Migdal et al, Equation (51)

Time bar (total: 6.2s)

start0.0ms (0%)

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

analyze99.0ms (1.6%)

Memory
-0.1MiB live, 135.7MiB allocated; 19ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%51.5%0%7
52.5%25%22.6%0.1%0%52.3%0%8
53.8%25%21.5%0.1%0%53.5%0%9
54.5%25%20.9%0.1%0%54%0%10
55.3%25%20.2%0.1%0%54.7%0%11
55.7%25%19.9%0.1%0%55.1%0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.0s (48.3%)

Memory
94.4MiB live, 3 593.7MiB allocated; 871ms collecting garbage
Samples
1.2s5 551×1invalid
804.0ms8 256×0valid
165.0ms476×2invalid
161.0ms249×0exit
20.0ms370×0invalid
Precisions
Click to see histograms. Total time spent on operations: 1.8s
ival-pow: 564.0ms (32% of total)
ival-mult!: 361.0ms (20.5% of total)
adjust: 276.0ms (15.7% of total)
ival-div!: 270.0ms (15.3% of total)
ival-sqrt: 202.0ms (11.5% of total)
ival-sub!: 89.0ms (5.1% of total)
ival-pi: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

preprocess100.0ms (1.6%)

Memory
-31.1MiB live, 60.7MiB allocated; 12ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033104
110890
234588
3150388
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 32 to 26 computations (18.8% saved)

series215.0ms (3.5%)

Memory
-8.9MiB live, 160.0MiB allocated; 225ms 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
169.0ms
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))
25.0ms
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))
14.0ms
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))

rewrite188.0ms (3%)

Memory
35.6MiB live, 218.8MiB allocated; 48ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01671003
0181956
1765852
06608834
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
50 → 216
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(+.f64 (/.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(pow.f64 k #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(sqrt.f64 k)
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
k
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
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(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 (*.f64 k k) #s(literal 1 binary64)) (-.f64 (neg.f64 k) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k))) (neg.f64 (+.f64 k #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k))) (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 k #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) (fma.f64 k k (+.f64 k #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) k)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(neg.f64 (+.f64 k #s(literal -1 binary64)))
(neg.f64 (+.f64 #s(literal -1 binary64) k))
(fma.f64 (neg.f64 k) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
(fma.f64 k #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (neg.f64 k) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 k k) k) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(-.f64 (neg.f64 k) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 k) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 k k) (neg.f64 k)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(+.f64 (neg.f64 k) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (fma.f64 k (/.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/8 binary64)) (*.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/48 binary64))) (sqrt.f64 k)) (*.f64 (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (-.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/8 binary64)) (*.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/48 binary64))) k) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (-.f64 #s(literal 1 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
#s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k))
#s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 (neg.f64 k) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt k)) (neg.f64 (/.f64 (sqrt.f64 k) k)))
#s(approx (sqrt k) (/.f64 (neg.f64 k) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k)) (neg.f64 k)))
#s(approx (- 1 k) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k)) (neg.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (* 2 (PI)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -2 binary64) (PI.f64)))))))

eval31.0ms (0.5%)

Memory
-43.5MiB live, 59.5MiB allocated; 14ms collecting garbage
Compiler

Compiled 4 775 to 825 computations (82.7% saved)

prune12.0ms (0.2%)

Memory
27.9MiB live, 27.9MiB allocated; 0ms collecting garbage
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New18715202
Fresh000
Picked101
Done000
Total18815203
Accuracy
100.0%
Counts
203 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
▶99.5%
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)))
▶99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
96.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
46.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
76.8%
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
▶99.5%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%
(*.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (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))))
41.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
47.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
99.6%
#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))))
▶36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
Compiler

Compiled 768 to 528 computations (31.3% saved)

series183.0ms (3%)

Memory
18.2MiB live, 294.8MiB allocated; 35ms collecting garbage
Counts
35 → 122
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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
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)))))))))))
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#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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* (sqrt 2) (* (sqrt (* 2 (/ (PI) n))) (sqrt (/ (PI) n))))) (* -2 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* (sqrt 2) (* (sqrt (* 2 (/ (PI) n))) (sqrt (/ (PI) n))))) (* -2 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) #s(hole binary64 (* -1 (* n (* (sqrt 2) (sqrt (* 2 (/ (PI) n))))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) n))))))
Calls

