Migdal et al, Equation (51)

Time bar (total: 10.0s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze112.0ms (1.1%)

Memory
31.4MiB live, 173.3MiB 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)

sample4.0s (40.3%)

Memory
-5.1MiB live, 4 855.1MiB allocated
Samples
1.8s8 256×0valid
842.0ms3 484×1invalid
403.0ms1 893×1exit
183.0ms446×2invalid
76.0ms499×0invalid
51.0ms201×0exit
Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-pow: 1.0s (40.8% of total)
ival-mult: 486.0ms (19% of total)
ival-div: 322.0ms (12.6% of total)
adjust: 225.0ms (8.8% of total)
ival-sqrt: 195.0ms (7.6% of total)
ival-sub: 160.0ms (6.2% of total)
ival-pi: 96.0ms (3.7% of total)
exact: 17.0ms (0.7% of total)
ival-true: 13.0ms (0.5% of total)
ival-assert: 6.0ms (0.2% of total)
Bogosity

explain160.0ms (1.6%)

Memory
-23.1MiB live, 354.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
194(6.747429450425676e-40 1.9117795040633735e+278)1(5.3992085673560354e-14 8.311256218367836e+75)(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)))sensitivity9434
Confusion
Predicted +Predicted -
+01
-94161
Precision
0.0
Recall
0.0
Confusion?
Predicted +Predicted MaybePredicted -
+010
-9433128
Precision?
0.0078125
Recall?
1.0
Freqs
test
numberfreq
0162
194
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
67.0ms512×0valid
Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 49.0ms
ival-div: 14.0ms (28.5% of total)
ival-mult: 14.0ms (28.5% of total)
ival-pow: 10.0ms (20.3% of total)
ival-sub: 4.0ms (8.1% of total)
ival-sqrt: 4.0ms (8.1% of total)
ival-pi: 2.0ms (4.1% of total)
exact: 1.0ms (2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess34.0ms (0.3%)

Memory
18.5MiB live, 63.6MiB 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
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.1MiB live, 1.1MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(*.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
16.7MiB live, 16.7MiB 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)

localize46.0ms (0.5%)

Memory
-4.0MiB live, 86.1MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.10282003162065376
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy0.1953125
(*.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))))
accuracy0.24609375
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy0.2578125
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Samples
37.0ms256×0valid
Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-pow: 11.0ms (46% of total)
ival-mult: 4.0ms (16.7% of total)
ival-div: 3.0ms (12.5% of total)
ival-sqrt: 2.0ms (8.4% of total)
ival-pi: 1.0ms (4.2% of total)
ival-sub: 1.0ms (4.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series74.0ms (0.7%)

Memory
-8.2MiB live, 145.1MiB 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
35.0ms
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))
8.0ms
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))

simplify125.0ms (1.2%)

Memory
19.2MiB live, 206.5MiB 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))))

rewrite267.0ms (2.7%)

Memory
-23.9MiB live, 266.6MiB 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)))
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(*.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))))
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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))

eval48.0ms (0.5%)

Memory
16.5MiB live, 62.6MiB allocated
Compiler

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

prune39.0ms (0.4%)

Memory
-14.7MiB live, 31.2MiB allocated
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New32612338
Fresh000
Picked101
Done000
Total32712339
Accuracy
100.0%
Counts
339 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
29.1%
(/.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 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%
(*.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))))
72.6%
(*.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)))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%
(*.f64 (/.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))))
99.6%
(*.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)))))
55.5%
(*.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)))))
54.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
60.4%
#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))
99.6%
#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))))
40.0%
#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 586 to 468 computations (20.1% saved)

simplify185.0ms (1.8%)

