Migdal et al, Equation (51)

Time bar (total: 9.9s)

start0.0ms (0%)

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

analyze171.0ms (1.7%)

Memory
-23.5MiB live, 182.7MiB allocated; 47ms 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)

sample4.0s (40.5%)

Memory
-104.3MiB live, 4 443.6MiB allocated; 1.6s collecting garbage
Samples
1.2s8 255×0valid
1.2s4 400×1invalid
736.0ms1 488×2invalid
38.0ms379×0invalid
30.0ms249×0exit
0.0ms1×1valid
Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-pow: 943.0ms (35.7% of total)
ival-mult: 560.0ms (21.2% of total)
ival-div: 372.0ms (14.1% of total)
ival-sqrt: 273.0ms (10.3% of total)
ival-sub: 200.0ms (7.6% of total)
adjust: 164.0ms (6.2% of total)
ival-pi: 98.0ms (3.7% of total)
exact: 23.0ms (0.9% of total)
ival-assert: 5.0ms (0.2% of total)
Bogosity

explain199.0ms (2%)

Memory
-3.3MiB live, 241.5MiB allocated; 39ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
472(1.0467540416284837e-271 5.921581158100909e-120)1(6.669075644278179e-5 3.131848763808647e-49)(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)))sensitivity7526
Confusion
Predicted +Predicted -
+31
-72180
Precision
0.04
Recall
0.75
Confusion?
Predicted +Predicted MaybePredicted -
+310
-7225155
Precision?
0.039603960396039604
Recall?
1.0
Freqs
test
numberfreq
0181
175
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
106.0ms512×0valid
Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 75.0ms
ival-pow: 46.0ms (61.4% of total)
ival-mult: 11.0ms (14.7% of total)
ival-div: 7.0ms (9.3% of total)
ival-sqrt: 4.0ms (5.3% of total)
ival-sub: 3.0ms (4% of total)
ival-pi: 2.0ms (2.7% of total)
ival-true: 1.0ms (1.3% of total)
exact: 1.0ms (1.3% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess198.0ms (2%)

Memory
23.1MiB live, 205.0MiB allocated; 34ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033104
17690
216288
338288
4161588
01316
02216
13714
25814
313614
453314
5320114
0809814
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
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))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (fma.f64 k #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

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

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated; 0ms collecting garbage
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 16 to 13 computations (18.8% saved)

series89.0ms (0.9%)

Memory
6.3MiB live, 148.2MiB allocated; 33ms 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
38.0ms
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))
31.0ms
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))
12.0ms
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))

rewrite49.0ms (0.5%)

Memory
6.3MiB live, 50.8MiB 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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #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)))) (pow.f64 k #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 k #s(literal 1/2 binary64)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 k #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/2 binary64)))
(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))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 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)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (/ 1 (sqrt k)) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
#s(approx (sqrt k) (pow.f64 k #s(literal 1/2 binary64)))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 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) (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) 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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (sqrt k) (*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 1/2 binary64))) #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 #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 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (pow.f64 k #s(literal -1 binary64)))) k) #s(literal -1 binary64)))
#s(approx (- 1 k) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 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 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (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 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval8.0ms (0.1%)

Memory
12.5MiB live, 12.5MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 864 to 289 computations (84.5% saved)

prune40.0ms (0.4%)

Memory
-10.2MiB live, 35.2MiB allocated; 6ms collecting garbage
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New65772
Fresh000
Picked101
Done000
Total66773
Accuracy
99.9%
Counts
73 → 7
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)))) (pow.f64 k #s(literal 1/2 binary64)))
99.6%
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 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)))))
▶70.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.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)))))
▶64.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
▶55.0%
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
▶96.0%
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
Compiler

Compiled 700 to 352 computations (49.7% saved)

series355.0ms (3.6%)

Memory
-14.8MiB live, 506.1MiB allocated; 96ms collecting garbage
Counts
71 → 283
Calls
Call 1
Inputs
(/.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)))) (pow.f64 k #s(literal 1/2 binary64)))
(*.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))))
#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 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
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))) (*.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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
(*.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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(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))))
(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)))
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
#s(literal -1 binary64)
(log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 k #s(literal -1 binary64))
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k)
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
(*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
#s(literal -1/48 binary64)
(*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(sqrt.f64 (pow.f64 k #s(literal 3 binary64)))
(pow.f64 k #s(literal 3 binary64))
#s(literal 3 binary64)
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
(*.f64 (PI.f64) n)
(*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)))
#s(literal 1/8 binary64)
(pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))
(*.f64 (*.f64 (PI.f64) n) k)
(*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)))
#s(literal -1/2 binary64)
(*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 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 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.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 (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 (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)))
Outputs
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow k 1/2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 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 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 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 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 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 (* 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 (/ (- 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))))
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#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k)))) (exp (* 1/2 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k))))))))
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Calls

6 calls:

TimeVariablePointExpression
77.0ms
k
@0
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow k 1/2)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (pow k 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (pow (pow k -1) 1/2)) (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (+ (* -1 k) 1) -1 (log (* (* (PI) 2) n)) (pow (pow k -1) 1/2) (pow k -1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2)) (sqrt (pow k 3)) (pow k 3) 3 (pow (* (PI) n) 1/2) (* (PI) n) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (* (PI) n) k) 1/2)) 1/8 (pow (* (* (PI) n) k) 1/2) (* (* (PI) n) k) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (* (PI) n) k) 1/2)) -1/2 (* (log (* (* (PI) 2) n)) (pow 2 1/2)) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (PI) n) 1/2)) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (PI) n) 1/2)) (* (pow (* (PI) n) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
72.0ms
n
@0
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow k 1/2)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (pow k 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (pow (pow k -1) 1/2)) (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (+ (* -1 k) 1) -1 (log (* (* (PI) 2) n)) (pow (pow k -1) 1/2) (pow k -1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2)) (sqrt (pow k 3)) (pow k 3) 3 (pow (* (PI) n) 1/2) (* (PI) n) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (* (PI) n) k) 1/2)) 1/8 (pow (* (* (PI) n) k) 1/2) (* (* (PI) n) k) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (* (PI) n) k) 1/2)) -1/2 (* (log (* (* (PI) 2) n)) (pow 2 1/2)) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (PI) n) 1/2)) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (PI) n) 1/2)) (* (pow (* (PI) n) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
65.0ms
n
@-inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow k 1/2)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (pow k 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (pow (pow k -1) 1/2)) (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (+ (* -1 k) 1) -1 (log (* (* (PI) 2) n)) (pow (pow k -1) 1/2) (pow k -1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2)) (sqrt (pow k 3)) (pow k 3) 3 (pow (* (PI) n) 1/2) (* (PI) n) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (* (PI) n) k) 1/2)) 1/8 (pow (* (* (PI) n) k) 1/2) (* (* (PI) n) k) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (* (PI) n) k) 1/2)) -1/2 (* (log (* (* (PI) 2) n)) (pow 2 1/2)) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (PI) n) 1/2)) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (PI) n) 1/2)) (* (pow (* (PI) n) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
53.0ms
n
@inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow k 1/2)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (pow k 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (pow (pow k -1) 1/2)) (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (+ (* -1 k) 1) -1 (log (* (* (PI) 2) n)) (pow (pow k -1) 1/2) (pow k -1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2)) (sqrt (pow k 3)) (pow k 3) 3 (pow (* (PI) n) 1/2) (* (PI) n) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (* (PI) n) k) 1/2)) 1/8 (pow (* (* (PI) n) k) 1/2) (* (* (PI) n) k) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (* (PI) n) k) 1/2)) -1/2 (* (log (* (* (PI) 2) n)) (pow 2 1/2)) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (PI) n) 1/2)) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (PI) n) 1/2)) (* (pow (* (PI) n) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
27.0ms
k
@-inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow k 1/2)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (pow k 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (pow (pow k -1) 1/2)) (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (+ (* -1 k) 1) -1 (log (* (* (PI) 2) n)) (pow (pow k -1) 1/2) (pow k -1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2)) (sqrt (pow k 3)) (pow k 3) 3 (pow (* (PI) n) 1/2) (* (PI) n) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (* (PI) n) k) 1/2)) 1/8 (pow (* (* (PI) n) k) 1/2) (* (* (PI) n) k) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (* (PI) n) k) 1/2)) -1/2 (* (log (* (* (PI) 2) n)) (pow 2 1/2)) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (PI) n) 1/2)) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (PI) n) 1/2)) (* (pow (* (PI) n) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))

rewrite246.0ms (2.5%)

Memory
18.2MiB live, 339.1MiB allocated; 66ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0104920376
0119116360
0515616193
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
354 → 613
Calls
Call 1
Inputs
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(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))
(PI.f64)
#s(literal 2 binary64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
k
(pow.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
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#s(literal -1/2 binary64)
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#s(approx (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) #s(hole binary64 (* -1 (* n (+ (* k (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* k (+ (* -1/48 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 3)))) (sqrt (/ (PI) n)))) (* 1/8 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2))))))))) (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (sqrt 2))))))))
#s(approx (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* k (+ (* -1/48 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 3)))) (sqrt (/ (PI) n)))) (* 1/8 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2))))))))))))
#s(approx (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) #s(hole binary64 (* -1 (* n (+ (* -1/48 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 3)))) (sqrt (/ (PI) n)))) (* 1/8 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2))))))))))
#s(approx (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) #s(hole binary64 (* -1 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 3)))) (sqrt (* n (PI)))))))
#s(approx (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) #s(hole binary64 (* k (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 3)))))
#s(approx (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) #s(hole binary64 (* k (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 3))))
#s(approx (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) #s(hole binary64 (* -1/8 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))))))
#s(approx (* 1/8 (pow (* (PI) n) 1/2)) #s(hole binary64 (* -1/8 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) #s(hole binary64 (* 1/2 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (* -1/2 (pow (* (PI) n) 1/2)) #s(hole binary64 (* 1/2 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (* (pow (* (PI) n) 1/2) (pow 2 1/2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k)))) (exp (* 1/2 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k))))))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k)))) (exp (* 1/2 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.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 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (neg.f64 (pow.f64 k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.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 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(literal 1 binary64)
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.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 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.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 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.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))
(PI.f64)
#s(literal 2 binary64)
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)
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))
(sqrt.f64 k)
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(*.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 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(+.f64 (cosh.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sinh.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(exp.f64 #s(literal 1/2 binary64))
(+.f64 (cosh.f64 #s(literal 1/2 binary64)) (sinh.f64 #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
(fma.f64 (log.f64 n) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
(fma.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 n) (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
(fma.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) k)))
(fma.f64 #s(literal 1 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal -1 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(+.f64 (*.f64 #s(literal 1 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (*.f64 #s(literal -1 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) k)))
(+.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
(log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 #s(literal -1 binary64) k))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 #s(literal -1 binary64) k)) #s(literal 1 binary64)) (-.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 #s(literal -1 binary64) k) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 1 binary64)))))
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
(fma.f64 k #s(literal -1 binary64) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) k))
(+.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))
#s(literal -1 binary64)
(/.f64 (-.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))))) (-.f64 (log.f64 n) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))
(/.f64 (fma.f64 (pow.f64 (log.f64 n) #s(literal 3/2 binary64)) (pow.f64 (log.f64 n) #s(literal 3/2 binary64)) (*.f64 (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))))) (fma.f64 (pow.f64 (log.f64 n) #s(literal 1 binary64)) (pow.f64 (log.f64 n) #s(literal 1 binary64)) (-.f64 (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (*.f64 (log.f64 n) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (PI.f64) n)))
(+.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (log.f64 n))
(+.f64 (log.f64 n) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))))
(log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 k #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 k #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/2 binary64)))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) k))
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#s(literal 3 binary64)
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#s(literal 1/8 binary64)
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#s(literal -1/2 binary64)
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#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
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#s(approx (- 1 k) #s(literal 1 binary64))
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#s(approx k k)
#s(approx (pow k 1/2) (pow.f64 k #s(literal 1/2 binary64)))
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#s(approx n n)
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#s(approx (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (*.f64 (*.f64 #s(literal -1 binary64) n) (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 (pow.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))))))
#s(approx (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (*.f64 (*.f64 #s(literal -1 binary64) n) (fma.f64 (*.f64 (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 (pow.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))))))))))
#s(approx (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) (*.f64 (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 (pow.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
#s(approx (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))))
#s(approx (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (*.f64 (pow.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64)) k))
#s(approx (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (*.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))))))))
#s(approx (* 1/8 (pow (* (PI) n) 1/2)) (*.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
#s(approx (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))))
#s(approx (* -1/2 (pow (* (PI) n) 1/2)) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
#s(approx (* (pow (* (PI) n) 1/2) (pow 2 1/2)) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (*.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (pow n (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k))))

eval239.0ms (2.4%)