6 calls:

TimeVariablePointExpression
70.0ms
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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
50.0ms
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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
38.0ms
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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
10.0ms
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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
6.0ms
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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))

rewrite211.0ms (3.4%)

Memory
-32.5MiB live, 300.8MiB allocated; 65ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05865210
06434261
129893983
0103483905
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
157 → 536
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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
#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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -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 (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2))) (sqrt k))) (/ (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) 2) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2))) (sqrt k))))) (/ (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) 3) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) 2) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2)) (sqrt k))))))) (/ (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2) (sqrt k)))))
#s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) #s(hole binary64 (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2)))
#s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2)))) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2))))
#s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2))) (* 1/8 (* k (* (pow (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) 2) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2)))))) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2))))
#s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) 3) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2)))) (* 1/8 (* (pow (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) 2) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2))))))) (pow (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI))))) 1/2))))
#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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (- 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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (+ 1 (* -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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))) (- 1 k)))) (sqrt k))))
#s(approx (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) #s(hole binary64 (* (sqrt 2) (* (sqrt (* 2 (* n (PI)))) (sqrt (* n (PI)))))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (sqrt (* 2 (* n (PI)))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* (sqrt 2) (* (sqrt (* 2 (/ (PI) n))) (sqrt (/ (PI) n))))) (* -2 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* (sqrt 2) (* (sqrt (* 2 (/ (PI) n))) (sqrt (/ (PI) n))))) (* -2 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) #s(hole binary64 (* (pow n 2) (* (sqrt 2) (* (sqrt (* 2 (/ (PI) n))) (sqrt (/ (PI) n)))))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) #s(hole binary64 (* n (* (sqrt 2) (sqrt (* 2 (/ (PI) n)))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* n (sqrt (/ (PI) n)))))
#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 (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* (sqrt 2) (* (sqrt (* 2 (/ (PI) n))) (sqrt (/ (PI) n))))) (* -2 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* (sqrt 2) (* (sqrt (* 2 (/ (PI) n))) (sqrt (/ (PI) n))))) (* -2 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) #s(hole binary64 (* -1 (* n (* (sqrt 2) (sqrt (* 2 (/ (PI) n))))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) n))))))
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))))
(/.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 (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)) (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)) (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 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (*.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (neg.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (neg.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 k #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(sqrt.f64 k)
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
k
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(PI.f64)
n
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eval67.0ms (1.1%)

Memory
31.4MiB live, 170.7MiB allocated; 16ms collecting garbage
Compiler

Compiled 17 067 to 2 075 computations (87.8% saved)

prune44.0ms (0.7%)

Memory
6.4MiB live, 83.7MiB allocated; 26ms collecting garbage
Pruning

24 alts after pruning (22 fresh and 2 done)

PrunedKeptTotal
New56118579
Fresh6410
Picked325
Done000
Total57024594
Accuracy
100.0%
Counts
594 → 24
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
▶99.7%
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
81.3%
(/.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 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
✓99.5%
(*.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)))
50.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)))))
96.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
46.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
46.6%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.6%
#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))))
46.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
36.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
24.6%
#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))))
36.6%
#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)))
22.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k)))
▶22.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
34.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
▶36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
34.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
49.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
▶36.0%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
Compiler

Compiled 1 198 to 893 computations (25.5% saved)

series135.0ms (2.2%)

Memory
11.8MiB live, 161.5MiB allocated; 55ms collecting garbage
Counts
28 → 95
Calls
Call 1
Inputs
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
#s(literal 1 binary64)
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)
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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
(sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 (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))
(-.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/6 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (sqrt k)))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k)))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* k (+ (* 1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt k)))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 1))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* k (+ (* 1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#s(approx 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 (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (* k (* n (PI)))))))
#s(approx (* (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (/ (sqrt (* k (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))))) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) k)))
#s(approx (/ (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 (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (pow (sqrt (* 2 (* n (PI)))) k)))
#s(approx (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 (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* k (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (sqrt (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) k))))
#s(approx (/ (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 (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* -1 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* k (sqrt (* 2 (/ (* n (PI)) k)))))))
#s(approx (/ (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 (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (sqrt (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (sqrt (* 4 (pow (PI) 2))))))
#s(approx (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) #s(hole binary64 (* 4 (* (pow n 2) (pow (PI) 2)))))
#s(approx (/ (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 (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k)))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* n (sqrt (* 2 (/ (* k (PI)) n))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (* n (sqrt (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (* k (PI)) n)))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (* -1 (* n (sqrt (* -1 (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* n (sqrt (* 4 (pow (PI) 2)))))))
#s(approx (/ (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
42.0ms
n
@0
((/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n 1 (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k))
41.0ms
n
@inf
((/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n 1 (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k))
20.0ms
n
@-inf
((/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n 1 (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k))
17.0ms
k
@inf
((/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n 1 (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k))
6.0ms
k
@-inf
((/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (* (sqrt (* (+ (PI) (PI)) n)) 1) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n 1 (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (sqrt (* (* (+ (PI) (PI)) n) k)) (* (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k))

