Migdal et al, Equation (51)

Time bar (total: 4.6s)

start0.0ms (0%)

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

analyze174.0ms (3.8%)

Memory
-13.9MiB live, 138.0MiB allocated; 43ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%51.5%0%7
52.5%25%22.6%0.1%0%52.3%0%8
53.8%25%21.5%0.1%0%53.5%0%9
54.5%25%20.9%0.1%0%54%0%10
55.3%25%20.2%0.1%0%54.7%0%11
55.7%25%19.9%0.1%0%55.1%0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample2.6s (55.1%)

Memory
51.7MiB live, 3 930.9MiB allocated; 491ms collecting garbage
Samples
1.0s5 483×1invalid
814.0ms8 256×0valid
105.0ms462×2invalid
35.0ms378×0invalid
23.0ms231×0exit
Precisions
Click to see histograms. Total time spent on operations: 1.4s
ival-pow: 516.0ms (35.8% of total)
ival-mult!: 245.0ms (17% of total)
adjust: 222.0ms (15.4% of total)
ival-sqrt: 202.0ms (14% of total)
ival-div!: 200.0ms (13.9% of total)
ival-sub!: 58.0ms (4% of total)
ival-pi: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

explain175.0ms (3.8%)

Memory
-27.0MiB live, 267.2MiB allocated; 55ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
377(6.380440949809345e-227 1.5169507123115685e+295)0-(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
00-0-k
00-0-n
00-0-(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
00-0-#s(literal 1 binary64)
00-0-(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
00-0-(sqrt.f64 k)
00-0-#s(literal 2 binary64)
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
00-0-(-.f64 #s(literal 1 binary64) k)
00-0-(*.f64 #s(literal 2 binary64) (PI.f64))
00-0-(*.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))))
00-0-(PI.f64)
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
pow.f64(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))sensitivity8026
Confusion
Predicted +Predicted -
+30
-77176
Precision
0.0375
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+300
-7726150
Precision?
0.02830188679245283
Recall?
1.0
Freqs
test
numberfreq
0176
180
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
47.0ms512×0valid
Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-pow: 10.0ms (39.4% of total)
ival-div!: 5.0ms (19.7% of total)
ival-sqrt: 4.0ms (15.8% of total)
ival-mult!: 4.0ms (15.8% of total)
ival-sub!: 2.0ms (7.9% of total)
adjust: 0.0ms (0% of total)

preprocess35.0ms (0.8%)

Memory
4.4MiB live, 49.8MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033104
17690
216288
338288
4161588
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)

series72.0ms (1.6%)

Memory
34.9MiB live, 131.3MiB allocated; 10ms collecting garbage
Counts
13 → 34
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Calls

6 calls:

TimeVariablePointExpression
30.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
27.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
8.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
3.0ms
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))
3.0ms
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))

rewrite55.0ms (1.2%)

Memory
-6.8MiB live, 85.5MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0181965
0195935
0833922
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
47 → 70
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
k
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ 1 (sqrt k)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
#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) #s(literal 2 binary64)) n)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) 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) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) 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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt k) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* 2 (PI)) n) (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval7.0ms (0.1%)

Memory
14.3MiB live, 14.3MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 532 to 285 computations (81.4% saved)

prune8.0ms (0.2%)

Memory
-33.1MiB live, 13.6MiB allocated; 2ms collecting garbage
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New51859
Fresh000
Picked101
Done000
Total52860
Accuracy
99.9%
Counts
60 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
▶58.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
45.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
45.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
▶99.6%
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
▶36.1%
#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))))
Compiler

Compiled 418 to 334 computations (20.1% saved)

series649.0ms (14%)

Memory
-65.0MiB live, 225.2MiB allocated; 861ms collecting garbage
Counts
46 → 120
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal -1 binary64))
k
#s(literal -1 binary64)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k)
(fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))
(*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))
(*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))
(*.f64 (pow.f64 k #s(literal 3 binary64)) n)
(pow.f64 k #s(literal 3 binary64))
#s(literal 3 binary64)
(sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(*.f64 (*.f64 (PI.f64) n) k)
Outputs
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (pow k -1)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow k -1) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ (* (PI) n) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (sqrt (* (pow k 3) (* n (PI))))))
#s(approx (* (* (pow k 3) n) (PI)) #s(hole binary64 (* (pow k 3) (* n (PI)))))
#s(approx (* (pow k 3) n) #s(hole binary64 (* (pow k 3) n)))
#s(approx (pow k 3) #s(hole binary64 (pow k 3)))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* (* (* (PI) n) k) 2) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* (* (PI) n) k) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (pow k -1)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1 (* k (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -2) (sqrt -1))))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -2) (sqrt -1)))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2))))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))) k))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2)))))
Calls