Memory
10.5MiB live, 56.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
#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))))
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)) #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)))))
cost-diff0
#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))))
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)) #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)))))
cost-diff1
(/.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-diff5
(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))
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
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
cost-diff0
(pow.f64 k #s(literal -1/2 binary64))
cost-diff0
(*.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))))
cost-diff1
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
051383
085364
1132358
2186358
3340358
4733358
51634348
62657348
73184348
83592348
93764348
103784348
113810348
123837348
133900348
143929348
153942348
163942348
173942348
183942348
194055348
204263348
214263348
04263347
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.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))))
(pow.f64 k #s(literal -1/2 binary64))
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 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.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 (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 #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 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
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))))
(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)
#s(literal 1/2 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)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
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))))
(*.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 (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)))
(fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k)
(log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
#s(literal -1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
Outputs
(*.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))))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 k #s(literal -1/2 binary64))
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)))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.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))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(-.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 n (PI.f64)) 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 n (PI.f64)) 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))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(PI.f64)
n
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))
(fma.f64 #s(literal -1/8 binary64) k #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
#s(literal 8 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 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
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))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (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 (*.f64 n #s(literal 2 binary64)) (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 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.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)
#s(literal 1/2 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)))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
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 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64))))
(*.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 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))
(*.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)))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64))
(*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k)
(*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)
(log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))
(log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
(*.f64 n #s(literal 2 binary64))
#s(literal 2 binary64)
n
(PI.f64)
#s(literal -1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 (PI.f64) n))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))

localize218.0ms (2.2%)

Memory
-28.3MiB live, 171.5MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.140625
(*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k)
accuracy0.19140625
(*.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)))))
accuracy0.265625
(*.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)))
accuracy28.335247650234145
(PI.f64)
accuracy0.12109375
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy0.140625
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy0.19140625
(*.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)))))
accuracy28.335247650234145
(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)
accuracy0.12109375
(*.f64 (PI.f64) n)
accuracy0.232753759768442
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
accuracy9.695031462608759
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy28.335247650234145
(PI.f64)
accuracy0.09891378162065376
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy0.12109375
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy0.19140625
(*.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))))
accuracy28.335247650234145
(PI.f64)
Samples
66.0ms117×0invalid
58.0ms139×0valid
Compiler

Compiled 318 to 42 computations (86.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 73.0ms
ival-div: 20.0ms (27.6% of total)
ival-mult: 19.0ms (26.2% of total)
ival-pow: 18.0ms (24.8% of total)
ival-sqrt: 6.0ms (8.3% of total)
ival-add: 3.0ms (4.1% of total)
ival-log: 3.0ms (4.1% of total)
ival-pi: 1.0ms (1.4% of total)
ival-sub: 1.0ms (1.4% of total)
exact: 1.0ms (1.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series131.0ms (1.3%)

Memory
37.1MiB live, 134.5MiB allocated
Counts
25 → 92
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.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))))
(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 (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))
(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 (/.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 #s(literal 1 binary64) (sqrt.f64 k))
(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)) #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 (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))))
(PI.f64)
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 (PI.f64) n)
(-.f64 #s(literal 1 binary64) k)
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.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 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k)
Outputs
1/2
(+ 1/2 (* -1/2 k))
(* (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 (* 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))
(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))
(sqrt k)
1
(+ 1 (* -1 k))
(* k (log (* 2 (* n (PI)))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 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))
(* -1 k)
(* k (- (/ 1 k) 1))
(* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI)))))
(* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (/ (sqrt 2) k) (sqrt (* n (PI))))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -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)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(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))))
(* -1 (* k (+ (* -1 (* (/ (sqrt 2) k) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(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
(* 2 (* n (PI)))
(* n (PI))
(* (sqrt (* n (PI))) (* (sqrt 2) (+ 1 (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* k (+ (log n) (log (* 2 (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))))
(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))))))
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(* (sqrt (* n (PI))) (* (sqrt 2) (+ 1 (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))
(* (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))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(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)))
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(+ (* -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))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ 1 (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
(* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))
Calls

6 calls:

TimeVariablePointExpression
45.0ms
k
@inf
((/ (- 1 k) 2) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (* 2 (PI)) n) (* (PI) n) (- 1 k) (* (* 2 n) (PI)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (* (log (* (* 2 n) (PI))) k))
26.0ms
k
@0
((/ (- 1 k) 2) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (* 2 (PI)) n) (* (PI) n) (- 1 k) (* (* 2 n) (PI)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (* (log (* (* 2 n) (PI))) k))
21.0ms
n
@0
((/ (- 1 k) 2) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (* 2 (PI)) n) (* (PI) n) (- 1 k) (* (* 2 n) (PI)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (* (log (* (* 2 n) (PI))) k))
12.0ms
n
@-inf
((/ (- 1 k) 2) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (* 2 (PI)) n) (* (PI) n) (- 1 k) (* (* 2 n) (PI)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (* (log (* (* 2 n) (PI))) k))
12.0ms
k
@-inf
((/ (- 1 k) 2) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (* 2 (PI)) n) (* (PI) n) (- 1 k) (* (* 2 n) (PI)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (* (log (* (* 2 n) (PI))) k))

simplify199.0ms (2%)