rewrite223.0ms (3.6%)

Memory
7.3MiB live, 234.9MiB allocated; 73ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04553539
04953159
121792962
091702923
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
123 → 517
Calls
Call 1
Inputs
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
#s(literal 1 binary64)
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)
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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k)
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
(sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)
(sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 (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))
(-.f64 #s(literal 1 binary64) k)
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/6 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (sqrt k)))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k)))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* k (+ (* 1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt k)))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 1))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* k (+ (* 1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#s(approx 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 (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (* k (* n (PI)))))))
#s(approx (* (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (/ (sqrt (* k (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))))) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) k)))
#s(approx (/ (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 (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (pow (sqrt (* 2 (* n (PI)))) k)))
#s(approx (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 (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* k (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (sqrt (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) k))))
#s(approx (/ (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 (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* -1 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (sqrt (* 2 (/ (* n (PI)) k))))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* k (sqrt (* 2 (/ (* n (PI)) k)))))))
#s(approx (/ (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 (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (sqrt (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (sqrt (* 4 (pow (PI) 2))))))
#s(approx (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) #s(hole binary64 (* 4 (* (pow n 2) (pow (PI) 2)))))
#s(approx (/ (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 (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k)))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* n (sqrt (* 2 (/ (* k (PI)) n))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (* n (sqrt (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (/ (* (sqrt (* (+ (PI) (PI)) n)) 1) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (* k (PI)) n)))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (* k (PI)) n)))))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) #s(hole binary64 (* -1 (* n (sqrt (* -1 (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* n (sqrt (* 4 (pow (PI) 2)))))))
#s(approx (/ (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 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (/.f64 n k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (/.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 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 (/.f64 n k)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
(*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal -1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (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 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (sqrt.f64 k)))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (sqrt.f64 k))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (sqrt.f64 k)))
(+.f64 (/.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.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 (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 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) #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 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 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 (sqrt.f64 (*.f64 n n)) (PI.f64))))
(*.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 (exp.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 (*.f64 #s(literal 4 binary64) (*.f64 n n)) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal -1 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 (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 1 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 (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 (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 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) #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)))
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(-.f64 #s(literal 1 binary64) k)
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#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(literal 1 binary64))
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#s(approx k k)
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (fma.f64 k (/.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k))) (sqrt.f64 k)) (*.f64 (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))) #s(literal -1/2 binary64))) k (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))
#s(approx (/ n k) (/.f64 n k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (*.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k) #s(literal 1/8 binary64))) (sqrt.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 k (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (sqrt.f64 (*.f64 k (*.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 k (*.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 k (*.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 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (* (+ (PI) (PI)) n) k) (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (/.f64 (sqrt.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (fma.f64 k (/.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k) #s(literal -1/6 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))) k (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (fma.f64 (neg.f64 k) (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (fma.f64 k (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (fma.f64 k (fma.f64 k (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 3 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k) #s(literal -1/6 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/2 binary64))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
#s(approx (- 1 k) (+.f64 (neg.f64 k) #s(literal 1 binary64)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (*.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) k))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k))
#s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
#s(approx (* (sqrt (/ 1 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)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (sqrt (/ 1 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)) k))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (* (sqrt (/ 1 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)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (*.f64 (neg.f64 k) (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
#s(approx (sqrt k) (*.f64 (neg.f64 k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (+.f64 (neg.f64 k) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (+.f64 (neg.f64 k) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (neg.f64 k) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (+.f64 (neg.f64 k) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (+.f64 (neg.f64 k) #s(literal 1 binary64))))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (/ 1 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) (* (+ (PI) (PI)) n))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))
#s(approx n n)
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k) (sqrt.f64 k)))
#s(approx (* (sqrt (/ 1 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 (/ 1 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 (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))
#s(approx (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n)) (*.f64 (*.f64 #s(literal 4 binary64) (*.f64 n n)) (*.f64 (PI.f64) (PI.f64))))
#s(approx (* (sqrt (/ 1 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 (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 n (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)) k))) (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)) k)) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)) k)))
#s(approx (* (sqrt (/ 1 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 (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) n))
#s(approx (* (sqrt (/ 1 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)) k) (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n) k))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) n))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)) (-.f64 #s(literal 1 binary64) k))))
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#s(approx (* (sqrt (* (+ (PI) (PI)) n)) 1) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) n)))
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#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) k)) k) (neg.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (neg.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)))
#s(approx (sqrt (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k)) (neg.f64 (*.f64 (sqrt.f64 (neg.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n)))) n)))
#s(approx (/ (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) k) (neg.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
#s(approx (sqrt (* (* (+ (PI) (PI)) n) (* (+ (PI) (PI)) n))) (neg.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.f64 #s(literal 1 binary64) k))))