6 calls:

TimeVariablePointExpression
524.0ms
k
@-inf
((* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) k -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* -1/2 k) -1/2 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k))
37.0ms
n
@-inf
((* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) k -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* -1/2 k) -1/2 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k))
19.0ms
k
@0
((* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) k -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* -1/2 k) -1/2 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k))
18.0ms
k
@inf
((* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) k -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* -1/2 k) -1/2 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k))
14.0ms
n
@inf
((* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) k -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) (* -1/2 k) -1/2 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k))

rewrite88.0ms (1.9%)

Memory
-5.3MiB live, 133.9MiB allocated; 27ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03904578
04584295
015784253
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
166 → 303
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal -1 binary64))
k
#s(literal -1 binary64)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
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(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k)
(fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))
(*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))
(*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))
(*.f64 (pow.f64 k #s(literal 3 binary64)) n)
(pow.f64 k #s(literal 3 binary64))
#s(literal 3 binary64)
(sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(*.f64 (*.f64 (PI.f64) n) k)
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (pow k -1)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow k -1) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ (* (PI) n) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (sqrt (* (pow k 3) (* n (PI))))))
#s(approx (* (* (pow k 3) n) (PI)) #s(hole binary64 (* (pow k 3) (* n (PI)))))
#s(approx (* (pow k 3) n) #s(hole binary64 (* (pow k 3) n)))
#s(approx (pow k 3) #s(hole binary64 (pow k 3)))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* (* (* (PI) n) k) 2) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* (* (PI) n) k) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
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#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
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#s(approx (sqrt (pow k -1)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1 (* k (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -2) (sqrt -1))))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (* (sqrt -2) (sqrt -1)))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2))))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2)))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (sqrt (/ (* k (PI)) n)) (sqrt 2))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))) k))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2)))))
Outputs
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) k)
(/.f64 #s(literal -1 binary64) (neg.f64 k))
(exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))
k
#s(literal -1 binary64)
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)
(fma.f64 (PI.f64) (/.f64 n k) (/.f64 (*.f64 (PI.f64) n) k))
(fma.f64 n (/.f64 (PI.f64) k) (/.f64 (*.f64 (PI.f64) n) k))
(+.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 (*.f64 (PI.f64) n) k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 n #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
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#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ (* (PI) n) k) 2) (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
#s(approx (/ (* (PI) n) k) (/.f64 (*.f64 (PI.f64) n) k))
#s(approx (sqrt (pow k -1)) (pow.f64 k #s(literal -1/2 binary64)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (* -1/2 k) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
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#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))
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#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
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#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))
#s(approx (* (* (pow k 3) n) (PI)) (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))
#s(approx (* (pow k 3) n) (*.f64 (pow.f64 k #s(literal 3 binary64)) n))
#s(approx (pow k 3) (pow.f64 k #s(literal 3 binary64)))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))
#s(approx (* (* (* (PI) n) k) 2) (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
#s(approx (* (* (PI) n) k) (*.f64 (*.f64 (PI.f64) n) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1 binary64)) k))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64)))) k))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (*.f64 (*.f64 k k) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal -1 binary64)))
#s(approx (sqrt (pow k -1)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64)))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1 binary64)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (sqrt k) (neg.f64 (*.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))))
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#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (neg.f64 (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64))))) (*.f64 k k)))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) #s(literal -1 binary64)))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) (neg.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* (PI) 2) n) (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))
#s(approx n n)
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (PI) n) (*.f64 (PI.f64) n))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* (PI) 2) n) (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* (PI) 2) n)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (*.f64 n (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64)))) k)))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64)))) n))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (neg.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64)))) n)) k))
#s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64)))) n)))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) #s(literal -1 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (neg.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) #s(literal -1 binary64))))

eval28.0ms (0.6%)

Memory
21.6MiB live, 66.5MiB allocated; 7ms collecting garbage
Compiler

Compiled 9 229 to 1 088 computations (88.2% saved)

prune24.0ms (0.5%)

