Migdal et al, Equation (51)

Time bar (total: 6.2s)

start0.0ms (0%)

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

analyze189.0ms (3.1%)

Memory
-10.1MiB live, 131.2MiB allocated; 88ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%51.5%0%7
52.5%25%22.6%0.1%0%52.3%0%8
53.8%25%21.5%0.1%0%53.5%0%9
54.5%25%20.9%0.1%0%54%0%10
55.3%25%20.2%0.1%0%54.7%0%11
55.7%25%19.9%0.1%0%55.1%0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.4s (55.7%)

Memory
91.8MiB live, 4 179.0MiB allocated; 841ms collecting garbage
Samples
1.0s4 407×1invalid
1.0s8 256×0valid
524.0ms1 481×2invalid
29.0ms219×0exit
29.0ms366×0invalid
Precisions
Click to see histograms. Total time spent on operations: 2.0s
ival-pow: 565.0ms (28.7% of total)
ival-mult: 455.0ms (23.1% of total)
ival-div: 286.0ms (14.5% of total)
adjust: 186.0ms (9.5% of total)
ival-sqrt: 186.0ms (9.5% of total)
ival-sub: 159.0ms (8.1% of total)
ival-pi: 100.0ms (5.1% of total)
exact: 23.0ms (1.2% of total)
ival-assert: 6.0ms (0.3% of total)
Bogosity

explain208.0ms (3.4%)

Memory
18.1MiB live, 254.4MiB allocated; 46ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1089(2.3763670560030896e-220 2.3889349361303498e-197)0-(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
00-0-k
00-0-n
00-0-(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
00-0-#s(literal 1 binary64)
00-0-(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
00-0-(sqrt.f64 k)
00-0-#s(literal 2 binary64)
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
00-0-(-.f64 #s(literal 1 binary64) k)
00-0-(*.f64 #s(literal 2 binary64) (PI.f64))
00-0-(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
00-0-(PI.f64)
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
pow.f64(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))sensitivity9919
Confusion
Predicted +Predicted -
+100
-89157
Precision
0.10101010101010101
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+1000
-8919138
Precision?
0.0847457627118644
Recall?
1.0
Freqs
test
numberfreq
0157
199
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
101.0ms512×0valid
Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 81.0ms
ival-sub: 48.0ms (59.3% of total)
ival-pow: 10.0ms (12.4% of total)
ival-mult: 9.0ms (11.1% of total)
ival-div: 7.0ms (8.7% of total)
ival-sqrt: 4.0ms (4.9% of total)
ival-pi: 2.0ms (2.5% of total)
exact: 1.0ms (1.2% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess155.0ms (2.5%)

Memory
-24.4MiB live, 129.6MiB allocated; 36ms 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 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

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

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 16 to 13 computations (18.8% saved)

series73.0ms (1.2%)

Memory
-18.3MiB live, 119.3MiB allocated; 13ms 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
33.0ms
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))
24.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
8.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
3.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
3.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))

rewrite57.0ms (0.9%)

Memory
22.5MiB live, 73.3MiB allocated; 9ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0181965
0195935
0833935
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
47 → 68
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
k
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(+.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) (+.f64 (*.f64 k k) (*.f64 #s(literal 1 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (+.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))))) k) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ 1 (sqrt k)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (+.f64 (neg.f64 k) #s(literal 1 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 k) #s(literal 1 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt k) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 k) #s(literal 1 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* 2 (PI)) n) (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval11.0ms (0.2%)

Memory
-28.2MiB live, 17.5MiB allocated; 4ms collecting garbage
Compiler

Compiled 1 720 to 294 computations (82.9% saved)

prune14.0ms (0.2%)

Memory
26.0MiB live, 26.0MiB allocated; 0ms collecting garbage
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New541670
Fresh000
Picked101
Done000
Total551671
Accuracy
99.8%
Counts
71 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.3%
(/.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)))) (sqrt.f64 k))
99.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
52.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
99.1%
(*.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)))))
75.6%
(*.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)))))
95.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (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)))))
95.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))))
95.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k)))))
▶58.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
64.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
▶48.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
48.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
99.3%
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
56.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))))) k) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
▶55.7%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (+.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64))) k))
▶36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
Compiler

Compiled 1 130 to 784 computations (30.6% saved)

series164.0ms (2.7%)