Memory
-20.1MiB live, 360.7MiB allocated; 129ms collecting garbage
Compiler

Compiled 124 246 to 5 723 computations (95.4% saved)

prune422.0ms (4.3%)

Memory
22.1MiB live, 529.3MiB allocated; 74ms collecting garbage
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1 15151 156
Fresh202
Picked235
Done000
Total1 15581 163
Accuracy
99.9%
Counts
1 163 → 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)))) (pow.f64 k #s(literal 1/2 binary64)))
▶96.3%
(/.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)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
▶64.8%
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64)))) k (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
✓70.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.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)))))
▶98.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
✓55.0%
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
▶96.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
▶61.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
Compiler

Compiled 1 071 to 481 computations (55.1% saved)

series728.0ms (7.3%)

Memory
25.4MiB live, 1 058.7MiB allocated; 253ms collecting garbage
Counts
94 → 356
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.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
(*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (PI.f64) #s(literal 1/2 binary64))
(PI.f64)
#s(literal 1/2 binary64)
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
#s(literal 2 binary64)
(pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
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(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64)))) k (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64)))) k (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64))
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
(*.f64 (PI.f64) n)
(*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))))
(log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64)))
(*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64))
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(*.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)
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(*.f64 (log.f64 k) #s(literal 1/2 binary64))
(log.f64 k)
Outputs
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2))))))) k)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log n) (* (pow (log (* 2 (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log n) 2) (* (log (* 2 (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log n) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (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 (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2))))) (* k (+ (* -1/16 (* (sqrt (* n (PI))) (* (log n) (* (pow (log (* 2 (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log n) 2) (* (log (* 2 (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log n) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 3) (sqrt 2))))))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (PI)) (sqrt 2))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (PI))) (sqrt 2))) (sqrt (PI)))) (* (sqrt (PI)) (sqrt 2)))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (PI))) 2) (sqrt 2))) (sqrt (PI)))))) (* (sqrt (PI)) (sqrt 2)))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (PI))) 3) (sqrt 2))) (sqrt (PI)))) (* 1/8 (* (sqrt (PI)) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))))))) (* (sqrt (PI)) (sqrt 2)))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (sqrt n)))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (+ (sqrt n) (* -1/2 (* (* k (log n)) (sqrt n))))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (+ (sqrt n) (* k (+ (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (* k (pow (log n) 2)) (sqrt n))))))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (+ (sqrt n) (* k (+ (* -1/2 (* (sqrt n) (log n))) (* k (+ (* -1/48 (* (* k (pow (log n) 3)) (sqrt n))) (* 1/8 (* (sqrt n) (pow (log n) 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 (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) 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 (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) 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)))
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Calls

6 calls:

TimeVariablePointExpression
222.0ms
k
@0
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117.0ms
n
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107.0ms
n
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86.0ms
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79.0ms
k
@-inf
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rewrite286.0ms (2.9%)

