Migdal et al, Equation (51)

Time bar (total: 11.1s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze180.0ms (1.6%)

Memory
6.0MiB live, 147.6MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%51.5%0%7
52.5%25%22.6%0.1%0%52.3%0%8
53.8%25%21.5%0.1%0%53.5%0%9
54.5%25%20.9%0.1%0%54%0%10
55.3%25%20.2%0.1%0%54.7%0%11
55.7%25%19.9%0.1%0%55.1%0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample4.2s (38.2%)

Memory
18.5MiB live, 5 758.2MiB allocated
Samples
1.6s3 604×1invalid
1.0s8 256×0valid
400.0ms1 943×1exit
152.0ms419×2invalid
70.0ms523×0invalid
37.0ms231×0exit
Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-mult: 1.1s (40.9% of total)
ival-pow: 571.0ms (22% of total)
ival-div: 336.0ms (12.9% of total)
adjust: 190.0ms (7.3% of total)
ival-sqrt: 146.0ms (5.6% of total)
ival-pi: 145.0ms (5.6% of total)
ival-sub: 107.0ms (4.1% of total)
exact: 19.0ms (0.7% of total)
ival-true: 13.0ms (0.5% of total)
ival-assert: 7.0ms (0.3% of total)
Bogosity

explain305.0ms (2.8%)

Memory
24.0MiB live, 214.3MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
773(5.778167114658237e-246 2.817251554145798e+279)2(4.873996318183359e-17 3.1975295189893854e-43)(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)))sensitivity7822
Confusion
Predicted +Predicted -
+52
-73176
Precision
0.0641025641025641
Recall
0.7142857142857143
Confusion?
Predicted +Predicted MaybePredicted -
+520
-7320156
Precision?
0.07
Recall?
1.0
Freqs
test
numberfreq
0178
178
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
72.0ms512×0valid
Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-pow: 10.0ms (27.6% of total)
ival-mult: 9.0ms (24.8% of total)
ival-div: 7.0ms (19.3% of total)
ival-sqrt: 4.0ms (11% of total)
ival-sub: 3.0ms (8.3% of total)
ival-pi: 2.0ms (5.5% of total)
exact: 1.0ms (2.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess58.0ms (0.5%)

Memory
-15.6MiB live, 37.3MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03188
17176
214574
322774
429674
536374
642874
750174
852874
954174
1054774
01316
02216
13714
25014
36714
48014
59814
613214
720214
822714
924714
1025714
025714
Stop Event
iter limit
saturated
iter limit
saturated
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
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify8.0ms (0.1%)

Memory
10.6MiB live, 10.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 k)
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff2
(*.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))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01354
02254
13752
25052
36752
48052
59852
613252
720252
822752
924752
1025752
025752
Stop Event
iter limit
saturated
iter 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))))
(/.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
(*.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))
(/.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)))
(pow.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) (PI.f64)) n)
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)

localize57.0ms (0.5%)

Memory
8.0MiB live, 52.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.1328125
(*.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))))
accuracy0.2232732627809995
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy0.26171875
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy0.265625
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Samples
48.0ms256×0valid
Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-pow: 5.0ms (26.4% of total)
ival-mult: 4.0ms (21.2% of total)
ival-div: 3.0ms (15.9% of total)
ival-sub: 2.0ms (10.6% of total)
ival-sqrt: 2.0ms (10.6% of total)
ival-pi: 1.0ms (5.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series100.0ms (0.9%)

Memory
-15.0MiB live, 130.9MiB allocated
Counts
5 → 22
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))
(sqrt.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* 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)
(/ (+ (* 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)
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* 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)))
(+ (* 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)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
Calls

6 calls:

TimeVariablePointExpression
37.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
33.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
24.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
3.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
2.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))

simplify234.0ms (2.1%)

Memory
6.4MiB live, 235.3MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0120502
1378489
21377453
34131453
08166441
Stop Event
iter limit
node limit
Counts
22 → 22
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* 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)
(/ (+ (* 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)
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* 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)))
(+ (* 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)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k)
(/ (+ (* 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)
(fma.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))))
(/ (+ (* 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)
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/8 binary64)))) k (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(+ (* 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)))
(fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 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)))
(fma.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n)))
(* 2 (* n (PI)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))

rewrite291.0ms (2.6%)

Memory
-44.6MiB live, 333.4MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01338
02238
18335
244635
3400729
0892129
Stop Event
iter limit
node limit
iter limit
Counts
5 → 321
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))
(sqrt.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Outputs
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))))
(*.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (/.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (sqrt.f64 k)))
(*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 0 binary64) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 #s(literal 0 binary64) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (*.f64 (*.f64 #s(literal 0 binary64) (sqrt.f64 n)) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 n (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 #s(literal 0 binary64) (sqrt.f64 n))) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (*.f64 (*.f64 #s(literal 0 binary64) (sqrt.f64 n)) #s(literal -1 binary64)) (*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (*.f64 #s(literal 0 binary64) (sqrt.f64 n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)) (sqrt.f64 k)))
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(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 n (PI.f64)))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64)) (*.f64 n (PI.f64)))
(fma.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 n (PI.f64)))
(fma.f64 (*.f64 n #s(literal 2 binary64)) (cosh.f64 (log.f64 (PI.f64))) (*.f64 (*.f64 n #s(literal 2 binary64)) (sinh.f64 (log.f64 (PI.f64)))))
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) n) (*.f64 n (PI.f64)))
(fma.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) n)) (*.f64 n (PI.f64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)) (*.f64 n (PI.f64)))
(fma.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64)) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))))
(fma.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 0 binary64) n) (*.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 0 binary64) n)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 n (PI.f64)))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 n (PI.f64)))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)) (*.f64 n (PI.f64)))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n)) (*.f64 n (PI.f64)))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n) (*.f64 n (PI.f64)))
(fma.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n (PI.f64)) (*.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n (PI.f64))))
(fma.f64 n (PI.f64) (*.f64 n (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 n (PI.f64)))
(-.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) n)))
(-.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (PI.f64)) n)))
(-.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 n) (PI.f64)))
(-.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) #s(literal 2 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)))
(+.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 0 binary64) n)) (*.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 0 binary64) n)))
(+.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))))
(+.f64 (*.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n (PI.f64))) (*.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n (PI.f64))))
(+.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (cosh.f64 (log.f64 (PI.f64)))) (*.f64 (*.f64 n #s(literal 2 binary64)) (sinh.f64 (log.f64 (PI.f64)))))
(+.f64 (cosh.f64 (log.f64 (*.f64 #s(literal 0 binary64) n))) (sinh.f64 (log.f64 (*.f64 #s(literal 0 binary64) n))))
(+.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n #s(literal 2 binary64)))))
(log.f64 (pow.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 0 binary64) n) n)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) (*.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 2 binary64))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) (PI.f64)) (*.f64 (*.f64 n #s(literal 2 binary64)) (*.f64 n #s(literal 2 binary64)))))
(log.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) n) (*.f64 #s(literal 0 binary64) n)))
(log.f64 (pow.f64 (*.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) (exp.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (PI.f64)) n) (pow.f64 (exp.f64 (PI.f64)) n)))
(log.f64 (*.f64 (pow.f64 (exp.f64 (PI.f64)) n) (pow.f64 (exp.f64 (PI.f64)) n)))
(log.f64 (pow.f64 #s(literal 1 binary64) n))