Memory
9.3MiB live, 242.7MiB allocated; 21ms collecting garbage
Counts
57 → 183
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)))) (sqrt.f64 k))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#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
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(+.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k)
(*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (PI.f64) n))
#s(literal -1/2 binary64)
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (+.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64))) k))
(/.f64 (+.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64))) k)
(+.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64)))
(sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(*.f64 (*.f64 (PI.f64) n) k)
(*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64))
(*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))
(*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))
(*.f64 (pow.f64 k #s(literal 3 binary64)) n)
(pow.f64 k #s(literal 3 binary64))
#s(literal 3 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))) k)
(-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 #s(literal -1/8 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(literal -1/8 binary64)
(*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)))
(pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))
Outputs
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ (* (PI) n) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (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 (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) #s(hole binary64 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) #s(hole binary64 (* k (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (/ (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -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 (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -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)))))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* (* (* (PI) n) k) 2) #s(hole binary64 (* 2 (* k (* n (PI))))))
#s(approx (* (* (PI) n) k) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (sqrt (* (pow k 3) (* n (PI))))))
#s(approx (* (* (pow k 3) n) (PI)) #s(hole binary64 (* (pow k 3) (* n (PI)))))
#s(approx (* (pow k 3) n) #s(hole binary64 (* (pow k 3) n)))
#s(approx (pow k 3) #s(hole binary64 (pow k 3)))
#s(approx (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) #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 (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) #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)))))))))
#s(approx (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) #s(hole binary64 (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) #s(hole binary64 (+ (* -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))))))))
#s(approx (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)))) #s(hole binary64 (* -1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))) #s(hole binary64 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#s(approx (/ (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* 1/8 (* (* (pow k 2) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* (pow k 2) (- (* -1/2 (* (/ (* (log (* 2 (* n (PI)))) (sqrt 2)) k) (sqrt (* n (PI))))) (* -1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))
#s(approx (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* (pow k 2) (- (+ (* -1/2 (* (/ (* (log (* 2 (* n (PI)))) (sqrt 2)) k) (sqrt (* n (PI))))) (* (/ (sqrt 2) (pow k 2)) (sqrt (* n (PI))))) (* -1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))
#s(approx (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) #s(hole binary64 (* 1/8 (* (* (pow k 2) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI)))))))
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#s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) #s(hole binary64 (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2)))))
#s(approx (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* n (+ (* k (- (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* -1/8 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))) (sqrt (/ (PI) n)))))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) #s(hole binary64 (* -1 (* k (* n (- (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* -1/8 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))) (sqrt (/ (PI) n))))))))))
#s(approx (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) #s(hole binary64 (* -1 (* n (- (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* -1/8 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))) (sqrt (/ (PI) n)))))))))
#s(approx (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 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 (sqrt (* (PI) n))) #s(hole binary64 (* 1/2 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)))) #s(hole binary64 (* 1/8 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))) (sqrt (* n (PI)))))))
#s(approx (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))) #s(hole binary64 (* -1 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))) (sqrt (* n (PI)))))))
#s(approx (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))))))
#s(approx (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2))))))
#s(approx (pow (log (* (* (PI) 2) n)) 2) #s(hole binary64 (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))
Calls

6 calls:

TimeVariablePointExpression
49.0ms
k
@0
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 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 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (PI) n)) -1/2 (sqrt (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) k) (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/2 (sqrt (* (PI) n))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)))) -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))) (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)) (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (pow (log (* (* (PI) 2) n)) 2))
26.0ms
k
@-inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 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 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (PI) n)) -1/2 (sqrt (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) k) (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/2 (sqrt (* (PI) n))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)))) -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))) (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)) (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (pow (log (* (* (PI) 2) n)) 2))
24.0ms
n
@-inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 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 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (PI) n)) -1/2 (sqrt (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) k) (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/2 (sqrt (* (PI) n))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)))) -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))) (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)) (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (pow (log (* (* (PI) 2) n)) 2))
20.0ms
n
@0
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 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 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (PI) n)) -1/2 (sqrt (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) k) (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/2 (sqrt (* (PI) n))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)))) -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))) (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)) (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (pow (log (* (* (PI) 2) n)) 2))
19.0ms
k
@inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 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 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (* (log (* (* (PI) 2) n)) (sqrt 2)) (log (* (* (PI) 2) n)) (sqrt 2) (sqrt (* (PI) n)) -1/2 (sqrt (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) k) (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/2 (sqrt (* (PI) n))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)))) -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))) (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)) (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (pow (log (* (* (PI) 2) n)) 2))

rewrite104.0ms (1.7%)

