 (/.f64 k n)) #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 (fma.f64 (PI.f64) (*.f64 k n) (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 (*.f64 k n) (*.f64 k n)))) n)))
#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 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) 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)))
(/.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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 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 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 k #s(literal 1 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
Outputs
(/.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))
Calls

4 calls:

25.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
13.0ms
k
13.0ms
n
Results
AccuracySegmentsBranch
99.4%1k
99.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.4%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.4%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes86.0ms (1.2%)

Memory
9.1MiB live, 108.6MiB allocated; 12ms collecting garbage
Counts
47 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.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) (*.f64 (sqrt.f64 k) (sqrt.f64 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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 n (+.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k n)) (sqrt.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k n))) (sqrt.f64 (PI.f64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#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))) 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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (*.f64 k n) (*.f64 (PI.f64) n)) (*.f64 n (*.f64 k n)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (exp.f64 (*.f64 (log.f64 (/.f64 k n)) #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 (fma.f64 (PI.f64) (*.f64 k n) (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 (*.f64 k n) (*.f64 k n)))) n)))
#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 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) 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)))
Outputs
#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)))
Calls

4 calls:

31.0ms
(*.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))))
30.0ms
n
12.0ms
k
12.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
99.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.4%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.4%1k
99.4%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes81.0ms (1.2%)

Memory
11.4MiB live, 45.6MiB allocated; 20ms collecting garbage
Counts
46 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.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) (*.f64 (sqrt.f64 k) (sqrt.f64 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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 n (+.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k n)) (sqrt.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k n))) (sqrt.f64 (PI.f64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#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))) 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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (*.f64 k n) (*.f64 (PI.f64) n)) (*.f64 n (*.f64 k n)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (exp.f64 (*.f64 (log.f64 (/.f64 k n)) #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 (fma.f64 (PI.f64) (*.f64 k n) (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 (*.f64 k n) (*.f64 k n)))) n)))
#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 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) n)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (sqrt.f64 k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k)))
Calls

4 calls:

11.0ms
n
11.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms
k
9.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
97.6%2k
79.6%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
97.6%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))))
79.6%3n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes60.0ms (0.9%)

Memory
-9.6MiB live, 39.8MiB allocated; 2ms collecting garbage
Counts
42 → 3
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.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) (*.f64 (sqrt.f64 k) (sqrt.f64 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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 n (+.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k n)) (sqrt.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k n))) (sqrt.f64 (PI.f64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#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))) 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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (*.f64 k n) (*.f64 (PI.f64) n)) (*.f64 n (*.f64 k n)))) n)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (sqrt.f64 k) 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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
Calls

4 calls:

28.0ms
k
10.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
10.0ms
n
9.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
76.0%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
76.0%3n
77.1%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))))
69.7%3k
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes52.0ms (0.7%)

Memory
-28.4MiB live, 28.2MiB allocated; 16ms collecting garbage
Counts
36 → 3
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.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) (*.f64 (sqrt.f64 k) (sqrt.f64 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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 n (+.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k n)) (sqrt.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k n))) (sqrt.f64 (PI.f64)))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.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 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
Calls

3 calls:

33.0ms
n
9.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
8.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
76.0%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
76.0%3n
74.0%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 21 to 21 computations (0% saved)

regimes39.0ms (0.6%)

Memory
5.1MiB live, 52.8MiB allocated; 4ms collecting garbage
Counts
30 → 3
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k n) (+.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) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))))
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))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 k k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
Calls

4 calls:

14.0ms
(*.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))))
8.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
8.0ms
k
8.0ms
n
Results
AccuracySegmentsBranch
59.1%2k
59.1%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
61.1%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
61.1%3n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes16.0ms (0.2%)

Memory
26.8MiB live, 26.8MiB allocated; 0ms 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 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 k n) (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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.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))))
#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) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64))) 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)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.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) n) k) #s(literal 2 binary64))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* (PI) n) k) 2)) (/.f64 n (sqrt.f64 (*.f64 k (/.f64 n (+.f64 (PI.f64) (PI.f64))))))))
Calls

2 calls:

7.0ms
n
7.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
59.2%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
59.2%2n
Compiler