Memory
-12.2MiB live, 44.0MiB allocated; 10ms collecting garbage
Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New22515240
Fresh033
Picked415
Done000
Total22919248
Accuracy
100.0%
Counts
248 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
45.2%
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (sqrt.f64 k))
▶99.6%
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
58.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
▶99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
▶45.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
▶45.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
45.5%
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))))
45.2%
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
99.6%
(*.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))))
52.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 k k) k) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
26.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))))) k))
19.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (*.f64 (*.f64 k k) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64)))))) k))
35.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
36.0%
#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))))
✓36.1%
#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))))
36.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
▶36.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
15.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64)))) k)))
Compiler

Compiled 1 477 to 988 computations (33.1% saved)

series83.0ms (1.8%)

Memory
-7.6MiB live, 183.6MiB allocated; 9ms collecting garbage
Counts
42 → 95
Calls
Call 1
Inputs
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)
(*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
Outputs
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx k #s(hole binary64 k))
#s(approx (pow k -1/2) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* n (/ (PI) k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* n (/ (PI) k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ (PI) k) #s(hole binary64 (/ (PI) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) #s(hole binary64 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) #s(hole binary64 (* k (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (pow k -1/2) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* k (+ (* -1 (* (/ (sqrt 2) k) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 n) (PI)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* 2 n) #s(hole binary64 (* 2 n)))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) #s(hole binary64 (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* n (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (sqrt 2))))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (* n (PI))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) #s(hole binary64 (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) #s(hole binary64 (* -1 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (* n (PI)))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) #s(hole binary64 (* k (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
Calls

6 calls:

TimeVariablePointExpression
19.0ms
k
@0
((* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (* 2 n) 2 n (PI) (/ (- 1 k) 2) (- 1 k) 1 k (pow k -1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
13.0ms
n
@inf
((* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (* 2 n) 2 n (PI) (/ (- 1 k) 2) (- 1 k) 1 k (pow k -1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
12.0ms
n
@-inf
((* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (* 2 n) 2 n (PI) (/ (- 1 k) 2) (- 1 k) 1 k (pow k -1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
12.0ms
k
@-inf
((* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (* 2 n) 2 n (PI) (/ (- 1 k) 2) (- 1 k) 1 k (pow k -1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
12.0ms
n
@0
((* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (* 2 n) 2 n (PI) (/ (- 1 k) 2) (- 1 k) 1 k (pow k -1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))

rewrite64.0ms (1.4%)

Memory
8.0MiB live, 101.9MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03383092
03952965
014142939
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
137 → 255
Calls
Call 1
Inputs
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)
(*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx k #s(hole binary64 k))
#s(approx (pow k -1/2) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* n (/ (PI) k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* n (/ (PI) k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ (PI) k) #s(hole binary64 (/ (PI) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) #s(hole binary64 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) #s(hole binary64 (* k (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (pow k -1/2) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* k (+ (* -1 (* (/ (sqrt 2) k) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 n) (PI)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* 2 n) #s(hole binary64 (* 2 n)))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
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#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
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#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 (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* n (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (sqrt 2))))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (* n (PI))))))
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#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) #s(hole binary64 (* -1 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (* n (PI)))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) #s(hole binary64 (* k (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
Outputs
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 n #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) n)
(+.f64 n n)
#s(literal 2 binary64)
n
(PI.f64)
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(*.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))
(exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))
#s(literal -1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)
(fma.f64 (/.f64 (PI.f64) k) n (/.f64 (*.f64 (PI.f64) n) k))
(fma.f64 n (/.f64 (PI.f64) k) (/.f64 (*.f64 (PI.f64) n) k))
(+.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 (*.f64 (PI.f64) n) k))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 k))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 (neg.f64 (PI.f64)) (neg.f64 k))
(/.f64 (PI.f64) k)
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(*.f64 #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (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 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(+.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))
#s(literal 1/2 binary64)
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))))
(*.f64 #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))) (sqrt.f64 k))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))))
(fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n) (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(fma.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(-.f64 (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
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#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (neg.f64 k) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64) (neg.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* 2 n) (PI)) (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
#s(approx (* 2 n) (*.f64 n #s(literal 2 binary64)))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (* (PI) 2) n)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
#s(approx (* (* 2 n) (PI)) (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
#s(approx (* (* 2 n) (PI)) (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (fma.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* (PI) 2) n)) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
#s(approx (sqrt (* (PI) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
#s(approx (* (PI) n) (*.f64 (PI.f64) n))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow k -1/2)) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (neg.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (* (PI) 2) n)) (neg.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 k) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (neg.f64 (*.f64 (*.f64 (neg.f64 k) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (sqrt (* (PI) n)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))

eval30.0ms (0.6%)