Memory
14.1MiB live, 108.4MiB allocated; 10ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06018591
07038030
025648030
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
240 → 391
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)))) (sqrt.f64 k))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#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
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
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(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) #s(hole binary64 (* 1/2 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (* n (PI)))))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) #s(hole binary64 (* -1 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (* n (PI)))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) #s(hole binary64 (* k (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) #s(hole binary64 (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) k) #s(hole binary64 (* -1 (/ (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))) k))))
#s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt (/ (* k (PI)) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) #s(hole binary64 (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2)))))
#s(approx (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* n (+ (* k (- (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* -1/8 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))) (sqrt (/ (PI) n)))))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) #s(hole binary64 (* -1 (* k (* n (- (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* -1/8 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))) (sqrt (/ (PI) n))))))))))
#s(approx (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) #s(hole binary64 (* -1 (* n (- (* -1/2 (* (sqrt (/ (PI) n)) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* -1/8 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))) (sqrt (/ (PI) n)))))))))
#s(approx (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 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 (sqrt (* (PI) n))) #s(hole binary64 (* 1/2 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)))) #s(hole binary64 (* 1/8 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))) (sqrt (* n (PI)))))))
#s(approx (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))) #s(hole binary64 (* -1 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))) (sqrt (* n (PI)))))))
#s(approx (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))))))
#s(approx (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2))))))
#s(approx (pow (log (* (* (PI) 2) n)) 2) #s(hole binary64 (pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)))
Outputs
(*.f64 (pow.f64 (sqrt.f64 k) #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))))
(*.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 (sqrt.f64 k) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(/.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 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
(*.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 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (*.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 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (*.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))
(+.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) (+.f64 (*.f64 k k) (*.f64 #s(literal 1 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
k
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)
(+.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 (*.f64 (PI.f64) n) k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (-.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) (-.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(-.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))
(*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 k (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 (*.f64 k (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) k)
(*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) k))
(*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (*.f64 (log.f64 n) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
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#s(approx (- 1 k) (+.f64 (neg.f64 k) #s(literal 1 binary64)))
#s(approx k k)
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#s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (neg.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64)))) n)))
#s(approx (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))))
#s(approx (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) (neg.f64 (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))))))
#s(approx (+ (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (sqrt (* (* (PI) 2) n))) (neg.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) #s(literal -1 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (neg.f64 k) (*.f64 (pow.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))
#s(approx (* (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) k) (*.f64 (neg.f64 k) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) #s(literal -1 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (neg.f64 k) (*.f64 (pow.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 (PI.f64) n)))) n)))
#s(approx (- (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))))) (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) #s(literal -1 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (neg.f64 k) (*.f64 (pow.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 (PI.f64) n)))) n)))
#s(approx (* (* -1/2 (sqrt (* (PI) n))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (*.f64 (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
#s(approx (* -1/2 (sqrt (* (PI) n))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1 binary64)))
#s(approx (* -1/8 (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)))) (*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (neg.f64 k) (*.f64 (pow.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (* k (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2))) (neg.f64 (*.f64 (*.f64 (neg.f64 k) (*.f64 (pow.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (* (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (sqrt 2)) (neg.f64 (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (sqrt (* (PI) n)) (pow (log (* (* (PI) 2) n)) 2)) (neg.f64 (*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)))))
#s(approx (pow (log (* (* (PI) 2) n)) 2) (pow.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)))

eval73.0ms (1.2%)

Memory
-14.8MiB live, 122.0MiB allocated; 12ms collecting garbage
Compiler

Compiled 32 028 to 2 705 computations (91.6% saved)

prune712.0ms (11.6%)