Memory
3.8MiB live, 374.8MiB allocated; 44ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0151029302
0169623183
0810622861
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
450 → 815
Calls
Call 1
Inputs
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(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
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n
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#s(approx (* (pow (/ (* (PI) k) n) 1/2) (pow 2 1/2)) #s(hole binary64 (* (sqrt (/ (* k (PI)) n)) (* (pow (sqrt -1) 2) (sqrt 2)))))
#s(approx (pow (/ (* (PI) k) n) 1/2) #s(hole binary64 (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))
#s(approx (* (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI))))) #s(hole binary64 (pow (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n)))))) 2)))
#s(approx (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) #s(hole binary64 (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n))))))))
#s(approx (- 0 (log n)) #s(hole binary64 (* -1 (+ (log -1) (* -1 (log (/ -1 n)))))))
#s(approx (log n) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 n))))))
#s(approx (* (* (* (pow (/ (* (pow k 3) (PI)) n) 1/2) (pow 2 1/2)) (pow (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) 3)) -1/48) #s(hole binary64 (* -1/48 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n)))))) 3)))))))
#s(approx (* (* (pow (/ (* (pow k 3) (PI)) n) 1/2) (pow 2 1/2)) (pow (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) 3)) #s(hole binary64 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n)))))) 3))))))
#s(approx (pow (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) 3) #s(hole binary64 (pow (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n)))))) 3)))
#s(approx (* (* -1/2 (pow (/ (* (PI) k) n) 1/2)) (* (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (pow 2 1/2))) #s(hole binary64 (* -1/2 (* (sqrt (/ (* k (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n))))))))))))
#s(approx (* -1/2 (pow (/ (* (PI) k) n) 1/2)) #s(hole binary64 (* -1/2 (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2)))))
#s(approx (* (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (pow 2 1/2)) #s(hole binary64 (* (sqrt 2) (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n)))))))))
#s(approx (* (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (pow k -1) 1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) 2))))
#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) 2)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) #s(hole binary64 (exp (* 1/4 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) #s(hole binary64 (* 1/2 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* n (* (PI) 2))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (* (pow (pow k -1) 1/2) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k)))) (exp (* 1/2 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k))))))))
#s(approx (+ (* (+ (* (+ (* (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1)))) (pow 2 1/2)) (* (* (* k (pow 2 1/2)) (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2))))) (* (pow (* (PI) n) 1/2) -1/48))) k) (* (* (pow (* (PI) n) 1/2) -1/2) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) k) (pow (* n (* (PI) 2)) 1/2)) #s(hole binary64 (* -1 (* n (+ (* k (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* k (+ (* -1/48 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2))))) (sqrt (/ (PI) n)))) (* 1/8 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2))))))))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (+ (* (+ (* (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1)))) (pow 2 1/2)) (* (* (* k (pow 2 1/2)) (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2))))) (* (pow (* (PI) n) 1/2) -1/48))) k) (* (* (pow (* (PI) n) 1/2) -1/2) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* k (+ (* -1/48 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2))))) (sqrt (/ (PI) n)))) (* 1/8 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2))))))))))))
#s(approx (+ (* (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1)))) (pow 2 1/2)) (* (* (* k (pow 2 1/2)) (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2))))) (* (pow (* (PI) n) 1/2) -1/48))) #s(hole binary64 (* -1 (* n (+ (* -1/48 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2))))) (sqrt (/ (PI) n)))) (* 1/8 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2))))))))))
#s(approx (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1)))) #s(hole binary64 (* -1/8 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2))))))
#s(approx (* (pow (* (PI) n) 1/2) 1/8) #s(hole binary64 (* -1/8 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
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#s(approx (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) #s(hole binary64 (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2)))
#s(approx (log (pow (* n (* (PI) 2)) -1)) #s(hole binary64 (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))
#s(approx (* (* (* k (pow 2 1/2)) (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2))))) (* (pow (* (PI) n) 1/2) -1/48)) #s(hole binary64 (* 1/48 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2))))) (sqrt (* n (PI)))))))
#s(approx (* (* k (pow 2 1/2)) (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2))))) #s(hole binary64 (* k (* (sqrt 2) (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2))))))
#s(approx (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2)))) #s(hole binary64 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (pow (+ (log (/ -1 n)) (log (/ -1/2 (PI)))) 2))))
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#s(approx (* (pow (* (PI) n) 1/2) -1/2) #s(hole binary64 (* 1/2 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (* (pow 2 1/2) (log (* n (* (PI) 2)))) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
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#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log 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 (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
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(*.f64 (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64))))) (pow.f64 k #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 k #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 k #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/2 binary64)))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 k)) #s(literal 1/2 binary64)))
#s(literal 1 binary64)
(pow.f64 (exp.f64 (log.f64 k)) #s(literal 1/2 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
k
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64))))
(*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
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(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(pow.f64 (PI.f64) #s(literal 1/2 binary64))
(sqrt.f64 (PI.f64))
(exp.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 1/2 binary64)))
(PI.f64)
#s(literal 1/2 binary64)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
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(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 #s(literal -2 binary64) #s(literal 1/2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
(*.f64 (pow.f64 n (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 n (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
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))
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(-.f64 #s(literal 1 binary64) k)
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#s(approx n n)
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#s(approx (/ (+ (* (+ (* (+ (* (* (* (pow (/ (* (PI) k) n) 1/2) (pow 2 1/2)) (* (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))))) 1/8) (* (* (* (pow (/ (* (pow k 3) (PI)) n) 1/2) (pow 2 1/2)) (pow (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) 3)) -1/48)) k) (* (* -1/2 (pow (/ (* (PI) k) n) 1/2)) (* (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (pow 2 1/2)))) k) (* (pow (/ (* (PI) k) n) 1/2) (pow 2 1/2))) k) (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))) (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64)))) #s(literal 1/8 binary64))) k (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (*.f64 n k)))
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#s(approx (+ (* (+ (* (* (* (pow (/ (* (PI) k) n) 1/2) (pow 2 1/2)) (* (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))))) 1/8) (* (* (* (pow (/ (* (pow k 3) (PI)) n) 1/2) (pow 2 1/2)) (pow (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) 3)) -1/48)) k) (* (* -1/2 (pow (/ (* (PI) k) n) 1/2)) (* (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (pow 2 1/2)))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))) (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64)))) #s(literal 1/8 binary64))) k (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))) n))
#s(approx (+ (* (* (* (pow (/ (* (PI) k) n) 1/2) (pow 2 1/2)) (* (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))))) 1/8) (* (* (* (pow (/ (* (pow k 3) (PI)) n) 1/2) (pow 2 1/2)) (pow (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) 3)) -1/48)) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))) (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64)))) #s(literal 1/8 binary64))) n))
#s(approx (* (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI))))) (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))))
#s(approx (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)))
#s(approx (- 0 (log n)) (*.f64 (log.f64 n) #s(literal -1 binary64)))
#s(approx (log n) (log.f64 n))
#s(approx (pow (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) 3) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))) (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n))))
#s(approx (* (+ (* (- 0 (log n)) -1) (+ (log 2) (log (PI)))) (pow 2 1/2)) (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
#s(approx (* (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (pow k -1) 1/2)) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
#s(approx (log (* n (* (PI) 2))) (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)))
#s(approx (* n (* (PI) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))
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#s(approx (* (pow (* (PI) n) 1/2) 1/8) (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)))
#s(approx (pow (* (PI) n) 1/2) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))
#s(approx (* (PI) n) (*.f64 n (PI.f64)))
#s(approx (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (*.f64 (fma.f64 (log.f64 n) #s(literal -1 binary64) (-.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (log.f64 n) #s(literal -1 binary64) (-.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (PI.f64))))))
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#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))))))
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#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))))
#s(approx (log (* n (* (PI) 2))) (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (+ (* (+ (* (+ (* (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1)))) (pow 2 1/2)) (* (* (* k (pow 2 1/2)) (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2))))) (* (pow (* (PI) n) 1/2) -1/48))) k) (* (* (pow (* (PI) n) 1/2) -1/2) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) k) (pow (* n (* (PI) 2)) 1/2)) (*.f64 (*.f64 #s(literal -1 binary64) n) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))))))) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))) k (*.f64 (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
#s(approx (+ (* (+ (* (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1)))) (pow 2 1/2)) (* (* (* k (pow 2 1/2)) (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2))))) (* (pow (* (PI) n) 1/2) -1/48))) k) (* (* (pow (* (PI) n) 1/2) -1/2) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) (*.f64 (*.f64 #s(literal -1 binary64) n) (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))))))) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))))))
#s(approx (+ (* (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1)))) (pow 2 1/2)) (* (* (* k (pow 2 1/2)) (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2))))) (* (pow (* (PI) n) 1/2) -1/48))) (*.f64 (*.f64 #s(literal -1 binary64) n) (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))))))) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)))))))))
#s(approx (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (*.f64 (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)))) #s(literal -1 binary64))))
#s(approx (* (pow (* (PI) n) 1/2) 1/8) (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1/8 binary64)))
#s(approx (pow (* (PI) n) 1/2) (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
#s(approx (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)))))
#s(approx (log (pow (* n (* (PI) 2)) -1)) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))))
#s(approx (* (* (* k (pow 2 1/2)) (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2))))) (* (pow (* (PI) n) 1/2) -1/48)) (*.f64 (*.f64 #s(literal 1/48 binary64) (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))))))) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))))
#s(approx (* (* k (pow 2 1/2)) (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2))))) (*.f64 (*.f64 (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))))) k))
#s(approx (* (* (log (pow (* n (* (PI) 2)) -1)) (log (pow (* n (* (PI) 2)) -1))) (log (* n (* (PI) 2)))) (*.f64 (*.f64 (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n))) (+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (PI.f64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)))) (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))))))
#s(approx (* (pow (* (PI) n) 1/2) -1/48) (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1/48 binary64)))
#s(approx (* (* (pow (* (PI) n) 1/2) -1/2) (* (pow 2 1/2) (log (* n (* (PI) 2))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))))
#s(approx (* (pow (* (PI) n) 1/2) -1/2) (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
#s(approx (* (pow 2 1/2) (log (* n (* (PI) 2)))) (fma.f64 (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
#s(approx (pow (* n (* (PI) 2)) 1/2) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval391.0ms (3.9%)