eval74.0ms (1.2%)

Memory
-15.7MiB live, 128.8MiB allocated; 41ms collecting garbage
Compiler

Compiled 16 166 to 2 138 computations (86.8% saved)

prune32.0ms (0.5%)

Memory
28.2MiB live, 74.3MiB allocated; 5ms collecting garbage
Pruning

34 alts after pruning (29 fresh and 5 done)

PrunedKeptTotal
New49820518
Fresh8917
Picked235
Done022
Total50834542
Accuracy
100.0%
Counts
542 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.6%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
▶56.4%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
54.9%
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k #s(literal 1 binary64))) (sqrt.f64 k)))
81.4%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k))
▶99.7%
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
96.6%
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
46.7%
(/.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
99.5%
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
✓99.5%
(*.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)))
46.6%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.6%
#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))))
36.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
24.6%
#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))))
22.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k)))
▶22.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)))
34.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
▶36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
34.4%
#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))))
▶49.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
35.8%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) k))
46.6%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k)) k))
35.9%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) k))
✓36.0%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
21.2%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)) k))
35.6%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n)) k)) k))
23.6%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) k))
33.8%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/2 binary64))) k))
46.4%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k))
41.9%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
Compiler

Compiled 1 695 to 1 257 computations (25.8% saved)

series84.0ms (1.4%)

Memory
-0.5MiB live, 145.8MiB allocated; 18ms collecting garbage
Counts
32 → 84
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) 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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
(sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k)))
(*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))
(/.f64 (+.f64 (PI.f64) (PI.f64)) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)))
(sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k)))
#s(approx (- 1 k) (neg.f64 k))
(neg.f64 k)
Outputs
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/6 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (sqrt k)))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k)))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* k (+ (* 1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt k)))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 1))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* k (+ (* 1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#s(approx 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 (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* n (/ (+ (PI) (PI)) k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (+ (PI) (PI)) k) #s(hole binary64 (* 2 (/ (PI) k))))
#s(approx (* (sqrt (/ (+ (PI) (PI)) (* n k))) 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 (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) #s(hole binary64 (/ (sqrt (* k (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))))) k)))
#s(approx (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) #s(hole binary64 (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) 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 (neg k) #s(hole binary64 (* -1 k)))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (pow (sqrt (* 2 (* n (PI)))) k)))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) 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 (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) #s(hole binary64 (sqrt (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* -1 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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 (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* n (+ (PI) (PI))) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 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 (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) #s(hole binary64 (sqrt (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) #s(hole binary64 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k)))
#s(approx (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) #s(hole binary64 (* n (sqrt (* 4 (pow (PI) 2))))))
#s(approx (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI))))) #s(hole binary64 (* 4 (* (pow n 2) (pow (PI) 2)))))
#s(approx (* n (* n (+ (PI) (PI)))) #s(hole binary64 (* 2 (* (pow n 2) (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 (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k)))))
#s(approx (sqrt (* n (+ (PI) (PI)))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 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 (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) #s(hole binary64 (* n (sqrt (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))))
#s(approx (sqrt (* n (+ (PI) (PI)))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) #s(hole binary64 (* -1 (* n (sqrt (* -1 (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) #s(hole binary64 (* -1 (* n (sqrt (* 4 (pow (PI) 2)))))))
#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
24.0ms
n
@0
((/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI))))) (* n (* n (+ (PI) (PI)))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (neg k))
22.0ms
n
@inf
((/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI))))) (* n (* n (+ (PI) (PI)))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (neg k))
20.0ms
n
@-inf
((/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI))))) (* n (* n (+ (PI) (PI)))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (neg k))
7.0ms
k
@0
((/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI))))) (* n (* n (+ (PI) (PI)))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (neg k))
5.0ms
k
@-inf
((/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI))))) (* n (* n (+ (PI) (PI)))) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (neg k))