Memory
-192.9MiB live, 84.8MiB allocated; 1.2s collecting garbage
Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New56017577
Fresh6511
Picked415
Done000
Total57023593
Accuracy
99.8%
Counts
593 → 23
Alt Table
Click to see full alt table
StatusAccuracyProgram
75.7%
(/.f64 (*.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)))) (sqrt.f64 k))
99.2%
(/.f64 (*.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)))) (sqrt.f64 k))
▶99.3%
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
52.3%
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 k))
58.9%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) k) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) (sqrt.f64 k))
49.0%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) (sqrt.f64 k))
95.9%
(/.f64 (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)))) (sqrt.f64 k))
95.5%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
95.7%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
64.5%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(literal -1/8 binary64))) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
48.3%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
99.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
95.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (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)))))
48.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (-.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
64.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
▶48.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
▶56.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n))))
▶99.3%
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
38.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
36.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
✓36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
▶36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
Compiler

Compiled 1 587 to 1 098 computations (30.8% saved)

series236.0ms (3.8%)

Memory
21.9MiB live, 349.8MiB allocated; 25ms collecting garbage
Counts
50 → 136
Calls
Call 1
Inputs
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
n
#s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal -1 binary64))
#s(literal -1 binary64)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n)))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n))
(*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n)
(+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))
(*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))
(/.f64 (PI.f64) n)
(*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))
(*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(neg.f64 (neg.f64 (log.f64 n)))
(neg.f64 (log.f64 n))
(log.f64 n)
(log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
Outputs
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* n (/ (PI) k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* n (/ (PI) k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ (PI) k) #s(hole binary64 (/ (PI) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (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 (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (pow k -1)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow k -1) #s(hole binary64 (/ 1 k)))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) #s(hole binary64 (* (sqrt (/ (PI) n)) (sqrt 2))))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (sqrt 2)))))
#s(approx (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) #s(hole binary64 (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (/ (PI) n))))))
#s(approx (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (/ (PI) n)))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 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 (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 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 (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#s(approx (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) #s(hole binary64 (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI)))))))
#s(approx (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) #s(hole binary64 (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (/ (PI) n))))))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (PI) n)) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))) (* (/ (sqrt 2) k) (sqrt (/ (PI) n)))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (pow k -1)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* k (+ (* -1 (* (/ (sqrt 2) k) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))))))
#s(approx (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) #s(hole binary64 (* -1 (* k (+ (* -1 (* (/ (sqrt 2) k) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))))))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) #s(hole binary64 (* -1 (* k (+ (* -1 (* (/ (sqrt 2) k) (sqrt (/ (PI) n)))) (* 1/2 (* (sqrt (/ (PI) n)) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) #s(hole binary64 (/ (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) n)))
#s(approx (sqrt (* (/ (PI) n) 2)) #s(hole binary64 (* (sqrt (/ (PI) n)) (sqrt 2))))
#s(approx (* (/ (PI) n) 2) #s(hole binary64 (* 2 (/ (PI) n))))
#s(approx (/ (PI) n) #s(hole binary64 (/ (PI) n)))
#s(approx (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) #s(hole binary64 (* (sqrt (/ (PI) n)) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (+ (neg (neg (log n))) (log (* (PI) 2))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (neg (neg (log n))) #s(hole binary64 (log n)))
#s(approx (neg (log n)) #s(hole binary64 (* -1 (log n))))
#s(approx (log n) #s(hole binary64 (log n)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 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 (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* n (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (sqrt 2))))))
#s(approx (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) #s(hole binary64 (* n (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (sqrt 2))))))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (sqrt 2)))))
#s(approx (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) #s(hole binary64 (* -1/2 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (PI) n))))))
#s(approx (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (PI) n)))))
#s(approx (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) #s(hole binary64 (* (sqrt (/ (PI) n)) (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (+ (neg (neg (log n))) (log (* (PI) 2))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (neg (neg (log n))) #s(hole binary64 (* -1 (log (/ 1 n)))))
#s(approx (neg (log n)) #s(hole binary64 (log (/ 1 n))))
#s(approx (log n) #s(hole binary64 (* -1 (log (/ 1 n)))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) #s(hole binary64 (* n (+ (* -1/2 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n)))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))))))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n)))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (/ (PI) n) 2)) #s(hole binary64 (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))))
#s(approx (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) #s(hole binary64 (* -1/2 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n)))))))) (sqrt (/ (PI) n))))))
#s(approx (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) #s(hole binary64 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n)))))))) (sqrt (/ (PI) n)))))
#s(approx (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) #s(hole binary64 (* (sqrt (/ (PI) n)) (* (sqrt -2) (* (sqrt -1) (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (+ (neg (neg (log n))) (log (* (PI) 2))) #s(hole binary64 (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (neg (neg (log n))) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 n))))))
#s(approx (neg (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))))))
Calls