Memory
-32.1MiB live, 154.7MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04003260
114572974
271752791
080282677
Stop Event
iter limit
node limit
Counts
92 → 92
Calls
Call 1
Inputs
1/2
(+ 1/2 (* -1/2 k))
(* (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 (* n (PI))) (sqrt 2))
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(* (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)
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(/ (+ (* 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))
(sqrt k)
1
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(* -1/8 k)
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0
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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))))
(+ (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))) (* (sqrt 2) (+ 1 (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))
(* (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))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(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 (/ (+ (* -1 (/ (* (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)))
(+ (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))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ 1 (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
(* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))
Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 k))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(* (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 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #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 (PI.f64) n) 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)
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(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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(* (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 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 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 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(+ (* 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 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 k k) (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(exp (* 1/8 (+ (log 0) (* 20 (log k)))))
(*.f64 (pow.f64 k #s(literal 5/2 binary64)) #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)))) (*.f64 (pow.f64 k #s(literal 5/2 binary64)) #s(literal 0 binary64)) (*.f64 (pow.f64 k #s(literal 5/2 binary64)) #s(literal 0 binary64)))
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(* (sqrt (/ 1 k)) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))
(*.f64 (*.f64 (pow.f64 k #s(literal 5/2 binary64)) #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
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(/ (+ (* 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)
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(/ (+ (* 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)
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1/8
#s(literal 1/8 binary64)
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1
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(+ (* 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)))))
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(+ (* 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))))))
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(* (sqrt (* n (PI))) (* (sqrt 2) (+ 1 (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
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(* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))
(*.f64 (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) 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)))
(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)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1 binary64))
(exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 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)))
(+ (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)))
(fma.f64 (*.f64 (*.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 (NAN.f64) n)) #s(literal -1/8 binary64) (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))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (* (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)))
(-.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 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.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))) (NAN.f64) (*.f64 (neg.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 (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))) n))) n))
(+ (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)))
(-.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 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.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))) (NAN.f64))) (-.f64 #s(literal 1 binary64) k) (/.f64 (fma.f64 (neg.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 (fma.f64 (pow.f64 (*.f64 (NAN.f64) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n) (*.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))) (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))))) (neg.f64 n))) n))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))
(*.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)))
(+ (* -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))))))
(fma.f64 (*.f64 (*.f64 (*.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 (NAN.f64) n)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.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))))
(+ (* -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))))))
(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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (*.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))) (NAN.f64) (*.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 (*.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))) n))) (neg.f64 n)))
(+ (* -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))))))
(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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (*.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))) (NAN.f64))) (-.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 (NAN.f64) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n))) (neg.f64 n))) (neg.f64 n)))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ 1 (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (fma.f64 (*.f64 (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))
(*.f64 (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) k)

rewrite241.0ms (2.4%)