Memory
-31.2MiB live, 63.9MiB allocated; 7ms collecting garbage
Compiler

Compiled 8 067 to 992 computations (87.7% saved)

prune17.0ms (0.4%)

Memory
38.1MiB live, 38.1MiB allocated; 0ms collecting garbage
Pruning

20 alts after pruning (17 fresh and 3 done)

PrunedKeptTotal
New2189227
Fresh5813
Picked325
Done011
Total22620246
Accuracy
100.0%
Counts
246 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
45.5%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))) (sqrt.f64 k))
▶45.2%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
45.2%
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
▶58.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
✓99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
45.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
45.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
44.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
45.1%
(*.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))))
▶41.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
45.2%
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
▶99.6%
(*.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))))
26.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))))) k))
35.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
36.0%
#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))))
✓36.1%
#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))))
▶36.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
✓36.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
15.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64)))) k)))
Compiler

Compiled 1 411 to 953 computations (32.5% saved)

series64.0ms (1.4%)

Memory
-9.0MiB live, 130.5MiB allocated; 6ms collecting garbage
Counts
45 → 140
Calls
Call 1
Inputs
(*.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)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 n k)
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
(*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 n #s(literal 2 binary64))
(sqrt.f64 k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k)))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k)
(fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)
Outputs
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* (PI) (/ n k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (PI) (/ n k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) #s(hole binary64 (* (/ (sqrt 2) k) (sqrt (* n (PI))))))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) #s(hole binary64 (/ (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) k)))
#s(approx (/ (sqrt (* (* n 2) (PI))) k) #s(hole binary64 (* (/ (sqrt 2) k) (sqrt (* n (PI))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) #s(hole binary64 (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) #s(hole binary64 (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* k (+ (* -1 (* (/ (sqrt 2) k) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))))))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) #s(hole binary64 (* -1 (* k (+ (* -1 (* (/ (sqrt 2) k) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (sqrt (* (* n 2) (PI))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (* n 2) (PI)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* n 2) #s(hole binary64 (* 2 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) #s(hole binary64 (+ (* -1/2 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (/ (sqrt 2) k) (sqrt (* n (PI)))))))
#s(approx (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) #s(hole binary64 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (log (* (* n 2) (PI))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* (* n 2) (PI))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* n (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (sqrt 2))))))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) #s(hole binary64 (* k (* n (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (/ (sqrt 2) k) (sqrt (/ (PI) n))))))))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) #s(hole binary64 (* n (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* (/ (sqrt 2) k) (sqrt (/ (PI) n)))))))
#s(approx (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) #s(hole binary64 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* (* n 2) (PI))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* n 2) (PI))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (sqrt (* (* n 2) (PI))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) #s(hole binary64 (* -1 (* k (* n (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (/ (* (sqrt -2) (sqrt -1)) k) (sqrt (/ (PI) n)))))))))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (/ (* (sqrt -2) (sqrt -1)) k) (sqrt (/ (PI) n))))))))
#s(approx (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (* (log (* (* n 2) (PI))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* n 2) (PI))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (/ (sqrt (* (* n 2) (PI))) k) #s(hole binary64 (* -1 (* (/ (* (sqrt -2) (sqrt -1)) k) (sqrt (* n (PI)))))))
Calls

6 calls:

TimeVariablePointExpression
15.0ms
n
@-inf
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt (* (* n 2) (PI))) (* (* n 2) (PI)) (* n 2) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (/ (- 1 k) 2) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) (sqrt (* (PI) n)) (* (PI) n) (* (log (* (* n 2) (PI))) (sqrt 2)) (log (* (* n 2) (PI))) (sqrt 2) (/ (sqrt (* (* n 2) (PI))) k))
13.0ms
n
@0
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt (* (* n 2) (PI))) (* (* n 2) (PI)) (* n 2) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (/ (- 1 k) 2) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) (sqrt (* (PI) n)) (* (PI) n) (* (log (* (* n 2) (PI))) (sqrt 2)) (log (* (* n 2) (PI))) (sqrt 2) (/ (sqrt (* (* n 2) (PI))) k))
12.0ms
n
@inf
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt (* (* n 2) (PI))) (* (* n 2) (PI)) (* n 2) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (/ (- 1 k) 2) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) (sqrt (* (PI) n)) (* (PI) n) (* (log (* (* n 2) (PI))) (sqrt 2)) (log (* (* n 2) (PI))) (sqrt 2) (/ (sqrt (* (* n 2) (PI))) k))
8.0ms
k
@-inf
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt (* (* n 2) (PI))) (* (* n 2) (PI)) (* n 2) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (/ (- 1 k) 2) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) (sqrt (* (PI) n)) (* (PI) n) (* (log (* (* n 2) (PI))) (sqrt 2)) (log (* (* n 2) (PI))) (sqrt 2) (/ (sqrt (* (* n 2) (PI))) k))
6.0ms
k
@0
((* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt (* (* n 2) (PI))) (* (* n 2) (PI)) (* n 2) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (/ (- 1 k) 2) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) (sqrt (* (PI) n)) (* (PI) n) (* (log (* (* n 2) (PI))) (sqrt 2)) (log (* (* n 2) (PI))) (sqrt 2) (/ (sqrt (* (* n 2) (PI))) k))