6 calls:

TimeVariablePointExpression
81.0ms
n
@-inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 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) (+ (* -1/2 k) 1/2) (* -1/2 k) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (sqrt (* (/ (PI) n) 2)) (* (/ (PI) n) 2) (/ (PI) n) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) (+ (neg (neg (log n))) (log (* (PI) 2))) (neg (neg (log n))) (neg (log n)) (log n) (log (* (PI) 2)))
43.0ms
n
@0
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 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) (+ (* -1/2 k) 1/2) (* -1/2 k) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (sqrt (* (/ (PI) n) 2)) (* (/ (PI) n) 2) (/ (PI) n) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) (+ (neg (neg (log n))) (log (* (PI) 2))) (neg (neg (log n))) (neg (log n)) (log n) (log (* (PI) 2)))
38.0ms
k
@0
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 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) (+ (* -1/2 k) 1/2) (* -1/2 k) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (sqrt (* (/ (PI) n) 2)) (* (/ (PI) n) 2) (/ (PI) n) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) (+ (neg (neg (log n))) (log (* (PI) 2))) (neg (neg (log n))) (neg (log n)) (log n) (log (* (PI) 2)))
27.0ms
n
@inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 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) (+ (* -1/2 k) 1/2) (* -1/2 k) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (sqrt (* (/ (PI) n) 2)) (* (/ (PI) n) 2) (/ (PI) n) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) (+ (neg (neg (log n))) (log (* (PI) 2))) (neg (neg (log n))) (neg (log n)) (log n) (log (* (PI) 2)))
23.0ms
k
@-inf
((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 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) (+ (* -1/2 k) 1/2) (* -1/2 k) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (* (PI) 2) n)) (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (sqrt (* (/ (PI) n) 2)) (* (/ (PI) n) 2) (/ (PI) n) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) (+ (neg (neg (log n))) (log (* (PI) 2))) (neg (neg (log n))) (neg (log n)) (log n) (log (* (PI) 2)))

rewrite75.0ms (1.2%)

Memory
-6.1MiB live, 86.4MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04305108
05004603
018254603
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
186 → 322
Calls
Call 1
Inputs
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
n
#s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal -1 binary64))
#s(literal -1 binary64)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n)))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n))
(*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n)
(+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))
(*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))
(/.f64 (PI.f64) n)
(*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))
(*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(neg.f64 (neg.f64 (log.f64 n)))
(neg.f64 (log.f64 n))
(log.f64 n)
(log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
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#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
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#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
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#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
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#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
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#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))))))
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#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (pow (sqrt -1) 2) (* (sqrt 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) #s(hole binary64 (* n (+ (* -1/2 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n)))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))))))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n)))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (/ (PI) n) 2)) #s(hole binary64 (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))))
#s(approx (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) #s(hole binary64 (* -1/2 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n)))))))) (sqrt (/ (PI) n))))))
#s(approx (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) #s(hole binary64 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n)))))))) (sqrt (/ (PI) n)))))
#s(approx (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) #s(hole binary64 (* (sqrt (/ (PI) n)) (* (sqrt -2) (* (sqrt -1) (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (+ (neg (neg (log n))) (log (* (PI) 2))) #s(hole binary64 (+ (log -1) (+ (log (* 2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (neg (neg (log n))) #s(hole binary64 (+ (log -1) (* -1 (log (/ -1 n))))))
#s(approx (neg (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))))))
Outputs
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 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))
(+.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
#s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)
(+.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 (*.f64 (PI.f64) n) k))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 k))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 (neg.f64 (PI.f64)) (neg.f64 k))
(/.f64 (PI.f64) k)
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (pow.f64 k #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 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(/.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 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 k))
(/.f64 #s(literal 1 binary64) k)
(exp.f64 (*.f64 (log.f64 k) #s(literal -1 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 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (*.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))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
(/.f64 (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) (+.f64 (*.f64 k k) (*.f64 #s(literal 1 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))))
(*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))
(*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)
(*.f64 n (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))))
(+.f64 (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) n) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) n))
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#s(approx n n)
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#s(approx (* (* (PI) 2) n) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (/.f64 (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) n))
#s(approx (sqrt (* (/ (PI) n) 2)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))))
#s(approx (* (/ (PI) n) 2) (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))
#s(approx (/ (PI) n) (/.f64 (PI.f64) n))
#s(approx (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (+ (neg (neg (log n))) (log (* (PI) 2))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (neg (neg (log n))) (log.f64 n))
#s(approx (neg (log n)) (neg.f64 (log.f64 n)))
#s(approx (neg (neg (log n))) (log.f64 n))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #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 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #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 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))
#s(approx (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)))
#s(approx (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (+ (neg (neg (log n))) (log (* (PI) 2))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (neg (neg (log n))) (log.f64 n))
#s(approx (neg (log n)) (neg.f64 (log.f64 n)))
#s(approx (neg (neg (log n))) (log.f64 n))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (neg.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt (* (* (PI) 2) n)) (neg.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (neg.f64 (*.f64 (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 k) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))
#s(approx (* (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) n) (*.f64 (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))) k)) (sqrt.f64 (/.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))
#s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))) k)) (sqrt.f64 (/.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (sqrt (* (/ (PI) n) 2)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))))
#s(approx (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))) k)) (sqrt.f64 (/.f64 (PI.f64) n))))
#s(approx (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))) k) (sqrt.f64 (/.f64 (PI.f64) n))))
#s(approx (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 (PI.f64) n))))
#s(approx (+ (neg (neg (log n))) (log (* (PI) 2))) (+.f64 (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))
#s(approx (neg (neg (log n))) (+.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))
#s(approx (neg (log n)) (neg.f64 (+.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))
#s(approx (neg (neg (log n))) (+.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))