eval42.0ms (0.4%)

Memory
28.6MiB live, 116.5MiB allocated
Compiler

Compiled 7 537 to 1 169 computations (84.5% saved)

prune22.0ms (0.2%)

Memory
14.3MiB live, 61.3MiB allocated
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New31820338
Fresh000
Picked101
Done000
Total31920339
Accuracy
99.9%
Counts
339 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
28.5%
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
99.5%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
72.5%
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
72.5%
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64))))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
72.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
72.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))))
59.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))))
53.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
96.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n)))))
42.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))))
41.2%
(*.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)))))
72.5%
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
96.6%
(*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
50.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/8 binary64)))) k (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)))
50.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k))
99.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
Compiler

Compiled 1 270 to 876 computations (31% saved)

simplify52.0ms (0.5%)

Memory
-40.5MiB live, 60.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 #s(literal 1 binary64) k)
cost-diff0
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
cost-diff0
(pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
cost-diff0
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
cost-diff0
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff0
(sqrt.f64 k)
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff2
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
cost-diff0
(sqrt.f64 k)
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff2
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff4
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
cost-diff0
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
cost-diff0
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
cost-diff0
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
cost-diff0
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
cost-diff0
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
cost-diff0
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
050359
084355
1130339
2190339
3295339
4449339
5656339
6820339
7877339
8899339
9908339
0908339
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.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 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(sqrt.f64 (PI.f64))
(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)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(PI.f64)
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 n (PI.f64))
n
(PI.f64)
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) n)
(*.f64 n #s(literal 2 binary64))
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(*.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)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.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))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.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)))
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(sqrt.f64 (PI.f64))
(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)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(/.f64 (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(PI.f64)
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
n
(PI.f64)
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

localize144.0ms (1.3%)

Memory
39.5MiB live, 323.0MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.20126761869777615
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy0.203125
(*.f64 n (PI.f64))
accuracy0.3834762695368841
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
accuracy16.468349061674505
(PI.f64)
accuracy0.19140625
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy0.34603500976844204
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy0.3984375
(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy16.468349061674505
(PI.f64)
accuracy0.21712875976844204
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
accuracy0.2232732627809995
(pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy0.734375
(sqrt.f64 (PI.f64))
accuracy16.468349061674505
(PI.f64)
accuracy0.29916000976844204
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
accuracy7.143489998520762
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy16.468349061674505
(PI.f64)
accuracy20.809547139878784
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
accuracy0.1328125
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy0.203125
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy0.2232732627809995
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy16.468349061674505
(PI.f64)
Samples
81.0ms188×0valid
32.0ms68×0exit
Compiler

Compiled 338 to 46 computations (86.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 88.0ms
ival-pow: 36.0ms (40.9% of total)
ival-mult: 29.0ms (33% of total)
ival-sqrt: 10.0ms (11.4% of total)
ival-div: 8.0ms (9.1% of total)
ival-pi: 1.0ms (1.1% of total)
ival-add: 1.0ms (1.1% of total)
ival-sub: 1.0ms (1.1% of total)
exact: 1.0ms (1.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series326.0ms (2.9%)

Memory
1.2MiB live, 508.1MiB allocated
Counts
24 → 93
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(pow.f64 #s(literal 2 binary64) (/.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 binary64) k)
(PI.f64)
(sqrt.f64 (PI.f64))
(pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 n (PI.f64))
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* 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)
(/ (+ (* 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)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* 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)))
(+ (* 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)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ 1 k))
(sqrt k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2))))))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))) (* k (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2))))))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt 2)
(+ (sqrt 2) (* -1/2 (* k (* (log 2) (sqrt 2)))))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2)))))))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* k (+ (* -1/48 (* k (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2))))))))
1/2
(+ 1/2 (* -1/2 k))
1
(+ 1 (* -1 k))
(sqrt (PI))
(+ (sqrt (PI)) (* -1/2 (* (* k (log (PI))) (sqrt (PI)))))
(+ (sqrt (PI)) (* k (+ (* -1/2 (* (sqrt (PI)) (log (PI)))) (* 1/8 (* (* k (pow (log (PI)) 2)) (sqrt (PI)))))))
(+ (sqrt (PI)) (* k (+ (* -1/2 (* (sqrt (PI)) (log (PI)))) (* k (+ (* -1/48 (* (* k (pow (log (PI)) 3)) (sqrt (PI)))) (* 1/8 (* (sqrt (PI)) (pow (log (PI)) 2))))))))
(sqrt (* n (PI)))
(+ (sqrt (* n (PI))) (* -1/2 (* (* k (log (* n (PI)))) (sqrt (* n (PI))))))
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* 1/8 (* (* k (pow (log (* n (PI))) 2)) (sqrt (* n (PI))))))))
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* k (+ (* -1/48 (* (* k (pow (log (* n (PI))) 3)) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (pow (log (* n (PI))) 2))))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 n)) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 n)) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (log (* n (PI))) (- 1 k))))))
(exp (* 1/2 (* (log 2) (- 1 k))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* -1 k)
(* k (- (/ 1 k) 1))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (PI)) (- 1 k))))
(exp (* 1/2 (* (log (* n (PI))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 n)) (+ 1 (* -1 k)))))))
(* (exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 n)) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (* (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))))
(exp (* 1/2 (* (log 2) (+ 1 (* -1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1 (/ 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k))))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* n (PI))
(exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k))))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
Calls