Memory
15.3MiB live, 522.4MiB allocated; 78ms collecting garbage
Compiler

Compiled 221 297 to 8 027 computations (96.4% saved)

prune950.0ms (9.6%)

Memory
20.8MiB live, 1 325.0MiB allocated; 296ms collecting garbage
Pruning

9 alts after pruning (2 fresh and 7 done)

PrunedKeptTotal
New1 39821 400
Fresh000
Picked145
Done033
Total1 39991 408
Accuracy
99.9%
Counts
1 408 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶95.9%
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
✓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)))) (pow.f64 k #s(literal 1/2 binary64)))
✓64.8%
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64)))) k (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
✓70.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.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)))))
✓98.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
▶95.4%
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
✓55.0%
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
✓96.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
✓61.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
Compiler

Compiled 675 to 315 computations (53.3% saved)

series821.0ms (8.3%)

Memory
-128.7MiB live, 434.9MiB allocated; 845ms collecting garbage
Counts
33 → 109
Calls
Call 1
Inputs
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64)))
(*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64)))
(exp.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))
(*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
(+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n))
(+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64)))
(log.f64 (PI.f64))
(PI.f64)
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(log.f64 n)
n
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
#s(literal -1 binary64)
k
#s(literal 1 binary64)
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 k #s(literal -1 binary64))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(*.f64 (log.f64 k) #s(literal 1/2 binary64))
(log.f64 k)
Outputs
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log 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 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log 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 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log 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 (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))))))
#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (pow k 3)) (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI)))))))) (* (sqrt k) (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))))) k)))
#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI)))))))) (* 1/8 (* (sqrt (pow k 3)) (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (pow (log (pow (exp 1/2) 2)) 2) (pow (+ (log 2) (+ (log n) (log (PI)))) 2))))))) (* (sqrt k) (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))))) k)))
#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI)))))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (pow (log (pow (exp 1/2) 2)) 3) (pow (+ (log 2) (+ (log n) (log (PI)))) 3))))) (* 1/8 (* (sqrt k) (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (pow (log (pow (exp 1/2) 2)) 2) (pow (+ (log 2) (+ (log n) (log (PI)))) 2))))))))) (* (sqrt k) (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))))) k)))
#s(approx (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) #s(hole binary64 (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI)))))))))
#s(approx (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) #s(hole binary64 (+ (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* -1/2 (* k (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI)))))))))))
#s(approx (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) #s(hole binary64 (+ (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* k (+ (* -1/2 (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* 1/8 (* k (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (pow (log (pow (exp 1/2) 2)) 2) (pow (+ (log 2) (+ (log n) (log (PI)))) 2))))))))))
#s(approx (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) #s(hole binary64 (+ (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* k (+ (* -1/2 (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* k (+ (* -1/48 (* k (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (pow (log (pow (exp 1/2) 2)) 3) (pow (+ (log 2) (+ (log n) (log (PI)))) 3))))) (* 1/8 (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (+ (log 2) (+ (log n) (log (PI))))))) (* (pow (log (pow (exp 1/2) 2)) 2) (pow (+ (log 2) (+ (log n) (log (PI)))) 2)))))))))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) #s(hole binary64 (* 1/2 (+ (log 2) (+ (log n) (log (PI)))))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) #s(hole binary64 (+ (* -1/2 (* k (+ (log 2) (+ (log n) (log (PI)))))) (* 1/2 (+ (log 2) (+ (log n) (log (PI))))))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) #s(hole binary64 (+ (log 2) (+ (log n) (log (PI))))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) #s(hole binary64 (+ (log 2) (+ (log n) (+ (log (PI)) (* -1 (* k (+ (log 2) (+ (log n) (log (PI)))))))))))
#s(approx (+ (* -1 k) 1) #s(hole binary64 1))
#s(approx (+ (* -1 k) 1) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx k #s(hole binary64 k))
#s(approx (pow (pow k -1) 1/2) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow k -1) #s(hole binary64 (/ 1 k)))
#s(approx (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log 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 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log 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 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* (sqrt (pow k 3)) (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 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) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 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) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* k (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/4)))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (* k (log (* 2 (* n (PI))))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (* n (PI)))))) (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (* k (pow (log (* 2 (* n (PI)))) 2)))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (* n (PI)))))) (* k (+ (* -1/384 (* (pow (* 2 (* n (PI))) 1/4) (* k (pow (log (* 2 (* n (PI)))) 3)))) (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (pow (log (* 2 (* n (PI)))) 2))))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (/ (/ (- 1 k) 2) 2) #s(hole binary64 1/4))
#s(approx (/ (/ (- 1 k) 2) 2) #s(hole binary64 (+ 1/4 (* -1/4 k))))
#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 (exp (* (log k) 1/2)) #s(hole binary64 (sqrt k)))
#s(approx (* (log k) 1/2) #s(hole binary64 (* 1/2 (log k))))
#s(approx (log k) #s(hole binary64 (log k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (* (+ (log 2) (+ (log n) (log (PI)))) (- 1 k))))))))
#s(approx (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) #s(hole binary64 (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (* (+ (log 2) (+ (log n) (log (PI)))) (- 1 k)))))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) #s(hole binary64 (* -1/2 (* k (+ (log 2) (+ (log n) (log (PI))))))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) #s(hole binary64 (* k (+ (* -1/2 (+ (log 2) (+ (log n) (log (PI))))) (* 1/2 (/ (+ (log 2) (+ (log n) (log (PI)))) k))))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) #s(hole binary64 (* -1 (* k (+ (log 2) (+ (log n) (log (PI))))))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) #s(hole binary64 (* k (+ (* -1 (+ (log 2) (+ (log n) (log (PI))))) (+ (/ (log 2) k) (+ (/ (log n) k) (/ (log (PI)) k)))))))
#s(approx (+ (* -1 k) 1) #s(hole binary64 (* -1 k)))
#s(approx (+ (* -1 k) 1) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (/ (- 1 k) 2) 2) #s(hole binary64 (* -1/4 k)))
#s(approx (/ (/ (- 1 k) 2) 2) #s(hole binary64 (* k (- (* 1/4 (/ 1 k)) 1/4))))
#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 (* (log k) 1/2) #s(hole binary64 (* -1/2 (log (/ 1 k)))))
#s(approx (log k) #s(hole binary64 (* -1 (log (/ 1 k)))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (* (+ 1 (* -1 k)) (+ (log 2) (+ (log n) (log (PI)))))))) (pow (sqrt -1) 2)))))
#s(approx (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) #s(hole binary64 (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (* (+ 1 (* -1 k)) (+ (log 2) (+ (log n) (log (PI))))))))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) #s(hole binary64 (* -1 (* k (+ (* -1/2 (/ (+ (log 2) (+ (log n) (log (PI)))) k)) (* 1/2 (+ (log 2) (+ (log n) (log (PI))))))))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) #s(hole binary64 (* -1 (* k (+ (log 2) (+ (log n) (+ (log (PI)) (* -1 (/ (+ (log 2) (+ (log n) (log (PI)))) k)))))))))
#s(approx (+ (* -1 k) 1) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (pow (pow k -1) 1/2) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2))))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (/ (- 1 k) 2) 2) #s(hole binary64 (* -1 (* k (- 1/4 (* 1/4 (/ 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 (exp (* (log k) 1/2)) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (log k) 1/2) #s(hole binary64 (* 1/2 (+ (log -1) (* -1 (log (/ -1 k)))))))
#s(approx (log k) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 k))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (* (+ 1 (* -1 k)) (+ (log 2) (+ (log n) (log (PI)))))))))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) #s(hole binary64 (* 1/2 (* (+ 1 (* -1 k)) (+ (log 2) (+ (log n) (log (PI))))))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log 2) (+ (log n) (log (PI)))))))
#s(approx (+ (+ (log (PI)) (log 2)) (log n)) #s(hole binary64 (+ (log 2) (+ (log n) (log (PI))))))
#s(approx (log n) #s(hole binary64 (log n)))
#s(approx n #s(hole binary64 n))
#s(approx (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (* (+ 1 (* -1 k)) (+ (log 2) (+ (log (PI)) (* -1 (log (/ 1 n))))))))))))
#s(approx (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) #s(hole binary64 (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (* (+ 1 (* -1 k)) (+ (log 2) (+ (log (PI)) (* -1 (log (/ 1 n)))))))))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) #s(hole binary64 (* 1/2 (* (+ 1 (* -1 k)) (+ (log 2) (+ (log (PI)) (* -1 (log (/ 1 n)))))))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log 2) (+ (log (PI)) (* -1 (log (/ 1 n))))))))
#s(approx (+ (+ (log (PI)) (log 2)) (log n)) #s(hole binary64 (+ (log 2) (+ (log (PI)) (* -1 (log (/ 1 n)))))))
#s(approx (log n) #s(hole binary64 (* -1 (log (/ 1 n)))))
#s(approx (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (* (+ 1 (* -1 k)) (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n)))))))))))))
#s(approx (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) #s(hole binary64 (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (* (+ 1 (* -1 k)) (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) #s(hole binary64 (* 1/2 (* (+ 1 (* -1 k)) (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n))))))))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n)))))))))
#s(approx (+ (+ (log (PI)) (log 2)) (log n)) #s(hole binary64 (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n))))))))
#s(approx (log n) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 n))))))
#s(approx (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Calls