eval37.0ms (0.6%)

Memory
25.7MiB live, 71.6MiB allocated; 3ms collecting garbage
Compiler

Compiled 15 922 to 1 450 computations (90.9% saved)

prune40.0ms (0.6%)

Memory
-31.1MiB live, 65.6MiB allocated; 7ms collecting garbage
Pruning

29 alts after pruning (27 fresh and 2 done)

PrunedKeptTotal
New31015325
Fresh51217
Picked415
Done011
Total31929348
Accuracy
99.8%
Counts
348 → 29
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.3%
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
75.7%
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
▶99.2%
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (sqrt.f64 k))
58.9%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) k) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) (sqrt.f64 k))
56.1%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))) (sqrt.f64 k))
95.9%
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
95.5%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
95.7%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
64.5%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(literal -1/8 binary64))) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
▶49.0%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
48.3%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
48.3%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
99.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
95.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (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)))))
48.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (-.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
64.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
▶48.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
48.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
48.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
48.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))))
48.3%
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
99.3%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.1%
(*.f64 (sqrt.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
38.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
36.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
✓36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
▶36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
✓36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
95.7%
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
Compiler

Compiled 2 016 to 1 408 computations (30.2% saved)

series96.0ms (1.6%)

Memory
8.0MiB live, 153.1MiB allocated; 23ms collecting garbage
Counts
39 → 129
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
#s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 n k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(sqrt.f64 #s(literal 2 binary64))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))
(*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))
Outputs
#s(approx (/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* n (* (PI) 2)) (/ (- 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 (* n (* (PI) 2)) (/ (- 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 (* n (* (PI) 2)) (/ (- 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 (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* (PI) (/ n k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (PI) (/ n k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 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 (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) #s(hole binary64 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/4)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 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 (* n (* (PI) 2)) (/ (/ (- 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 (* n (* (PI) 2)) (/ (/ (- 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 (/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* n (* (PI) 2)) (/ (- 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 (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 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 (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) #s(hole binary64 (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 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 (/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (pow (* n (* (PI) 2)) (/ (- 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 (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) #s(hole binary64 (* -1 (* k (+ (* -1 (* (/ (sqrt 2) k) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))))))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 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 (/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* n (* (PI) 2)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (sqrt (* (PI) n)) (sqrt 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) #s(hole binary64 (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) #s(hole binary64 (* -1/2 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI)))))))
#s(approx (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log n) (log (* 2 (PI)))))) (sqrt (* n (PI))))))
#s(approx (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) #s(hole binary64 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (log n) (log (* 2 (PI))))))))
#s(approx (sqrt (* n (* (PI) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (log (* n (* (PI) 2))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) #s(hole binary64 (* n (+ (* -1/2 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (sqrt 2))))))
#s(approx (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) #s(hole binary64 (* -1/2 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (* n (PI)))))))
#s(approx (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) #s(hole binary64 (* (* k (* (sqrt 2) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt (* n (PI))))))
#s(approx (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) #s(hole binary64 (* (sqrt (* n (PI))) (* (sqrt 2) (+ (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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (sqrt (* (PI) n)) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) #s(hole binary64 (* 1/2 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (* n (PI)))))))
#s(approx (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) #s(hole binary64 (* -1 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (* n (PI)))))))
#s(approx (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (sqrt (* n (* (PI) 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (log (* n (* (PI) 2))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Calls