6 calls:

TimeVariablePointExpression
88.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow k -1/2))) (pow 2 (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2)))
85.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow k -1/2))) (pow 2 (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2)))
75.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow k -1/2))) (pow 2 (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2)))
46.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow k -1/2))) (pow 2 (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2)))
25.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow k -1/2))) (pow 2 (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2)))

simplify193.0ms (1.7%)

Memory
15.9MiB live, 249.8MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04222411
115572173
269312128
084512030
Stop Event
iter limit
node limit
Counts
93 → 93
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* 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)
(/ (+ (* 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)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* 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)))
(+ (* 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)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ 1 k))
(sqrt k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2))))))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))) (* k (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2))))))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt 2)
(+ (sqrt 2) (* -1/2 (* k (* (log 2) (sqrt 2)))))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2)))))))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* k (+ (* -1/48 (* k (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2))))))))
1/2
(+ 1/2 (* -1/2 k))
1
(+ 1 (* -1 k))
(sqrt (PI))
(+ (sqrt (PI)) (* -1/2 (* (* k (log (PI))) (sqrt (PI)))))
(+ (sqrt (PI)) (* k (+ (* -1/2 (* (sqrt (PI)) (log (PI)))) (* 1/8 (* (* k (pow (log (PI)) 2)) (sqrt (PI)))))))
(+ (sqrt (PI)) (* k (+ (* -1/2 (* (sqrt (PI)) (log (PI)))) (* k (+ (* -1/48 (* (* k (pow (log (PI)) 3)) (sqrt (PI)))) (* 1/8 (* (sqrt (PI)) (pow (log (PI)) 2))))))))
(sqrt (* n (PI)))
(+ (sqrt (* n (PI))) (* -1/2 (* (* k (log (* n (PI)))) (sqrt (* n (PI))))))
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* 1/8 (* (* k (pow (log (* n (PI))) 2)) (sqrt (* n (PI))))))))
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* k (+ (* -1/48 (* (* k (pow (log (* n (PI))) 3)) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (pow (log (* n (PI))) 2))))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 n)) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 n)) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (log (* n (PI))) (- 1 k))))))
(exp (* 1/2 (* (log 2) (- 1 k))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
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(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
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(* (exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 n)) (+ 1 (* -1 k))))))
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(* 2 (* n (PI)))
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(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k)))))
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(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* n (PI))
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(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k))))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* 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)
(/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* 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)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))) k (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 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)))
(fma.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (*.f64 k (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 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)))
(fma.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 k k) (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/48 binary64)) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2))))))) k)
(/.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (log.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (fma.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/48 binary64)) (fma.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (log.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) k (*.f64 (*.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (log.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) (fma.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))))) k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))) (* k (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2))))))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (log.f64 (PI.f64))) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (fma.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/48 binary64)) (fma.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) k))) k (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) (fma.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))))) k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k)
(/.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (fma.f64 (pow.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/48 binary64)) (fma.f64 (pow.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) k (*.f64 (*.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -1/2 (* k (* (log 2) (sqrt 2)))))
(fma.f64 (*.f64 k (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2)))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) k)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)))) k (sqrt.f64 #s(literal 2 binary64)))
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1/2
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(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
1
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(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k))))))
(*.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) (*.f64 (+.f64 (log.f64 n) (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k)))))
(pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) (*.f64 (+.f64 (log.f64 n) (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))))
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(* n (PI))
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rewrite223.0ms (2%)

Memory
-13.4MiB live, 317.1MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
050252
084221
1258208
21212208
08196208
Stop Event
iter limit
node limit
iter limit
Counts
24 → 1 089
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
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(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
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(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(pow.f64 #s(literal 2 binary64) (/.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 binary64) k)
(PI.f64)
(sqrt.f64 (PI.f64))
(pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 n (PI.f64))
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))) (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))))
(*.f64 (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(pow.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k))
(neg.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.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 (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))))
(*.f64 (exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(*.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 n (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 n (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
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(sqrt.f64 (exp.f64 (*.f64 (log.f64 (PI.f64)) (-.f64 #s(literal 1 binary64) k))))
(fabs.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (*.f64 (log.f64 (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(exp.f64 (fma.f64 (log.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) (*.f64 (log.f64 (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) (*.f64 (log.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(exp.f64 (*.f64 (log.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(exp.f64 (*.f64 (log.f64 (PI.f64)) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64))))
(exp.f64 (*.f64 (log.f64 (PI.f64)) (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (neg.f64 (neg.f64 n)) (PI.f64))
(*.f64 (exp.f64 (log.f64 n)) (PI.f64))
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (neg.f64 n) (neg.f64 (PI.f64)))
(*.f64 (neg.f64 (PI.f64)) (neg.f64 n))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 (PI.f64) (neg.f64 (neg.f64 n)))
(*.f64 (PI.f64) (exp.f64 (log.f64 n)))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(neg.f64 (*.f64 (neg.f64 n) (PI.f64)))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(+.f64 (cosh.f64 (log.f64 (*.f64 (PI.f64) n))) (sinh.f64 (log.f64 (*.f64 (PI.f64) n))))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
(*.f64 (pow.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (pow.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64))))
(*.f64 (pow.f64 (*.f64 n (sqrt.f64 (PI.f64))) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (pow.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64))) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64))))
(*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64))))
(*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (exp.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64)))
(pow.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(pow.f64 (*.f64 (PI.f64) n) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64)))
(pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) (*.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))) (-.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (-.f64 (*.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) (*.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))))))
(/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
(sqrt.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))))
(fabs.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(exp.f64 (fma.f64 (log.f64 n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (*.f64 (log.f64 n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))

eval183.0ms (1.7%)

Memory
19.4MiB live, 343.3MiB allocated
Compiler

Compiled 45 005 to 5 178 computations (88.5% saved)

prune36.0ms (0.3%)

Memory
14.0MiB live, 107.3MiB allocated
Pruning

18 alts after pruning (16 fresh and 2 done)