Compiled 6 to 8 computations (-33.3% saved)

regimes26.0ms (0.4%)

Memory
-25.3MiB live, 20.8MiB allocated; 5ms collecting garbage
Counts
19 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.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 (PI.f64) (PI.f64)) (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) 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 (*.f64 (PI.f64) n) k) #s(literal 2 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 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 k n)))))
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))))
#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:

20.0ms
n
5.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
59.2%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
59.2%2n
Compiler

Compiled 6 to 8 computations (-33.3% saved)

regimes30.0ms (0.4%)

Memory
-10.6MiB live, 36.0MiB allocated; 3ms collecting garbage
Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
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:

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))))
4.0ms
k
4.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms
n
Results
AccuracySegmentsBranch
47.4%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
47.4%1k
47.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
47.4%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes11.0ms (0.2%)

Memory
30.9MiB live, 30.9MiB allocated; 0ms collecting garbage
Counts
8 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
Calls

4 calls:

3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms
k
3.0ms
n
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
35.4%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
35.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
35.4%1n
35.4%1k
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes13.0ms (0.2%)

Memory
-29.5MiB live, 19.9MiB allocated; 4ms collecting garbage
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
Calls

4 calls:

8.0ms
k
2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
n
1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
35.4%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
35.4%1k
35.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
35.4%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes4.0ms (0.1%)

Memory
14.2MiB live, 14.2MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

4 calls:

1.0ms
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
35.4%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
35.4%1k
35.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
35.4%1n
Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch20.0ms (0.3%)

Memory
-5.7MiB live, 41.8MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
19.0ms
0.0021248053636240835
11.63818755431952
Samples
14.0ms128×0valid
Compiler

Compiled 395 to 386 computations (2.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-sqrt: 6.0ms (56.2% of total)
ival-pow: 2.0ms (18.7% of total)
ival-div!: 1.0ms (9.4% of total)
ival-mult!: 1.0ms (9.4% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated; 0ms collecting garbage
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
4.2275804465177944e+285
+inf
0.0ms
0.0
9.756658893621806e-143
Compiler

Compiled 18 to 18 computations (0% saved)

bsearch32.0ms (0.5%)

Memory
-9.3MiB live, 85.4MiB allocated; 3ms collecting garbage
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
18.0ms
1.703779117921311e+33
6.634517958417848e+45
12.0ms
3262687637049052.0
27760690565099370.0
Samples
19.0ms256×0valid
Compiler

Compiled 857 to 828 computations (3.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-pow: 5.0ms (37.9% of total)
ival-mult!: 3.0ms (22.7% of total)
ival-sqrt: 2.0ms (15.2% of total)
ival-div!: 2.0ms (15.2% of total)
ival-sub!: 1.0ms (7.6% of total)
adjust: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory
6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
1.0ms
1.703779117921311e+33
6.634517958417848e+45
1.0ms
3262687637049052.0
27760690565099370.0
Compiler

Compiled 761 to 762 computations (-0.1% saved)

bsearch2.0ms (0%)

Memory
5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
2.0ms
1.1195724294509787e+55
4.9933814541736174e+60
Samples
1.0ms16×0valid
Compiler

Compiled 66 to 64 computations (3% 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)

bsearch19.0ms (0.3%)

Memory
-10.6MiB live, 35.9MiB allocated; 9ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
18.0ms
27760690565099370.0
4.3507671550225e+20
Samples
8.0ms128×0valid
Compiler

Compiled 403 to 394 computations (2.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-pow: 2.0ms (35.5% of total)
ival-sqrt: 1.0ms (17.8% of total)
ival-div!: 1.0ms (17.8% of total)
ival-mult!: 1.0ms (17.8% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

derivations713.0ms (10.2%)

Memory
34.1MiB live, 1 012.4MiB allocated; 290ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 252 to 144 computations (42.9% saved)

preprocess147.0ms (2.1%)

Memory
45.5MiB live, 419.0MiB allocated; 44ms collecting garbage
Remove

(abs k)

Compiler

Compiled 1 351 to 1 067 computations (21% saved)

end0.0ms (0%)

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

Profiling

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