6 calls:

TimeVariablePointExpression
27.0ms
n
@-inf
((/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) (* -1/2 k) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt 2) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))) (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
14.0ms
k
@0
((/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) (* -1/2 k) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt 2) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))) (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
13.0ms
n
@0
((/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) (* -1/2 k) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt 2) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))) (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
13.0ms
k
@-inf
((/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) (* -1/2 k) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt 2) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))) (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
12.0ms
k
@inf
((/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) (* -1/2 k) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt 2) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))) (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))

rewrite82.0ms (1.3%)

Memory
15.8MiB live, 108.3MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04465118
05024531
019734531
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
168 → 267
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
#s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 n k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(sqrt.f64 #s(literal 2 binary64))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))
(*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
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#s(approx (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (sqrt (* (PI) n)) (sqrt 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (/ (PI) n)))) (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1))))))))
#s(approx (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) #s(hole binary64 (* 1/2 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (* n (PI)))))))
#s(approx (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) #s(hole binary64 (* -1 (* (* k (* (sqrt -2) (* (sqrt -1) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt (* n (PI)))))))
#s(approx (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (sqrt (* n (* (PI) 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (log (* n (* (PI) 2))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
Outputs
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(*.f64 (fabs.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(*.f64 (pow.f64 n #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 2 binary64) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (+.f64 (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 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 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
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)
#s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))
(*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))
(*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))
(/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k)
(+.f64 (*.f64 (/.f64 n k) (PI.f64)) (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 k))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 (neg.f64 n) (neg.f64 k))
(/.f64 n k)
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (sqrt.f64 k))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
#s(literal 1 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (-.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64))) (-.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (*.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))))
(-.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(+.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) k)
(*.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
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#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) (*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n))
#s(approx (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)))
#s(approx (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) (*.f64 k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))
#s(approx (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (log (* n (* (PI) 2))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (*.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) (neg.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (sqrt (* (PI) n)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (+ (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (sqrt (* n (* (PI) 2)))) (neg.f64 (*.f64 (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) k)) (sqrt.f64 (/.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))
#s(approx (* (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) -1/2) (*.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)))
#s(approx (* k (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2))))) (neg.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) k) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (* (sqrt (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (* (sqrt (* (PI) n)) (sqrt 2)) (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (log (* n (* (PI) 2))) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (*.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval48.0ms (0.8%)

Memory
-11.3MiB live, 84.6MiB allocated; 10ms collecting garbage
Compiler

Compiled 14 993 to 1 295 computations (91.4% saved)

prune48.0ms (0.8%)

Memory
12.7MiB live, 107.4MiB allocated; 3ms collecting garbage
Pruning

35 alts after pruning (32 fresh and 3 done)

PrunedKeptTotal
New36913382
Fresh31922
Picked415
Done022
Total37635411
Accuracy
99.8%
Counts
411 → 35
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.2%
(/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
99.3%
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
52.3%
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
75.7%
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
71.3%
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (sqrt.f64 k))
98.8%
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))) (sqrt.f64 k))
96.6%
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 k))
58.9%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) k) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) (sqrt.f64 k))
56.1%
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))) (sqrt.f64 k))
95.9%
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
95.5%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
95.7%
(/.f64 #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)))) (sqrt.f64 k))
48.9%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (-.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k))
64.5%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(literal -1/8 binary64))) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
49.0%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
48.3%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
99.1%
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sqrt.f64 k)))
48.3%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
99.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
95.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (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)))))
48.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (-.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
64.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
✓48.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
48.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
48.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
48.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))))
48.3%
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
99.3%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.1%
(*.f64 (sqrt.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
38.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
✓36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
36.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
95.7%
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
Compiler