PrunedKeptTotal
New1 385141 399
Fresh13215
Picked325
Done000
Total1 401181 419
Accuracy
100.0%
Counts
1 419 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
28.5%
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
99.7%
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
41.2%
(*.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)))))
99.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
41.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
99.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
99.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
99.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
99.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k))))
72.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
30.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
30.3%
#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 980 to 757 computations (22.8% saved)

simplify41.0ms (0.4%)

Memory
-19.3MiB live, 47.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
cost-diff0
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
cost-diff2
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64))
cost-diff0
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))
cost-diff2
(*.f64 #s(literal 0 binary64) n)
cost-diff3
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
cost-diff6
(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))
cost-diff0
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))
cost-diff0
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
cost-diff0
(/.f64 (*.f64 (PI.f64) n) k)
cost-diff0
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
cost-diff0
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
cost-diff0
#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))))
cost-diff0
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k)
cost-diff0
(*.f64 (pow.f64 (pow.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)))))
cost-diff0
(*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k)))
cost-diff0
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
048342
077317
1120311
2181311
3267311
4320311
5381311
6493311
7722311
8867311
9923311
10953311
0953311
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (pow.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)))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k)
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #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(literal -1/2 binary64)
k
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 k)
k
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))
(*.f64 #s(literal 0 binary64) n)
#s(literal 0 binary64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
#s(literal 8 binary64)
(sqrt.f64 k)
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 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(literal 1 binary64)
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64)))
(/.f64 k #s(literal 2 binary64))
k
(sqrt.f64 k)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64)) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64)) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(*.f64 (pow.f64 (pow.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)))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64)) k))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k)
(pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64)) k)
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(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 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 k)
k
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
#s(literal 0 binary64)
(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))
#s(literal 0 binary64)
(*.f64 #s(literal 0 binary64) n)
#s(literal 0 binary64)
#s(literal 0 binary64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
#s(literal 8 binary64)
(sqrt.f64 k)
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
#s(literal 1 binary64)
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64)))
(/.f64 k #s(literal 2 binary64))
k
(sqrt.f64 k)

localize174.0ms (1.6%)

Memory
-9.1MiB live, 313.8MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.04296875
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
accuracy0.11328125
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy0.16796875
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
accuracy35.842877369526924
(PI.f64)
accuracy0.0
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))
accuracy0.0
(-.f64 #s(literal 1 binary64) k)
accuracy0.0
(*.f64 #s(literal 0 binary64) n)
accuracy0.0
(sqrt.f64 k)
accuracy0.1171875
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
accuracy0.17806625976844204
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))
accuracy1.4354895321793715
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
accuracy35.842877369526924
(PI.f64)
accuracy0.11328125
(*.f64 (PI.f64) n)
accuracy1.4354895321793715
#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))))
accuracy7.100240972503172
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
accuracy35.842877369526924
(PI.f64)
accuracy0.0625
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64))
accuracy0.11328125
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy0.1328125
(*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k)))
accuracy35.842877369526924
(PI.f64)
Samples
63.0ms108×0valid
57.0ms148×0invalid
Compiler

Compiled 302 to 44 computations (85.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 96.0ms
ival-div: 36.0ms (37.5% of total)
ival-pow: 25.0ms (26.1% of total)
ival-mult: 21.0ms (21.9% of total)
ival-sqrt: 11.0ms (11.5% of total)
ival-pi: 1.0ms (1% of total)
ival-sub: 1.0ms (1% of total)
exact: 1.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series243.0ms (2.2%)

Memory
36.0MiB live, 275.2MiB allocated
Counts
25 → 96
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (pow.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)))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 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))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
(*.f64 #s(literal 0 binary64) n)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(PI.f64)
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(*.f64 (PI.f64) n)
(sqrt.f64 k)
(-.f64 #s(literal 1 binary64) k)
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* 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)
(/ (+ (* 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)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
1
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))))
(* 2 (/ (* n (PI)) k))
(/ (* n (PI)) k)
(sqrt (/ (* n (PI)) k))
(exp (* 1/8 (+ (log 0) (* 20 (log k)))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))
(/ (+ (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))) k)
(/ (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))))) (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k)
1/8
(+ 1/8 (* -1/8 k))
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt k)
(+ 1 (* -1 k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)
(exp (* 1/8 (* (log 0) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (- 1 k)))))
(* -1/8 k)
(* k (- (* 1/8 (/ 1 k)) 1/8))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* -1 k)
(* k (- (/ 1 k) 1))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(exp (* 1/8 (* (log 0) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (+ 1 (* -1 k))))))
(* -1 (* k (- 1/8 (* 1/8 (/ 1 k)))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* k (- 1 (/ 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n)))))
(exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* 1/8 (* n (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* n (+ (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* n (+ (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))) (* n (+ (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k))))))) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))))
(+ (* 1/8 (* (sqrt (/ 1 k)) (* n (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))))
(+ (* n (+ (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))) (* (sqrt (/ 1 k)) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))))
(+ (* n (+ (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))) (* n (+ (* (sqrt (/ 1 k)) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))))
0
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* n (PI))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)) (+ (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) (pow n 3)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2)))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))))
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))))
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (+ (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2)))))
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (+ (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) (+ (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) (pow n 3))) (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
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(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))) n)) (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))))) n)))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))
(+ (* -1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n))) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))) n)) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
Calls

6 calls:

TimeVariablePointExpression
131.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt k) (- 1 k))
51.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt k) (- 1 k))
39.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt k) (- 1 k))
7.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt k) (- 1 k))
7.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt k) (- 1 k))

simplify236.0ms (2.1%)