Memory
42.9MiB live, 220.6MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
051272
085257
1251241
21233241
08250241
Stop Event
iter limit
node limit
iter limit
Counts
25 → 557
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.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))))
(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 (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))
(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 (/.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 #s(literal 1 binary64) (sqrt.f64 k))
(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)) #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 (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))))
(PI.f64)
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 (PI.f64) n)
(-.f64 #s(literal 1 binary64) k)
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.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 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k)
Outputs
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k)) (neg.f64 (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (neg.f64 (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 3 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (*.f64 k k) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (*.f64 (neg.f64 k) k) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 2 binary64))))
(*.f64 (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
(*.f64 (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
(*.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))) (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))))
(*.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))) (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))))
(*.f64 (/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.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 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 n #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 (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 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 n #s(literal 2 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 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 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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 (*.f64 (PI.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 (/.f64 (pow.f64 (*.f64 (PI.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 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (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 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (neg.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) (neg.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(*.f64 (neg.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (neg.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
(*.f64 (fabs.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) (fabs.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(*.f64 (fabs.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (fabs.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
(*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (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 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (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 (PI.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 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal -1 binary64)) (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (neg.f64 (neg.f64 (sqrt.f64 k)))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k)))
(neg.f64 (/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(fma.f64 (pow.f64 k #s(literal -1/2 binary64)) (cosh.f64 (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sinh.f64 (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))))
(fma.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64) (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))))
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(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (neg.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 3 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (neg.f64 (fma.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))))))
(/.f64 (*.f64 (fma.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 3 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (fma.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))))
(fma.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal 3 binary64)) (fma.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 (fma.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))) #s(literal -1 binary64))))
(fma.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))
(fma.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))))
(fma.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))))
(fma.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal 3 binary64)) (fma.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 (fma.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))) #s(literal -1 binary64))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))))
(*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) k)
(*.f64 k (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(/.f64 (-.f64 (*.f64 (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) k) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) k)) (*.f64 (*.f64 (log.f64 (PI.f64)) k) (*.f64 (log.f64 (PI.f64)) k))) (-.f64 (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) k) (*.f64 (log.f64 (PI.f64)) k)))
(/.f64 (-.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k)) (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k))) (*.f64 (*.f64 k (log.f64 (PI.f64))) (*.f64 k (log.f64 (PI.f64))))) (-.f64 (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k)) (*.f64 k (log.f64 (PI.f64)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) k) #s(literal 3 binary64)) (pow.f64 (*.f64 (log.f64 (PI.f64)) k) #s(literal 3 binary64))) (fma.f64 (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) k) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) k) (-.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) k) (*.f64 (log.f64 (PI.f64)) k)) (*.f64 (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) k) (*.f64 (log.f64 (PI.f64)) k)))))
(/.f64 (+.f64 (pow.f64 (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k)) #s(literal 3 binary64)) (pow.f64 (*.f64 k (log.f64 (PI.f64))) #s(literal 3 binary64))) (fma.f64 (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k)) (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k)) (-.f64 (*.f64 (*.f64 k (log.f64 (PI.f64))) (*.f64 k (log.f64 (PI.f64)))) (*.f64 (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k)) (*.f64 k (log.f64 (PI.f64)))))))
(fma.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) k (*.f64 (log.f64 (PI.f64)) k))
(fma.f64 k (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k (log.f64 n)))
(fma.f64 k (log.f64 n) (*.f64 k (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(fma.f64 k (log.f64 #s(literal 2 binary64)) (*.f64 k (log.f64 (*.f64 n (PI.f64)))))
(fma.f64 k (log.f64 (PI.f64)) (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k)))
(fma.f64 k (log.f64 (*.f64 n #s(literal 2 binary64))) (*.f64 k (log.f64 (PI.f64))))
(-.f64 (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) k) (*.f64 (neg.f64 (log.f64 (PI.f64))) k))
(-.f64 (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k)) (*.f64 (neg.f64 k) (log.f64 (PI.f64))))
(+.f64 (*.f64 k (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k (log.f64 n)))
(+.f64 (*.f64 k (log.f64 n)) (*.f64 k (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (*.f64 k (log.f64 #s(literal 2 binary64))) (*.f64 k (log.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) k) (*.f64 (log.f64 (PI.f64)) k))
(+.f64 (*.f64 k (log.f64 (PI.f64))) (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k)))
(+.f64 (log.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k)) (*.f64 k (log.f64 (PI.f64))))
(log.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))

eval472.0ms (4.7%)

Memory
17.1MiB live, 384.9MiB allocated
Compiler

Compiled 28 004 to 3 619 computations (87.1% saved)

prune85.0ms (0.9%)

Memory
-6.2MiB live, 88.0MiB allocated
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New84211853
Fresh437
Picked415
Done000
Total85015865
Accuracy
100.0%
Counts
865 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
55.7%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))) (sqrt.f64 k))
29.1%
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
19.5%
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
55.0%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
99.4%
(*.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) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
54.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
60.4%
#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))
55.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
99.6%
#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))))
39.9%
#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))))
55.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))))
55.0%
#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)))))
40.0%
#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))))
40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
Compiler

Compiled 758 to 615 computations (18.9% saved)

simplify37.0ms (0.4%)

Memory
-25.1MiB live, 31.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 18 expressions of interest:

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

Useful iterations: 1 (0.0ms)

IterNodesCost
042293
065290
190284
2106284
3130284
4152284
5176284
6220284
7302284
8326284
9346284
10356284
0356284
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(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 k)
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
#s(literal 0 binary64)
(sqrt.f64 k)
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(PI.f64)
(sqrt.f64 k)
k
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#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)
Outputs
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(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 k)
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
#s(literal 0 binary64)
#s(literal 0 binary64)
(sqrt.f64 k)
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(PI.f64)
(sqrt.f64 k)
k
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
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 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#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 (PI.f64) (*.f64 n #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 (PI.f64) (*.f64 n #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 (PI.f64) (*.f64 n #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 (PI.f64) (*.f64 n #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)

localize119.0ms (1.2%)