rewrite85.0ms (1.8%)

Memory
-29.9MiB live, 80.7MiB allocated; 25ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04225452
04875093
016965021
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
185 → 327
Calls
Call 1
Inputs
(*.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)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 n k)
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
(*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 n #s(literal 2 binary64))
(sqrt.f64 k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k)))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k)
(fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
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#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
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#s(approx (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) #s(hole binary64 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (log (* (* n 2) (PI))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* n 2) (PI))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (sqrt (* (* n 2) (PI))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) #s(hole binary64 (* -1 (* k (* n (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (/ (* (sqrt -2) (sqrt -1)) k) (sqrt (/ (PI) n)))))))))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (/ (* (sqrt -2) (sqrt -1)) k) (sqrt (/ (PI) n))))))))
#s(approx (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (* (log (* (* n 2) (PI))) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* n 2) (PI))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (/ (sqrt (* (* n 2) (PI))) k) #s(hole binary64 (* -1 (* (/ (* (sqrt -2) (sqrt -1)) k) (sqrt (* n (PI)))))))
Outputs
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(+.f64 (PI.f64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(pow.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))
(*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))
(*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))
(/.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)
(fma.f64 (/.f64 n k) (PI.f64) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (PI.f64) (/.f64 n k) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 n (/.f64 (PI.f64) k) (*.f64 (/.f64 n k) (PI.f64)))
(+.f64 (*.f64 (/.f64 n k) (PI.f64)) (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 k))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 (neg.f64 n) (neg.f64 k))
(/.f64 n k)
(*.f64 #s(literal 1 binary64) (/.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k)))
(/.f64 (neg.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k))
(*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.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 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 n #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) n)
(+.f64 n n)
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 n #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (+.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(+.f64 (PI.f64) (PI.f64))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
(*.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k)))) (sqrt.f64 k))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k)))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k)
(*.f64 k (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)))
(fma.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64)) k (*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k) k))
(fma.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64)) (*.f64 k (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)))
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#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (* n 2) (PI))) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
#s(approx (* (+ (PI) (PI)) n) (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
#s(approx (* n 2) (*.f64 n #s(literal 2 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (+ (PI) (PI)) n) (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (fma.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)))
#s(approx (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (sqrt (* (PI) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
#s(approx (* (PI) n) (*.f64 (PI.f64) n))
#s(approx (* (log (* (* n 2) (PI))) (sqrt 2)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* n 2) (PI))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) (*.f64 (*.f64 k n) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) k))))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) k)) n))
#s(approx (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (log (* (* n 2) (PI))) (sqrt 2)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* n 2) (PI))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) (neg.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (* n 2) (PI))) (neg.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 k) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))
#s(approx (* (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) k) (*.f64 (neg.f64 k) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (PI.f64) n))) (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) k)) n)))
#s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (PI.f64) n))) (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) k)) n)))
#s(approx (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) (neg.f64 (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (* (PI) n)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (* (log (* (* n 2) (PI))) (sqrt 2)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (log (* (* n 2) (PI))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (/ (sqrt (* (* n 2) (PI))) k) (neg.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)))

eval41.0ms (0.9%)

Memory
3.5MiB live, 48.7MiB allocated; 3ms collecting garbage
Compiler

Compiled 11 000 to 1 172 computations (89.3% saved)

prune52.0ms (1.1%)

Memory
2.3MiB live, 48.8MiB allocated; 2ms collecting garbage
Pruning

23 alts after pruning (19 fresh and 4 done)