Memory
-50.8MiB live, 208.0MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04863741
117743470
080413265
Stop Event
iter limit
node limit
Counts
96 → 96
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* 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)
(/ (+ (* 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)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
1
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
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(* 2 (/ (* n (PI)) k))
(/ (* n (PI)) k)
(sqrt (/ (* n (PI)) k))
(exp (* 1/8 (+ (log 0) (* 20 (log k)))))
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(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))
(/ (+ (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))) k)
(/ (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))))) (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k)
1/8
(+ 1/8 (* -1/8 k))
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt k)
(+ 1 (* -1 k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
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(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)
(exp (* 1/8 (* (log 0) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (- 1 k)))))
(* -1/8 k)
(* k (- (* 1/8 (/ 1 k)) 1/8))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* -1 k)
(* k (- (/ 1 k) 1))
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(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
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(+ (* n (+ (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))) (* n (+ (* (sqrt (/ 1 k)) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))))
0
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* n (PI))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))
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(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2))))
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
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(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* 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)
(/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* 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)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (*.f64 k k) (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) k) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(fma.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k #s(literal 1 binary64))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
(fma.f64 (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))) k #s(literal 1 binary64))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) k) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 3 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) #s(literal 1/2 binary64))) k (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))) k #s(literal 1 binary64))
(* 2 (/ (* n (PI)) k))
(*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(exp (* 1/8 (+ (log 0) (* 20 (log k)))))
(pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))
(fma.f64 (*.f64 k (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))))
(fma.f64 (fma.f64 (*.f64 k (fma.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) #s(literal 2 binary64)) #s(literal 1/2 binary64) (fma.f64 (NAN.f64) #s(literal -1/8 binary64) #s(literal 0 binary64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))) k (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 (NAN.f64) #s(literal -1/8 binary64) #s(literal 0 binary64)) (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) (fma.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) #s(literal 3 binary64)) #s(literal 1/6 binary64) #s(literal 0 binary64))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))))) k (*.f64 (fma.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) #s(literal 2 binary64)) #s(literal 1/2 binary64) (fma.f64 (NAN.f64) #s(literal -1/8 binary64) #s(literal 0 binary64))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))) k (*.f64 (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))) k (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))
(/ (+ (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))) k)
(/.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (sqrt.f64 k))) k)
(/ (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k)
(/.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 k) (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (*.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (fma.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) #s(literal 2 binary64)) #s(literal 1/2 binary64) (fma.f64 (NAN.f64) #s(literal -1/8 binary64) #s(literal 0 binary64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))) k (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (sqrt.f64 k))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))))) (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 k) (fma.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) #s(literal 2 binary64)) #s(literal 1/2 binary64) (fma.f64 (NAN.f64) #s(literal -1/8 binary64) #s(literal 0 binary64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (*.f64 (fma.f64 (fma.f64 (NAN.f64) #s(literal -1/8 binary64) #s(literal 0 binary64)) (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) (fma.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) #s(literal 3 binary64)) #s(literal 1/6 binary64) #s(literal 0 binary64))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))))))) k (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (sqrt.f64 k)) (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))))) k (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (sqrt.f64 k))) k)
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -1/8 k))
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(fma.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (NAN.f64) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))))) (-.f64 #s(literal 1 binary64) k) (/.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (fma.f64 (*.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (NAN.f64) (NAN.f64)) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (NAN.f64)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64)) #s(literal 1/128 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n))) (neg.f64 n))) (neg.f64 n)))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))

rewrite167.0ms (1.5%)

Memory
25.5MiB live, 299.6MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048260
077229
1236201
21045100
0979197
Stop Event
iter limit
node limit
iter limit
Counts
25 → 1 278
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (pow.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)))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 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))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
(*.f64 #s(literal 0 binary64) n)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(PI.f64)
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(*.f64 (PI.f64) n)
(sqrt.f64 k)
(-.f64 #s(literal 1 binary64) k)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n))) #s(literal 0 binary64))
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) #s(literal 0 binary64))
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 n (*.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n))) #s(literal 0 binary64))
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 n)) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 n)) #s(literal 0 binary64))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) #s(literal 1 binary64)) #s(literal 0 binary64))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n))) #s(literal 0 binary64))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 #s(literal 0 binary64) (pow.f64 (pow.f64 n #s(literal -1/2 binary64)) k)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (*.f64 #s(literal 0 binary64) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) k)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) k))
(*.f64 (*.f64 #s(literal 0 binary64) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) k))
(*.f64 (*.f64 #s(literal 0 binary64) (pow.f64 n (*.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (*.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (*.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(*.f64 (*.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (*.f64 (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) #s(literal 0 binary64)) (*.f64 (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) #s(literal 0 binary64)))
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) k) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) k) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)))))
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) k) #s(literal 1/4 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) k) #s(literal 1/4 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (*.f64 (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 (/.f64 #s(literal 0 binary64) k) #s(literal 1/4 binary64))) (*.f64 (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 (/.f64 #s(literal 0 binary64) k) #s(literal 1/4 binary64))))
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 (/.f64 #s(literal 0 binary64) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 (/.f64 #s(literal 0 binary64) k) #s(literal 1/4 binary64))))
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 (/.f64 #s(literal 0 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (/.f64 #s(literal 0 binary64) k) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 2 binary64))) (pow.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 #s(literal 0 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (/.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 0 binary64) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 0 binary64) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal 0 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 (*.f64 #s(literal 2 binary64) n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
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(*.f64 (*.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (neg.f64 (neg.f64 n)) (PI.f64))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (neg.f64 n) (neg.f64 (PI.f64)))
(*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) n)))
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) n))
(*.f64 (neg.f64 (PI.f64)) (neg.f64 n))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(*.f64 (PI.f64) (neg.f64 (neg.f64 n)))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(neg.f64 (*.f64 (neg.f64 n) (PI.f64)))
(fma.f64 (cosh.f64 (log.f64 (PI.f64))) n (*.f64 (sinh.f64 (log.f64 (PI.f64))) n))
(fma.f64 n (cosh.f64 (log.f64 (PI.f64))) (*.f64 n (sinh.f64 (log.f64 (PI.f64)))))
(+.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) n) (*.f64 (sinh.f64 (log.f64 (PI.f64))) n))
(+.f64 (*.f64 n (cosh.f64 (log.f64 (PI.f64)))) (*.f64 n (sinh.f64 (log.f64 (PI.f64)))))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(*.f64 (neg.f64 (pow.f64 k #s(literal 1/4 binary64))) (neg.f64 (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 k #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 k) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 k))
(pow.f64 (exp.f64 (log.f64 k)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 k k) #s(literal 1/4 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(neg.f64 (neg.f64 (sqrt.f64 k)))
(sqrt.f64 k)
(exp.f64 (log.f64 (sqrt.f64 k)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 k))) (sinh.f64 (log.f64 (sqrt.f64 k))))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))))) (+.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))) (+.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64)))))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k))) (neg.f64 (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k))) (+.f64 k #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))))) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))) (*.f64 (+.f64 k #s(literal 1 binary64)) (*.f64 k k))) (*.f64 (+.f64 k #s(literal 1 binary64)) (+.f64 k #s(literal 1 binary64))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k)) (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (neg.f64 (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 k #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (neg.f64 (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)))
(-.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))))
(-.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 k) k) (+.f64 k #s(literal 1 binary64))))
(+.f64 #s(literal 1 binary64) (neg.f64 k))

eval260.0ms (2.4%)