6 calls:

TimeVariablePointExpression
575.0ms
n
@0
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (* (exp 1/2) (exp 1/2)) (exp 1/2) 1/2 (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) (+ (+ (log (PI)) (log 2)) (log n)) (+ (log (PI)) (log 2)) (log (PI)) (PI) (log 2) 2 (log n) n (+ (* -1 k) 1) -1 k 1 (pow (pow k -1) 1/2) (pow k -1) (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (- 1 k) (exp (* (log k) 1/2)) (* (log k) 1/2) (log k))
78.0ms
n
@-inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (* (exp 1/2) (exp 1/2)) (exp 1/2) 1/2 (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) (+ (+ (log (PI)) (log 2)) (log n)) (+ (log (PI)) (log 2)) (log (PI)) (PI) (log 2) 2 (log n) n (+ (* -1 k) 1) -1 k 1 (pow (pow k -1) 1/2) (pow k -1) (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (- 1 k) (exp (* (log k) 1/2)) (* (log k) 1/2) (log k))
60.0ms
n
@inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (* (exp 1/2) (exp 1/2)) (exp 1/2) 1/2 (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) (+ (+ (log (PI)) (log 2)) (log n)) (+ (log (PI)) (log 2)) (log (PI)) (PI) (log 2) 2 (log n) n (+ (* -1 k) 1) -1 k 1 (pow (pow k -1) 1/2) (pow k -1) (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (- 1 k) (exp (* (log k) 1/2)) (* (log k) 1/2) (log k))
59.0ms
k
@inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (* (exp 1/2) (exp 1/2)) (exp 1/2) 1/2 (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) (+ (+ (log (PI)) (log 2)) (log n)) (+ (log (PI)) (log 2)) (log (PI)) (PI) (log 2) 2 (log n) n (+ (* -1 k) 1) -1 k 1 (pow (pow k -1) 1/2) (pow k -1) (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (- 1 k) (exp (* (log k) 1/2)) (* (log k) 1/2) (log k))
15.0ms
k
@-inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (* (exp 1/2) (exp 1/2)) (exp 1/2) 1/2 (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) (+ (+ (log (PI)) (log 2)) (log n)) (+ (log (PI)) (log 2)) (log (PI)) (PI) (log 2) 2 (log n) n (+ (* -1 k) 1) -1 k 1 (pow (pow k -1) 1/2) (pow k -1) (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (- 1 k) (exp (* (log k) 1/2)) (* (log k) 1/2) (log k))

rewrite97.0ms (1%)