PrunedKeptTotal
New2228230
Fresh11112
Picked325
Done123
Total22723250
Accuracy
100.0%
Counts
250 → 23
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
45.5%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))) (sqrt.f64 k))
45.1%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k))
44.9%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))) (sqrt.f64 k))
45.0%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
45.2%
(/.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k))
45.2%
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
✓58.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
45.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
44.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
45.1%
(*.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))))
40.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
45.2%
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
99.6%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
45.5%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))))
26.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))))) k))
35.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
36.0%
#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))))
36.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓36.1%
#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))))
✓36.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
✓36.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
15.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64)))) k)))
Compiler

Compiled 2 240 to 839 computations (62.5% saved)

regimes54.0ms (1.2%)

Memory
-5.4MiB live, 89.1MiB allocated; 11ms collecting garbage
Counts
41 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (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) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 k k) k) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) k) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (*.f64 (*.f64 k k) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64)))) #s(literal 2 binary64)))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n))))))) k))
Outputs
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
Calls

4 calls:

18.0ms
k
13.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms
n
9.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
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)

regimes42.0ms (0.9%)

Memory
-0.6MiB live, 88.7MiB allocated; 6ms collecting garbage
Counts
34 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (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) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 k k) k) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (fma.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
Outputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
Calls

4 calls:

13.0ms
k
10.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
9.0ms
n
8.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
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)

regimes27.0ms (0.6%)

Memory
-1.3MiB live, 57.9MiB allocated; 4ms collecting garbage
Counts
21 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
Outputs
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
Calls

4 calls:

8.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
6.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
6.0ms
k
6.0ms
n
Results
AccuracySegmentsBranch
62.8%3(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
98.7%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))))
98.7%2k
62.8%3n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes24.0ms (0.5%)

Memory
8.3MiB live, 54.8MiB allocated; 2ms collecting garbage
Counts
19 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (sqrt.f64 k))
Outputs
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
Calls

4 calls:

7.0ms
n
5.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
5.0ms
k
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))))
Results
AccuracySegmentsBranch
45.2%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
45.2%1n
45.2%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))))
45.2%1k
Compiler

Compiled 23 to 23 computations (0% saved)

regimes21.0ms (0.4%)

Memory
-1.3MiB live, 45.4MiB allocated; 1ms collecting garbage
Counts
16 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (* (* (sqrt (* (PI) n)) (* (log (* (* n 2) (PI))) (sqrt 2))) -1/2) (/ (sqrt (* (* n 2) (PI))) k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)) k))))
Outputs
(/.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (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))))
5.0ms
k
5.0ms
n
5.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
45.2%1k
45.2%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))))
45.2%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
45.2%1n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes10.0ms (0.2%)

Memory
20.1MiB live, 20.1MiB allocated; 0ms collecting garbage
Counts
6 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (sqrt (* (* (* (PI) n) k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
Calls

4 calls:

2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
n
2.0ms
k
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
38.6%2k
45.3%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))))
45.0%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
45.0%2n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes35.0ms (0.8%)

Memory
-30.8MiB live, 16.4MiB allocated; 1ms collecting garbage
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
Calls

4 calls:

30.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
k
2.0ms
n
1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
36.1%1k
36.1%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.1%1n
36.1%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 23 to 23 computations (0% saved)

regimes4.0ms (0.1%)

Memory
9.0MiB live, 9.0MiB allocated; 0ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

4 calls:

1.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
n
1.0ms
k
1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
36.1%1k
36.1%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
36.1%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.1%1n
Compiler

Compiled 23 to 23 computations (0% saved)

bsearch20.0ms (0.4%)

Memory
26.5MiB live, 26.5MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
18.0ms
1.7971635020226356e-5
437211713.502187
Samples
12.0ms160×0valid
Compiler

Compiled 469 to 418 computations (10.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-pow: 4.0ms (50% of total)
ival-sqrt: 1.0ms (12.5% of total)
ival-div!: 1.0ms (12.5% of total)
ival-mult!: 1.0ms (12.5% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.9680115762191646e+138
8.102916186532088e+138
Compiler

Compiled 19 to 18 computations (5.3% saved)

derivations49.0ms (1.1%)

Memory
-26.6MiB live, 70.2MiB allocated; 7ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 282 to 99 computations (64.9% saved)

preprocess43.0ms (0.9%)

Memory
3.4MiB live, 93.1MiB allocated; 7ms collecting garbage
Compiler

Compiled 596 to 224 computations (62.4% saved)

end0.0ms (0%)

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

Profiling

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