Memory
-14.1MiB live, 462.3MiB allocated
Compiler

Compiled 48 800 to 5 836 computations (88% saved)

prune66.0ms (0.6%)

Memory
0.0MiB live, 150.0MiB allocated
Pruning

26 alts after pruning (21 fresh and 5 done)

PrunedKeptTotal
New1 586121 598
Fresh2911
Picked235
Done022
Total1 590261 616
Accuracy
100.0%
Counts
1 616 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.7%
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
28.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
99.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
41.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
99.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
99.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
99.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
72.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
99.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
41.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
30.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
30.3%
#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))))
30.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
4.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
4.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64))))
30.3%
#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))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
75.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (*.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) k) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))))
32.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
Compiler

Compiled 1 451 to 1 113 computations (23.3% saved)

simplify54.0ms (0.5%)

Memory
12.8MiB live, 56.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.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))))
cost-diff0
(sqrt.f64 k)
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff2
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
cost-diff0
(*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))
cost-diff0
(sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))
cost-diff0
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
cost-diff4
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
cost-diff0
(*.f64 (PI.f64) #s(literal 2 binary64))
cost-diff0
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff0
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
cost-diff0
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
cost-diff0
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
cost-diff0
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k)
cost-diff0
(*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
cost-diff0
(*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
cost-diff0
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
056413
088409
1128383
2185383
3364383
4677383
51150383
61535383
71750383
81867383
91870383
101870383
01870383
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k)
#s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))
#s(literal 1 binary64)
(*.f64 n (PI.f64))
n
(PI.f64)
k
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(sqrt.f64 (/.f64 n k))
(/.f64 n k)
n
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k)
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 n (sqrt.f64 (PI.f64)))
n
(sqrt.f64 (PI.f64))
(PI.f64)
k
#s(literal 2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.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)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal -2 binary64)
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) k)))
(*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) k))
(*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) k))
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k)
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) k)
#s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
#s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
#s(literal 1 binary64)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
n
(PI.f64)
k
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 (PI.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 (PI.f64) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(sqrt.f64 (/.f64 n k))
(/.f64 n k)
n
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))
(*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k)
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (PI.f64) n)
(*.f64 n (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) n)
n
(sqrt.f64 (PI.f64))
(PI.f64)
k
#s(literal 2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(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 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal -2 binary64)

localize179.0ms (1.6%)

Memory
3.0MiB live, 233.3MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy0.19140625
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy0.203125
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy0.22500860515192628
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))
accuracy16.468349061674505
(PI.f64)
accuracy0.734375
(sqrt.f64 (PI.f64))
accuracy7.139303472503172
(sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))
accuracy16.468349061674505
(PI.f64)
accuracy20.809547139878784
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
accuracy0.734375
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy7.140029582818521
(sqrt.f64 (/.f64 n k))
accuracy16.468349061674505
(PI.f64)
accuracy20.809547139878784
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
accuracy26.786522553618177
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
accuracy0.203125
(*.f64 n (PI.f64))
accuracy0.21875
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))
accuracy0.3756637695368841
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
accuracy16.468349061674505
(PI.f64)
Samples
108.0ms188×0valid
32.0ms68×0exit
Compiler

Compiled 318 to 47 computations (85.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 84.0ms
ival-mult: 29.0ms (34.6% of total)
ival-sqrt: 20.0ms (23.9% of total)
ival-pow: 18.0ms (21.5% of total)
ival-div: 13.0ms (15.5% of total)
ival-pi: 1.0ms (1.2% of total)
ival-sub: 1.0ms (1.2% of total)
exact: 1.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series140.0ms (1.3%)

Memory
12.6MiB live, 201.2MiB allocated
Counts
25 → 72
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(/.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))))
(PI.f64)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(sqrt.f64 (/.f64 n k))
(sqrt.f64 (PI.f64))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* 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)
(/ (+ (* 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)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
1
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))))
(* 2 (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))
(+ (* -1/2 (* (/ (* k (log (* 2 (* n (PI))))) (sqrt 1/2)) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(+ (* k (- (* -1 (* k (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(sqrt (/ n k))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n)))))
(* n (PI))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(/ 1 (* n (PI)))
(exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
Calls

6 calls:

TimeVariablePointExpression
62.0ms
n
@inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (* n (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2)) (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2))) (PI) (* (sqrt 1/2) (sqrt (/ 1 (* n (PI))))) (/ 1 (* n (PI))) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (pow (* n (* (PI) 2)) (/ (- 1 k) -2)) (* n (* (PI) 2)))
25.0ms
k
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (* n (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2)) (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2))) (PI) (* (sqrt 1/2) (sqrt (/ 1 (* n (PI))))) (/ 1 (* n (PI))) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (pow (* n (* (PI) 2)) (/ (- 1 k) -2)) (* n (* (PI) 2)))
24.0ms
n
@-inf
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (* n (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2)) (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2))) (PI) (* (sqrt 1/2) (sqrt (/ 1 (* n (PI))))) (/ 1 (* n (PI))) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (pow (* n (* (PI) 2)) (/ (- 1 k) -2)) (* n (* (PI) 2)))
18.0ms
n
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (* n (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2)) (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2))) (PI) (* (sqrt 1/2) (sqrt (/ 1 (* n (PI))))) (/ 1 (* n (PI))) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (pow (* n (* (PI) 2)) (/ (- 1 k) -2)) (* n (* (PI) 2)))
5.0ms
k
@0
((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (* n (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2)) (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2))) (PI) (* (sqrt 1/2) (sqrt (/ 1 (* n (PI))))) (/ 1 (* n (PI))) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (pow (* n (* (PI) 2)) (/ (- 1 k) -2)) (* n (* (PI) 2)))

simplify149.0ms (1.3%)