rewrite228.0ms (3.7%)

Memory
-26.9MiB live, 204.1MiB allocated; 23ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04253065
04712790
119852617
083552584
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
116 → 449
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) 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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
(sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k)))
(*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))
(/.f64 (+.f64 (PI.f64) (PI.f64)) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)))
(sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k)))
#s(approx (- 1 k) (neg.f64 k))
(neg.f64 k)
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/6 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (sqrt k)))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k)))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (+ (sqrt k) (* k (+ (* k (+ (* 1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt k)))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt k))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 1))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* k (+ (* 1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#s(approx 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 (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* n (/ (+ (PI) (PI)) k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (+ (PI) (PI)) k) #s(hole binary64 (* 2 (/ (PI) k))))
#s(approx (* (sqrt (/ (+ (PI) (PI)) (* n k))) 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 (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) #s(hole binary64 (/ (sqrt (* k (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))))) k)))
#s(approx (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) #s(hole binary64 (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) 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 (neg k) #s(hole binary64 (* -1 k)))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (pow (sqrt (* 2 (* n (PI)))) k)))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) 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 (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) #s(hole binary64 (sqrt (/ (sqrt (* 4 (* (pow n 2) (pow (PI) 2)))) k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* -1 (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (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 (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* n (+ (PI) (PI))) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 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 (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) #s(hole binary64 (sqrt (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) #s(hole binary64 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k)))
#s(approx (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) #s(hole binary64 (* n (sqrt (* 4 (pow (PI) 2))))))
#s(approx (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI))))) #s(hole binary64 (* 4 (* (pow n 2) (pow (PI) 2)))))
#s(approx (* n (* n (+ (PI) (PI)))) #s(hole binary64 (* 2 (* (pow n 2) (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 (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k)))))
#s(approx (sqrt (* n (+ (PI) (PI)))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 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 (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) #s(hole binary64 (* n (sqrt (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))))
#s(approx (sqrt (* n (+ (PI) (PI)))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) #s(hole binary64 (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* n (/ (+ (PI) (PI)) k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (sqrt (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k)) #s(hole binary64 (* -1 (* n (sqrt (* -1 (/ (sqrt (* 4 (pow (PI) 2))) (* k n))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) #s(hole binary64 (* -1 (/ (* n (sqrt (* 4 (pow (PI) 2)))) k))))
#s(approx (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) #s(hole binary64 (* -1 (* n (sqrt (* 4 (pow (PI) 2)))))))
#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 (sqrt.f64 n) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 k #s(literal 2 binary64)))))
(*.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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)))
(*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (neg.f64 (neg.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n))) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k))))
(/.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
(+.f64 (/.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (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 (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 (sqrt.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) n))))
(*.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 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64))
(pow.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) n) (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 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))
(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 (fabs.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (fabs.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
(*.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 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) 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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) n) (+.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1 binary64))
(/.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64))) (fma.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n n) (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n n)) (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n n)))))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(sqrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) n) (+.f64 (PI.f64) (PI.f64))))
(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)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) n) (+.f64 (PI.f64) (PI.f64)))) #s(literal 1/2 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))
(pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(/.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)))))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)))
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#s(approx n n)
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#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)))) (-.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 (sqrt (/ (* (+ (PI) (PI)) n) k)) (neg.f64 (*.f64 (sqrt.f64 (neg.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n)))) n)))
#s(approx (/ (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) k) (neg.f64 (*.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)))
#s(approx (sqrt (* (+ (PI) (PI)) (* n (* n (+ (PI) (PI)))))) (neg.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (-.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))))

eval64.0ms (1%)