Memory
16.1MiB live, 150.4MiB allocated; 11ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04934516
05393516
024773475
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
142 → 242
Calls
Call 1
Inputs
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64)))
(*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64)))
(exp.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))
(*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
(+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n))
(+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64)))
(log.f64 (PI.f64))
(PI.f64)
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(log.f64 n)
n
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
#s(literal -1 binary64)
k
#s(literal 1 binary64)
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 k #s(literal -1 binary64))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
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#s(approx (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) #s(hole binary64 (exp (* 1/2 (* (log (pow (exp 1/2) 2)) (* (+ 1 (* -1 k)) (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) #s(hole binary64 (* 1/2 (* (+ 1 (* -1 k)) (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n))))))))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n)))))))))
#s(approx (+ (+ (log (PI)) (log 2)) (log n)) #s(hole binary64 (+ (log -1) (+ (log 2) (+ (log (PI)) (* -1 (log (/ -1 n))))))))
#s(approx (log n) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 n))))))
#s(approx (/ (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (exp (* (log k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) #s(literal 2 binary64))))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) #s(literal 2 binary64)))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (exp.f64 #s(literal 1/2 binary64))) (neg.f64 (exp.f64 #s(literal 1/2 binary64))))
(*.f64 (fabs.f64 (exp.f64 #s(literal 1/2 binary64))) (fabs.f64 (exp.f64 #s(literal 1/2 binary64))))
(*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 #s(literal 1 binary64))
(exp.f64 #s(literal 1/2 binary64))
(+.f64 (cosh.f64 #s(literal 1/2 binary64)) (sinh.f64 #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))) #s(literal -2 binary64))
(/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))
(*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1 binary64) k) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))
(fma.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (+.f64 (log.f64 n) (log.f64 (PI.f64)))))
(fma.f64 (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal -1 binary64) (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))
(fma.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1 binary64) k) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(fma.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1 binary64) k)))
(fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
(fma.f64 #s(literal -1 binary64) (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)) (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -1 binary64) k) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal -1 binary64) k) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (*.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
(+.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1 binary64) k)))
(+.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1 binary64) k)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(+.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (+.f64 (log.f64 n) (log.f64 (PI.f64)))))
(+.f64 (*.f64 (*.f64 #s(literal -1 binary64) k) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))
(/.f64 (-.f64 (*.f64 (log.f64 n) (log.f64 n)) (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))))) (-.f64 (log.f64 n) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))
(/.f64 (-.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64))) (*.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (+.f64 (log.f64 n) (log.f64 (PI.f64))))) (-.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (PI.f64)))))
(/.f64 (-.f64 (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (*.f64 (log.f64 n) (log.f64 n))) (-.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (log.f64 n)))
(/.f64 (+.f64 (pow.f64 (log.f64 n) #s(literal 3 binary64)) (pow.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) #s(literal 3 binary64))) (+.f64 (*.f64 (log.f64 n) (log.f64 n)) (-.f64 (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (*.f64 (log.f64 n) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))))
(/.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) #s(literal 3 binary64))) (+.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64))) (-.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (+.f64 (log.f64 n) (log.f64 (PI.f64)))) (*.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (PI.f64)))))))
(/.f64 (+.f64 (pow.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (log.f64 n) #s(literal 3 binary64))) (fma.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (-.f64 (*.f64 (log.f64 n) (log.f64 n)) (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (log.f64 n)))))
(+.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 n)) (log.f64 (PI.f64)))
(+.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))) (log.f64 n))
(+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))
(+.f64 (log.f64 n) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 n) (log.f64 (PI.f64))))
(+.f64 (log.f64 (PI.f64)) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 n)))
(log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))
(/.f64 (-.f64 (*.f64 (log.f64 (PI.f64)) (log.f64 (PI.f64))) (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64)))) (-.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 (*.f64 (log.f64 (PI.f64)) (log.f64 (PI.f64))) (-.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))
(+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(log.f64 (PI.f64))
(PI.f64)
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(log.f64 n)
n
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 #s(literal -1 binary64) k)) #s(literal 1 binary64)) (-.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 #s(literal -1 binary64) k))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 #s(literal -1 binary64) k) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1 binary64) k) (*.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
(fma.f64 k #s(literal -1 binary64) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) k))
(+.f64 (*.f64 #s(literal -1 binary64) k) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))
#s(literal -1 binary64)
k
#s(literal 1 binary64)
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/2 binary64)))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 k)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))) (neg.f64 (pow.f64 k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.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) (PI.f64)) n) (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
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#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) (+.f64 (+.f64 (fma.f64 (*.f64 #s(literal -1 binary64) k) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (log.f64 (PI.f64))) (log.f64 n)) (log.f64 #s(literal 2 binary64))))
#s(approx (+ (* -1 k) 1) #s(literal 1 binary64))
#s(approx (+ (* -1 k) 1) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
#s(approx k k)
#s(approx (pow (pow k -1) 1/2) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
#s(approx (pow k -1) (pow.f64 k #s(literal -1 binary64)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/2 binary64))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (/.f64 (fma.f64 (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) k) #s(literal 1/2 binary64))) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
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#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))) k) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) #s(literal 1/8 binary64) (*.f64 (fma.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal -1/192 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k)) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (fma.f64 (*.f64 #s(literal -1/4 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64))) (log.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/32 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64))) (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))) k) (*.f64 (*.f64 #s(literal -1/4 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))) k (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/384 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64))) (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))) k) (*.f64 (*.f64 #s(literal 1/32 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64))) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))) k (*.f64 (*.f64 #s(literal -1/4 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))) k (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64))))
#s(approx (/ (/ (- 1 k) 2) 2) #s(literal 1/4 binary64))
#s(approx (/ (/ (- 1 k) 2) 2) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)))
#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 (exp (* (log k) 1/2)) (pow.f64 k #s(literal 1/2 binary64)))
#s(approx (* (log k) 1/2) (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
#s(approx (log k) (log.f64 k))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (log.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (log.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) (*.f64 (fma.f64 (/.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) k) #s(literal 1/2 binary64) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) k))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) (*.f64 (*.f64 #s(literal -1 binary64) k) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) (*.f64 (fma.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) #s(literal -1 binary64) (/.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) k)) k))
#s(approx (+ (* -1 k) 1) (*.f64 #s(literal -1 binary64) k))
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#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
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#s(approx (/ (/ (- 1 k) 2) 2) (*.f64 #s(literal -1/4 binary64) k))
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#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
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#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) k))
#s(approx (- 1 k) (*.f64 (-.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1 binary64)) k))
#s(approx (* (log k) 1/2) (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 k)) #s(literal -1/2 binary64)))
#s(approx (log k) (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 k)) #s(literal -1 binary64)))
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#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
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#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) (*.f64 (*.f64 #s(literal -1 binary64) k) (fma.f64 (/.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) k) #s(literal -1/2 binary64) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
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#s(approx (+ (* -1 k) 1) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1 binary64))) k) #s(literal -1 binary64)))
#s(approx (pow (pow k -1) 1/2) (*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
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#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))))
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#s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 k #s(literal -1 binary64)))) k) #s(literal -1 binary64)))
#s(approx (/ (- 1 k) 2) (*.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))) k) #s(literal -1 binary64)))
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#s(approx (log k) (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 k)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))))
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#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64)))))
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#s(approx (log n) (log.f64 n))
#s(approx n n)
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
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#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (+.f64 (log.f64 n) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* 2 (PI)) n) (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))
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#s(approx (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))))))
#s(approx (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
#s(approx (+ (+ (log (PI)) (log 2)) (log n)) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))
#s(approx (log n) (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64)))
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#s(approx (* (pow (* (exp 1/2) (exp 1/2)) (/ (* (+ (+ (log (PI)) (log 2)) (log n)) (+ (* -1 k) 1)) 2)) (pow (pow k -1) 1/2)) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (+.f64 (+.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (log.f64 (PI.f64))) (log.f64 #s(literal 2 binary64))) (log.f64 #s(literal -1 binary64))))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
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#s(approx (* (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval48.0ms (0.5%)