Memory
-20.6MiB live, 176.9MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03131853
110841765
243921724
081241680
Stop Event
iter limit
node limit
Counts
72 → 72
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* 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)
(/ (+ (* 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)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
1
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))))
(* 2 (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))
(+ (* -1/2 (* (/ (* k (log (* 2 (* n (PI))))) (sqrt 1/2)) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(+ (* k (- (* -1 (* k (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(sqrt (/ n k))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
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(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n)))))
(* n (PI))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(/ 1 (* n (PI)))
(exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* 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)
(/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* 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)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))) k (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (*.f64 k k) (fma.f64 (*.f64 #s(literal 1/6 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 3 binary64))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(fma.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k #s(literal 1 binary64))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))) k #s(literal 1 binary64))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) k) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 3 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) #s(literal 1/2 binary64))) k (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))) k #s(literal 1 binary64))
(* 2 (/ (* n (PI)) k))
(*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (/.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (sqrt.f64 #s(literal 1/2 binary64))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64))) (/.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (/.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (*.f64 (*.f64 (sqrt.f64 k) #s(literal 1/8 binary64)) (*.f64 (/.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64)))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))) k)
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
(* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1/2 (* (/ (* k (log (* 2 (* n (PI))))) (sqrt 1/2)) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) k) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* k (- (* -1 (* k (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(fma.f64 (fma.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64))) (/.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) (/.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) k (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (/.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))) k (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (/.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) k (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) (/.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) k (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt (/ n k))
(sqrt.f64 (/.f64 n k))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(fma.f64 (*.f64 k #s(literal 1/8 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) k) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (*.f64 k k) (fma.f64 (*.f64 #s(literal 1/48 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) (*.f64 (*.f64 k (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) #s(literal 1/8 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) k) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)
(pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) k)
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))))
(*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))) (pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) k))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64)))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 n k)))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(*.f64 (*.f64 (pow.f64 n (neg.f64 k)) (pow.f64 (*.f64 (sqrt.f64 (/.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(*.f64 (*.f64 (pow.f64 n (neg.f64 k)) (pow.f64 (*.f64 (sqrt.f64 (/.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n)))))
(*.f64 (pow.f64 n (neg.f64 k)) (pow.f64 (*.f64 (sqrt.f64 (/.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) k))
(* n (PI))
(*.f64 n (PI.f64))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))
(/ 1 (* n (PI)))
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))
(exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k)))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))
(exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(*.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) k))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(*.f64 (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) k))
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) k)
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(* (sqrt (/ 1 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 n k)) #s(literal 1 binary64))
(exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))

rewrite199.0ms (1.8%)

Memory
39.5MiB live, 277.9MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
056320
088294
1243270
21068266
08478266
Stop Event
iter limit
node limit
iter limit
Counts
25 → 1 490
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(/.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))))
(PI.f64)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(sqrt.f64 (/.f64 n k))
(sqrt.f64 (PI.f64))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 n)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)))) (neg.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)))) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 n))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) (*.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (pow.f64 k #s(literal 1/4 binary64))))
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(/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))))
(sqrt.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (neg.f64 (-.f64 #s(literal 1 binary64) k)))))
(fabs.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))
(exp.f64 (fma.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -4 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 (cosh.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal -2 binary64)))) (/.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal -2 binary64)))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) (sinh.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 (*.f64 n #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 n (cbrt.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (exp.f64 (log.f64 n)))
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (PI.f64)) n))
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))) n))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 (cbrt.f64 (PI.f64)) n (*.f64 (cbrt.f64 (PI.f64)) n)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) n))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 n #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (cbrt.f64 (PI.f64)) (fma.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n))
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (PI.f64) (*.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 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (-.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)))
(/.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64))) (fma.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n) (-.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)))))
(/.f64 (*.f64 n #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (PI.f64) (PI.f64) #s(literal 0 binary64)))
(fma.f64 (*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))) (*.f64 (PI.f64) n))
(fma.f64 (*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) n))
(fma.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (PI.f64) n))
(fma.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (PI.f64) n))
(fma.f64 (*.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (PI.f64) n))
(fma.f64 (neg.f64 (*.f64 (neg.f64 n) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)) (*.f64 (PI.f64) n))
(fma.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (PI.f64) n))
(fma.f64 (*.f64 n #s(literal 2 binary64)) (cosh.f64 (log.f64 (PI.f64))) (*.f64 (*.f64 n #s(literal 2 binary64)) (sinh.f64 (log.f64 (PI.f64)))))
(fma.f64 (*.f64 #s(literal 2 binary64) n) (cosh.f64 (log.f64 (PI.f64))) (*.f64 (*.f64 #s(literal 2 binary64) n) (sinh.f64 (log.f64 (PI.f64)))))
(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 (PI.f64) n))
(fma.f64 (*.f64 (neg.f64 n) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) n))
(fma.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) n)) (*.f64 (PI.f64) n))
(fma.f64 (neg.f64 (PI.f64)) (neg.f64 n) (*.f64 (PI.f64) n))
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 n) (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) n))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)) (*.f64 (PI.f64) n))
(fma.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64)) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))))
(fma.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) n) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) n)))
(fma.f64 (neg.f64 n) (neg.f64 (PI.f64)) (*.f64 (PI.f64) n))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 (PI.f64) n))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n)) (*.f64 (PI.f64) n))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)) (*.f64 (PI.f64) n))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n) (*.f64 (PI.f64) n))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (*.f64 (PI.f64) n))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64)) (*.f64 (PI.f64) n))
(fma.f64 (sqrt.f64 (PI.f64)) (neg.f64 (*.f64 (neg.f64 n) (sqrt.f64 (PI.f64)))) (*.f64 (PI.f64) n))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(-.f64 (*.f64 (PI.f64) n) (*.f64 (neg.f64 n) (PI.f64)))
(exp.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))
(+.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))))
(+.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) n)) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) n)))
(+.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (cosh.f64 (log.f64 (PI.f64)))) (*.f64 (*.f64 n #s(literal 2 binary64)) (sinh.f64 (log.f64 (PI.f64)))))
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (cosh.f64 (log.f64 (PI.f64)))) (*.f64 (*.f64 #s(literal 2 binary64) n) (sinh.f64 (log.f64 (PI.f64)))))
(+.f64 (cosh.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sinh.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)) n))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) #s(literal 2 binary64)))
(log.f64 (*.f64 (pow.f64 (exp.f64 (PI.f64)) n) (pow.f64 (exp.f64 (PI.f64)) n)))

eval375.0ms (3.4%)