Memory
38.3MiB live, 225.1MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.10282003162065376
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy0.14453125
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
accuracy0.1953125
(*.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)))
accuracy0.2578125
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy0.2578125
(*.f64 (PI.f64) n)
accuracy0.3515576177835908
(sqrt.f64 (*.f64 (PI.f64) n))
accuracy0.47951127930532605
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy28.51009728160764
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy0.2578125
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
accuracy0.36556625976844204
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
accuracy0.38670750498874384
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
accuracy28.536650363278138
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
accuracy0.0
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
accuracy0.0
(sqrt.f64 k)
accuracy0.0
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
accuracy0.10282003162065376
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy0.20150375976844204
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
accuracy0.2578125
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
Samples
96.0ms256×0valid
Compiler

Compiled 236 to 37 computations (84.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 75.0ms
ival-mult: 34.0ms (45.1% of total)
ival-pow: 18.0ms (23.9% of total)
ival-div: 10.0ms (13.3% of total)
ival-sqrt: 8.0ms (10.6% of total)
ival-pi: 1.0ms (1.3% of total)
ival-add: 1.0ms (1.3% of total)
ival-sub: 1.0ms (1.3% of total)
exact: 1.0ms (1.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series48.0ms (0.5%)

Memory
-32.5MiB live, 104.6MiB allocated
Counts
20 → 40
Calls
Call 1
Inputs
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.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 (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 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(sqrt.f64 (/.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 (* 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)))
0
(sqrt k)
(sqrt (/ 1 k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(sqrt (* n (PI)))
(* 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))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -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)))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
Calls

6 calls:

TimeVariablePointExpression
14.0ms
n
@-inf
((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* n 2) (PI)) (+ (* -1/2 k) 1/2)) (* (* n 2) (PI)) (/ 0 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* n 2) (PI))) (sqrt k)) (sqrt (* (* n 2) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 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)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt (/ 1 k)))
12.0ms
n
@inf
((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* n 2) (PI)) (+ (* -1/2 k) 1/2)) (* (* n 2) (PI)) (/ 0 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* n 2) (PI))) (sqrt k)) (sqrt (* (* n 2) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 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)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt (/ 1 k)))
9.0ms
n
@0
((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* n 2) (PI)) (+ (* -1/2 k) 1/2)) (* (* n 2) (PI)) (/ 0 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* n 2) (PI))) (sqrt k)) (sqrt (* (* n 2) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 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)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt (/ 1 k)))
4.0ms
k
@-inf
((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* n 2) (PI)) (+ (* -1/2 k) 1/2)) (* (* n 2) (PI)) (/ 0 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* n 2) (PI))) (sqrt k)) (sqrt (* (* n 2) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 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)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt (/ 1 k)))
4.0ms
k
@0
((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* n 2) (PI)) (+ (* -1/2 k) 1/2)) (* (* n 2) (PI)) (/ 0 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* n 2) (PI))) (sqrt k)) (sqrt (* (* n 2) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 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)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt (/ 1 k)))

simplify292.0ms (2.9%)

Memory
23.0MiB live, 321.0MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0153716
1500695
21855625
35611613
08462601
Stop Event
iter limit
node limit
Counts
40 → 40
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)))
0
(sqrt k)
(sqrt (/ 1 k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(sqrt (* n (PI)))
(* 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))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -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)))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (pow (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 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (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)))) 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 (*.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 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.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)))))) #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 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 (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 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 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))) #s(literal 1/8 binary64)))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))))) #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 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 (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* 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 n (PI.f64))) (fma.f64 (*.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))) #s(literal 1/8 binary64)) k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (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 k k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.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))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (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 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 n (PI.f64)))))
0
#s(literal 0 binary64)
(sqrt k)
(sqrt.f64 k)
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (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 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (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 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (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 n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* n (PI))
(*.f64 n (PI.f64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (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 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (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 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* -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))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(*.f64 (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))

rewrite184.0ms (1.8%)