Memory
26.9MiB live, 69.7MiB allocated; 8ms collecting garbage
Compiler

Compiled 12 960 to 1 770 computations (86.3% saved)

prune69.0ms (1.1%)

Memory
-36.2MiB live, 69.7MiB allocated; 32ms collecting garbage
Pruning

38 alts after pruning (29 fresh and 9 done)

PrunedKeptTotal
New37911390
Fresh61824
Picked055
Done145
Total38638424
Accuracy
100.0%
Counts
424 → 38
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.6%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
✓56.4%
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
81.4%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k))
✓99.7%
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
54.9%
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64))) (sqrt.f64 k)))
46.7%
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (sqrt.f64 k)))
96.6%
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
99.5%
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
46.6%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
99.6%
#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))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
36.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
36.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
24.6%
#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))))
✓22.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)))
34.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
✓36.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
34.4%
#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))))
46.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)) n)))
49.9%
#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)))
49.7%
#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)))
35.7%
#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)))
40.0%
#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)))
47.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) n)))
✓49.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
47.5%
#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)))
46.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 #s(approx (sqrt (/ (+ (PI) (PI)) (* n k))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
35.8%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) k))
46.6%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k)) k))
35.9%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) k))
✓36.0%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
21.2%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)) k))
23.6%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) k))
33.8%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/2 binary64))) k))
41.9%
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
Compiler

Compiled 2 929 to 1 135 computations (61.2% saved)

regimes92.0ms (1.5%)

Memory
-2.4MiB live, 90.0MiB allocated; 6ms collecting garbage
Counts
65 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#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 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k 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 (* (/ 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #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)) k)) (sqrt.f64 n)) 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 #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 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)))
#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))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #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 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n)) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 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))) #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)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/2 binary64))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) n)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
#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 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k #s(literal 1 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k))
(*.f64 (/.f64 #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 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 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)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 k (neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
Calls

4 calls:

33.0ms
k
17.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
16.0ms
n
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))))
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 23 to 23 computations (0% saved)

regimes64.0ms (1%)

Memory
27.4MiB live, 124.4MiB allocated; 13ms collecting garbage
Counts
55 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#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 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k 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 (* (/ 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #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)) k)) (sqrt.f64 n)) 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 #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 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)))
#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))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #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 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n)) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 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))) #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)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/2 binary64))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) #s(literal 1/2 binary64))) n)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
#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 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (*.f64 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k #s(literal 1 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k))
(*.f64 (/.f64 #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)))))
Outputs
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
Calls

4 calls:

19.0ms
k
16.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
14.0ms
n
12.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%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 23 to 23 computations (0% saved)

regimes89.0ms (1.4%)

Memory
-8.7MiB live, 82.6MiB allocated; 10ms collecting garbage
Counts
42 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#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 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k 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 (* (/ 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #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)) k)) (sqrt.f64 n)) 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 #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 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)))
#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))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #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 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n)) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 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))) #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)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/2 binary64))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 (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 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
Calls

4 calls:

36.0ms
n
30.0ms
(*.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
77.2%4(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
98.3%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
98.3%2k
77.2%4n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes52.0ms (0.8%)

Memory
4.6MiB live, 94.8MiB allocated; 18ms collecting garbage
Counts
39 → 3
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#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 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k 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 (* (/ 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #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)) k)) (sqrt.f64 n)) 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 #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 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)))
#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))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #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 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 n n))) n)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 n)) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (*.f64 k (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 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))) #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 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k))
Calls

4 calls:

16.0ms
(*.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))))
14.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
10.0ms
n
10.0ms
k
Results
AccuracySegmentsBranch
71.7%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
71.7%3n
72.1%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))))
69.1%3k
Compiler

Compiled 23 to 23 computations (0% saved)

regimes30.0ms (0.5%)

Memory
24.0MiB live, 67.1MiB allocated; 6ms collecting garbage
Counts
31 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#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 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k 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 (* (/ 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #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)) k)) (sqrt.f64 n)) 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 #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 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) k)))
#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))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 #s(approx (sqrt (/ (+ (PI) (PI)) (* n k))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.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 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Calls

3 calls:

12.0ms
n
9.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
69.9%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
69.9%2n
69.9%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 22 to 21 computations (4.5% saved)

regimes19.0ms (0.3%)