Memory
-19.1MiB live, 490.9MiB allocated
Compiler

Compiled 80 334 to 9 373 computations (88.3% saved)

prune93.0ms (0.8%)

Memory
23.2MiB live, 175.9MiB allocated
Pruning

27 alts after pruning (22 fresh and 5 done)

PrunedKeptTotal
New2 137152 152
Fresh9716
Picked325
Done235
Total2 151272 178
Accuracy
100.0%
Counts
2 178 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
75.2%
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))))
99.7%
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
99.4%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) (sqrt.f64 k)))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))))
99.5%
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.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)))))
28.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
99.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
41.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)))
99.5%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
75.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))))
30.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
41.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64)))))
41.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
41.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
41.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
41.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
30.3%
#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))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))))
30.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
4.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
4.8%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
30.3%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))))
30.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
32.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
Compiler

Compiled 2 538 to 900 computations (64.5% saved)

regimes80.0ms (0.7%)

Memory
0.5MiB live, 145.9MiB allocated
Counts
62 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.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)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (*.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) k) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.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 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k))
(*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 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 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64))))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/8 binary64)))) k (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
Calls

4 calls:

21.0ms
n
21.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
17.0ms
k
Results
AccuracySegmentsBranch
99.8%1k
99.8%1n
99.8%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))))
99.8%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 23 to 23 computations (0% saved)

regimes67.0ms (0.6%)

Memory
-2.3MiB live, 86.8MiB allocated
Counts
45 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.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)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (*.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) k) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
Calls

4 calls:

25.0ms
n
15.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms
k
11.0ms
(*.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
99.8%1k
99.8%1n
99.8%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))))
99.8%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 23 to 23 computations (0% saved)

regimes109.0ms (1%)

Memory
-5.0MiB live, 92.3MiB allocated
Counts
40 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.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)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
Outputs
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
Calls

4 calls:

45.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
40.0ms
n
11.0ms
k
10.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.7%1k
99.7%1n
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 23 to 23 computations (0% saved)

regimes97.0ms (0.9%)

Memory
0.9MiB live, 86.9MiB allocated
Counts
39 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))))
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.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)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
Calls

4 calls:

53.0ms
n
20.0ms
(*.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))))
11.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms
k
Results
AccuracySegmentsBranch
99.5%1k
99.5%1n
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 23 to 23 computations (0% saved)

regimes40.0ms (0.4%)

Memory
-2.2MiB live, 44.2MiB allocated
Counts
29 → 3
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
Calls

4 calls:

13.0ms
k
9.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
9.0ms
n
8.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
74.9%3k
58.5%2n
97.2%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))))
58.5%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 23 to 23 computations (0% saved)

regimes17.0ms (0.2%)

Memory
24.5MiB live, 24.5MiB allocated
Counts
27 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
Calls

2 calls:

8.0ms
k
7.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
70.7%2k
70.8%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 17 to 15 computations (11.8% saved)

regimes25.0ms (0.2%)

Memory
-80.3MiB live, 10.7MiB allocated
Counts
17 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
Calls

1 calls:

24.0ms
(*.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
70.8%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)

regimes4.0ms (0%)

Memory
2.8MiB live, 2.8MiB allocated
Counts
11 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
Calls

1 calls:

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
70.8%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)

regimes7.0ms (0.1%)

Memory
4.8MiB live, 4.8MiB allocated
Counts
9 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#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))))
Calls

2 calls:

3.0ms
k
3.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
59.7%2k
59.8%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 17 to 15 computations (11.8% saved)

regimes6.0ms (0.1%)

Memory
6.1MiB live, 6.1MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
Calls

4 calls:

1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
1.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
k
1.0ms
n
Results
AccuracySegmentsBranch
32.0%1n
32.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
33.8%2k
34.1%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 23 to 23 computations (0% saved)

regimes5.0ms (0%)

Memory
5.8MiB live, 5.8MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
Calls

4 calls:

1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
1.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
n
1.0ms
k
Results
AccuracySegmentsBranch
32.0%1n
32.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
32.0%1k
32.0%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 23 to 23 computations (0% saved)

bsearch1.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
2.0826522937397566e+268
+inf
0.0ms
0.0
9.081821480916652e-125
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
0.0
9.081821480916652e-125
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
0.0
9.081821480916652e-125
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
0.0
9.081821480916652e-125
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
0.0
9.081821480916652e-125
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
0.0
9.081821480916652e-125
Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify26.0ms (0.2%)

Memory
-13.8MiB live, 30.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
098599
1119565
2134565
3155565
4172565
5191565
6225565
7296565
8327565
9360565
10370565
Stop Event
saturated
Calls
Call 1
Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) (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 39999999999999998937528994166409092235100742444912950023748503679485838560977786267761776179074747560605966704919852367606632983360925877640733989572365418529924904538372564282961571672462773168785953956301720167915620487511778795854816831741326539736938915682603499520 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) 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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) 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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #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)))))
(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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal -1 binary64))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64)))))
(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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) (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 39999999999999998937528994166409092235100742444912950023748503679485838560977786267761776179074747560605966704919852367606632983360925877640733989572365418529924904538372564282961571672462773168785953956301720167915620487511778795854816831741326539736938915682603499520 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) (if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 39999999999999998937528994166409092235100742444912950023748503679485838560977786267761776179074747560605966704919852367606632983360925877640733989572365418529924904538372564282961571672462773168785953956301720167915620487511778795854816831741326539736938915682603499520 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64))))))
(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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) 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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) 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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #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)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #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)))))
(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 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))

soundness1.5s (13.2%)

Memory
45.4MiB live, 1 143.8MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
056320
088294
1243270
21068266
08478266
0120502
1378489
21377453
34131453
08166441
04863741
117743470
080413265
01338
02238
18335
244635
3400729
0892129
050252
084221
1258208
21212208
08196208
048260
077229
1236201
21045100
0979197
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 1 366 to 738 computations (46% saved)

preprocess66.0ms (0.6%)

Memory
0.5MiB live, 93.6MiB allocated
Compiler

Compiled 1 230 to 230 computations (81.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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