Compiled 3 383 to 1 256 computations (62.9% saved)

regimes67.0ms (1.1%)

Memory
2.2MiB live, 98.0MiB allocated; 5ms collecting garbage
Counts
62 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (-.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1/2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (-.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
(/.f64 (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)))) (sqrt.f64 k))
(/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (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 (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)))) (sqrt.f64 k))
(*.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 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (+.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64))) k))
(/.f64 (*.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)))) (sqrt.f64 k))
(*.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)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64))) (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal -1/2 binary64))) n))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
(/.f64 #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)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
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#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
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(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))))) k) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(literal -1/8 binary64))) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+.f64 (*.f64 (+.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))))
Outputs
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
Calls

4 calls:

17.0ms
n
15.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
15.0ms
k
15.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.3%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))))
99.3%1k
99.3%1n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes21.0ms (0.3%)

Memory
-14.7MiB live, 32.0MiB allocated; 2ms collecting garbage
Counts
16 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
Outputs
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
Calls

4 calls:

6.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
5.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
5.0ms
k
5.0ms
n
Results
AccuracySegmentsBranch
61.3%4(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
95.8%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
95.8%2k
61.3%4n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes18.0ms (0.3%)

Memory
30.0MiB live, 30.0MiB allocated; 0ms collecting garbage
Counts
15 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (* (PI) 2) n))) (*.f64 #s(approx (+ (sqrt (* (/ (PI) n) 2)) (* (* k (* (sqrt (* (/ (PI) n) 2)) (+ (neg (neg (log n))) (log (* (PI) 2))))) -1/2)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
Outputs
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
Calls

4 calls:

5.0ms
k
4.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms
n
4.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
48.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
48.3%1n
48.3%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))))
48.3%1k
Compiler

Compiled 23 to 23 computations (0% saved)

regimes12.0ms (0.2%)

Memory
-28.2MiB live, 18.9MiB allocated; 2ms collecting garbage
Counts
7 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k))
Calls

4 calls:

3.0ms
n
3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
k
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
48.4%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
39.8%2k
48.2%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
48.2%2n
Compiler

Compiled 23 to 23 computations (0% saved)

regimes8.0ms (0.1%)

Memory
16.7MiB live, 16.7MiB allocated; 0ms collecting garbage
Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
Calls

4 calls:

2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
n
2.0ms
k
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
36.3%1k
36.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
36.3%1n
36.3%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 23 to 23 computations (0% saved)

bsearch41.0ms (0.7%)

Memory
-28.1MiB live, 18.9MiB allocated; 2ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
13.0ms
0.20276293213121208
2.887879850899691
Samples
9.0ms96×0valid
Compiler

Compiled 253 to 234 computations (7.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-mult: 2.0ms (31.5% of total)
ival-pow: 2.0ms (31.5% of total)
ival-div: 1.0ms (15.8% of total)
ival-sqrt: 1.0ms (15.8% 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)

bsearch0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
4.62215330372399e+147
5.5657773104829265e+152
Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify41.0ms (0.7%)

Memory
45.1MiB live, 45.1MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
073210
1115204
2226204
3656204
42887204
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 1 binary64)) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5000000000000000244883632875752602897861135017653719443725211872950841317966923780806157646236382318965565323407551383810267164593312926085511380992 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
Outputs
(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 1 binary64)) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5000000000000000244883632875752602897861135017653719443725211872950841317966923780806157646236382318965565323407551383810267164593312926085511380992 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (+ (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (pow k 3) n) (PI)))) -1/2)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))

derivations57.0ms (0.9%)

Memory
-16.5MiB live, 33.2MiB allocated; 3ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 210 to 76 computations (63.8% saved)

preprocess39.0ms (0.6%)

Memory
-8.4MiB live, 38.2MiB allocated; 3ms collecting garbage
Compiler

Compiled 452 to 178 computations (60.6% saved)

end0.0ms (0%)

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

Profiling

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