Memory
-13.9MiB live, 92.0MiB allocated; 28ms collecting garbage
Compiler

Compiled 15 781 to 1 307 computations (91.7% saved)

prune99.0ms (1%)

Memory
41.5MiB live, 186.5MiB allocated; 9ms collecting garbage
Pruning

9 alts after pruning (1 fresh and 8 done)

PrunedKeptTotal
New3121313
Fresh000
Picked112
Done077
Total3139322
Accuracy
99.9%
Counts
322 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
95.9%
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 #s(approx (- 1 k) (*.f64 (-.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1 binary64)) k)) #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
✓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)))) (pow.f64 k #s(literal 1/2 binary64)))
✓64.8%
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64)))) k (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
✓70.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.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)))))
✓98.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
✓95.4%
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
✓55.0%
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
✓96.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
✓61.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
Compiler

Compiled 1 627 to 544 computations (66.6% saved)

regimes21.0ms (0.2%)

Memory
0.1MiB live, 47.3MiB allocated; 1ms collecting garbage
Counts
16 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 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 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64)))) k (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 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 #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)))) (exp.f64 (*.f64 (log.f64 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)))) (pow.f64 k #s(literal 1/2 binary64)))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 #s(approx (- 1 k) (*.f64 (-.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1 binary64)) k)) #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
Outputs
(/.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)))) (pow.f64 k #s(literal 1/2 binary64)))
Calls

4 calls:

5.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
5.0ms
n
5.0ms
k
4.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%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)

regimes18.0ms (0.2%)

Memory
-5.7MiB live, 41.6MiB allocated; 2ms collecting garbage
Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 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 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64)))) k (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 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 #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)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
Outputs
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Calls

4 calls:

5.0ms
n
4.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms
k
4.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%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)

regimes16.0ms (0.2%)

Memory
-17.0MiB live, 30.0MiB allocated; 1ms collecting garbage
Counts
11 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 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 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64))) (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/48 binary64)))) k (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Calls

4 calls:

5.0ms
n
4.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms
k
3.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%1k
99.5%1n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes13.0ms (0.1%)

Memory
25.6MiB live, 25.6MiB allocated; 0ms collecting garbage
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 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 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 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)))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 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)))))
Calls

4 calls:

3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms
n
3.0ms
k
3.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.0%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))))
99.0%1k
99.0%1n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes14.0ms (0.1%)

Memory
-21.7MiB live, 26.5MiB allocated; 4ms collecting garbage
Counts
8 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 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 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) #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)))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
Calls

4 calls:

3.0ms
k
3.0ms
n
3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
98.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
98.4%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
98.4%1n
98.4%1k
Compiler

Compiled 23 to 23 computations (0% saved)

regimes11.0ms (0.1%)

Memory
-21.3MiB live, 25.6MiB allocated; 2ms collecting garbage
Counts
6 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 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 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
Calls

4 calls:

3.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
k
2.0ms
n
Results
AccuracySegmentsBranch
96.0%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))))
96.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.1%2k
96.0%1n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes7.0ms (0.1%)

Memory
15.8MiB live, 15.9MiB allocated; 0ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#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) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (exp (* (log k) 1/2))) (*.f64 (pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 #s(literal 2 binary64))) (log.f64 n)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
Outputs
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
Calls

3 calls:

2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
k
2.0ms
n
Results
AccuracySegmentsBranch
96.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
96.0%1n
96.0%1k
Compiler

Compiled 7 to 10 computations (-42.9% saved)

regimes6.0ms (0.1%)

Memory
13.9MiB live, 13.9MiB allocated; 0ms collecting garbage
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 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
96.0%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))))
96.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
96.0%1k
96.0%1n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes5.0ms (0%)

Memory
14.1MiB live, 14.1MiB 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))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
Calls

4 calls:

1.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
k
1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
1.0ms
n
Results
AccuracySegmentsBranch
61.5%1k
61.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
61.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
61.5%1n
Compiler

Compiled 23 to 23 computations (0% saved)

bsearch18.0ms (0.2%)

Memory
-16.9MiB live, 29.8MiB allocated; 2ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
16.0ms
8.892022290618974e-7
6.167618246112313e-6
Samples
9.0ms96×0valid
0.0ms2×0invalid
Compiler

Compiled 997 to 468 computations (53.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-mult: 2.0ms (29.3% of total)
ival-pow: 2.0ms (29.3% of total)
ival-div: 1.0ms (14.7% of total)
ival-sqrt: 1.0ms (14.7% of total)
ival-pi: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

simplify64.0ms (0.6%)

Memory
10.0MiB live, 56.7MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0146590
1224567
2496565
32202560
46290560
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.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)))) (pow.f64 k #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 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 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(if (<=.f64 k #s(literal 4722366482869645/1180591620717411303424 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))))
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
Outputs
(/.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)))) (pow.f64 k #s(literal 1/2 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 k #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 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 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(if (<=.f64 k #s(literal 4722366482869645/1180591620717411303424 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))))
#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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (*.f64 n (/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal -1 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (fma.f64 (*.f64 #s(literal -1 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))))) #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal -1 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal -1 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))))

derivations108.0ms (1.1%)

Memory
-16.8MiB live, 75.9MiB allocated; 9ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 602 to 151 computations (74.9% saved)

preprocess166.0ms (1.7%)

Memory
34.2MiB live, 174.8MiB allocated; 27ms collecting garbage
Compiler

Compiled 1 236 to 328 computations (73.5% saved)

end0.0ms (0%)

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

Profiling

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