Memory
-6.4MiB live, 38.5MiB allocated; 5ms collecting garbage
Counts
26 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#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 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k 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 (* (/ 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #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)) k)) (sqrt.f64 n)) 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k))
Outputs
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (sqrt (* (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Calls

2 calls:

10.0ms
n
7.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
69.9%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
69.9%2n
Compiler

Compiled 6 to 8 computations (-33.3% saved)

regimes35.0ms (0.6%)

Memory
-25.8MiB live, 77.9MiB allocated; 12ms collecting garbage
Counts
25 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#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 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k 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 (* (/ 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (*.f64 k n))) n)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #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)) k)) (sqrt.f64 n)) 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))))
Outputs
#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))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 n k))) n)))
Calls

4 calls:

11.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
10.0ms
k
7.0ms
n
6.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
60.7%2k
60.7%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
60.8%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
60.8%2n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes19.0ms (0.3%)

Memory
4.7MiB live, 52.0MiB allocated; 2ms collecting garbage
Counts
14 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
#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 #s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) k) (sqrt k)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (*.f64 k n))) k))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
Calls

4 calls:

5.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
4.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms
n
4.0ms
k
Results
AccuracySegmentsBranch
46.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
46.7%1k
46.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
46.7%1n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes12.0ms (0.2%)

Memory
32.8MiB live, 32.8MiB 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 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
Calls

4 calls:

3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms
n
3.0ms
k
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
46.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
46.6%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))))
46.6%1n
46.6%1k
Compiler

Compiled 23 to 23 computations (0% saved)

regimes9.0ms (0.1%)

Memory
-24.0MiB live, 23.1MiB allocated; 2ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
Calls

4 calls:

3.0ms
k
2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
n
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
36.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
36.7%1k
36.7%1n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes7.0ms (0.1%)

Memory
20.1MiB live, 20.1MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

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

4 calls:

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

Compiled 23 to 23 computations (0% saved)

bsearch56.0ms (0.9%)

Memory
-41.0MiB live, 30.3MiB allocated; 97ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
54.0ms
0.37654751874152376
10.641164167045552
Samples
50.0ms112×0valid
Compiler

Compiled 313 to 263 computations (16% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-pow: 2.0ms (39.2% of total)
ival-sqrt: 1.0ms (19.6% of total)
ival-div!: 1.0ms (19.6% of total)
ival-mult!: 1.0ms (19.6% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated; 0ms collecting garbage
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
1.4363839968051145e+287
+inf
0.0ms
0.0
9.323877632155013e-126
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch8.0ms (0.1%)

Memory
17.4MiB live, 17.4MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
7.0ms
5.181615218594458e-19
1.3478640143619423e-18
Samples
5.0ms64×0valid
Compiler

Compiled 351 to 250 computations (28.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-sqrt: 1.0ms (33% of total)
ival-div!: 1.0ms (33% of total)
ival-pow: 1.0ms (33% of total)
ival-mult!: 1.0ms (33% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch18.0ms (0.3%)

Memory
-14.5MiB live, 34.1MiB allocated; 6ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
17.0ms
1.9399271827067823e-16
1.5761717278508498e-14
Samples
12.0ms112×0valid
Compiler

Compiled 537 to 396 computations (26.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-pow: 3.0ms (52.3% of total)
ival-sqrt: 1.0ms (17.4% of total)
ival-div!: 1.0ms (17.4% of total)
ival-mult!: 1.0ms (17.4% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch10.0ms (0.2%)

Memory
20.8MiB live, 20.8MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
9.0ms
3.655658346691168e-11
1.5459626680077064e-10
Samples
5.0ms80×0valid
Compiler

Compiled 324 to 248 computations (23.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-sqrt: 1.0ms (26.9% of total)
ival-div!: 1.0ms (26.9% of total)
ival-pow: 1.0ms (26.9% of total)
ival-mult!: 1.0ms (26.9% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

derivations495.0ms (8%)

Memory
23.4MiB live, 475.0MiB allocated; 70ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 554 to 117 computations (78.9% saved)

preprocess120.0ms (1.9%)

Memory
-20.6MiB live, 218.0MiB allocated; 55ms collecting garbage
Compiler

Compiled 570 to 130 computations (77.2% saved)

end0.0ms (0%)

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

Profiling

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