Memory
8.2MiB live, 290.1MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
042236
065228
1200218
2904170
09162170
Stop Event
iter limit
node limit
iter limit
Counts
20 → 1 411
Calls
Call 1
Inputs
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.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 (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 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
Outputs
(/.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.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))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.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 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(neg.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.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))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal -1/2 binary64)) k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
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(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.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 (*.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 (*.f64 n (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.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 (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 (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) n)
(*.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 (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1 binary64)) (pow.f64 k #s(literal -1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (neg.f64 k))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(fabs.f64 (pow.f64 k #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (log.f64 (sqrt.f64 k))))
(exp.f64 (/.f64 (neg.f64 (log.f64 k)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(+.f64 (cosh.f64 (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (sinh.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))))

eval164.0ms (1.6%)

Memory
-5.1MiB live, 423.8MiB allocated
Compiler

Compiled 34 660 to 3 941 computations (88.6% saved)

prune53.0ms (0.5%)

Memory
9.1MiB live, 102.4MiB allocated
Pruning

20 alts after pruning (16 fresh and 4 done)

PrunedKeptTotal
New1 094121 106
Fresh549
Picked235
Done011
Total1 101201 121
Accuracy
100.0%
Counts
1 121 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
55.5%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
99.5%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
99.6%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
55.7%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))) (sqrt.f64 k))
29.1%
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
54.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
19.5%
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
54.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
5.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
11.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
5.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
55.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
54.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
54.9%
#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))))
5.2%
#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 (PI.f64) k))))
39.9%
#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))))
55.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))))
40.0%
#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))))
40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
9.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
Compiler

Compiled 883 to 712 computations (19.4% saved)

simplify21.0ms (0.2%)

Memory
-21.4MiB live, 24.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 #s(literal 1 binary64) k)
cost-diff0
#s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
cost-diff0
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
cost-diff4
(pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))
cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
cost-diff0
(sqrt.f64 n)
cost-diff0
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
cost-diff0
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))))
cost-diff0
(+.f64 (PI.f64) (PI.f64))
cost-diff0
(sqrt.f64 (+.f64 (PI.f64) (PI.f64)))
cost-diff0
(/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))
cost-diff0
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
cost-diff0
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
cost-diff0
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
cost-diff0
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
cost-diff0
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
cost-diff4
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
047254
070229
1105219
2149219
3199203
4253203
5346203
6498203
7666203
8720203
9763203
0763203
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) n)
(sqrt.f64 (PI.f64))
(PI.f64)
n
(*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))
#s(literal 2 binary64)
(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 k)
#s(approx (/ 0 (sqrt k)) #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) (PI.f64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))
(sqrt.f64 (+.f64 (PI.f64) (PI.f64)))
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(sqrt.f64 k)
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
(sqrt.f64 n)
n
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(PI.f64)
k
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
#s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(sqrt.f64 k)
Outputs
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (sqrt.f64 (PI.f64)) n)
(sqrt.f64 (PI.f64))
(PI.f64)
n
(*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
#s(literal 2 binary64)
(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 k)
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
#s(approx (pow (* 0 n) (/ (- 1 k) 8)) #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) (PI.f64))) (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))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k))
(sqrt.f64 (+.f64 (PI.f64) (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (PI.f64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
(sqrt.f64 k)
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n)))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))
(sqrt.f64 n)
n
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(PI.f64)
k
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) #s(literal 0 binary64)) (sqrt.f64 k))
#s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
#s(approx (pow (* 0 n) (/ (- 1 k) 8)) #s(literal 0 binary64))
(pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))
#s(literal 0 binary64)
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(sqrt.f64 k)

localize112.0ms (1.1%)

Memory
23.0MiB live, 209.3MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
accuracy0.0
(-.f64 #s(literal 1 binary64) k)
accuracy0.0
(sqrt.f64 k)
accuracy0.0
#s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
accuracy0.11328125
(/.f64 (PI.f64) k)
accuracy0.170253759768442
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
accuracy0.25
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
accuracy28.335247650234145
(PI.f64)
accuracy0.27572250976844204
(/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))
accuracy0.54296875
(sqrt.f64 (+.f64 (PI.f64) (PI.f64)))
accuracy28.335247650234145
(PI.f64)
accuracy32.30420145647867
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
accuracy0.0
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
accuracy0.185878759768442
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
accuracy0.19759750976844204
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
accuracy0.54296875
(sqrt.f64 (PI.f64))
accuracy28.335247650234145
(PI.f64)
Samples
51.0ms139×0valid
39.0ms117×0invalid
Compiler

Compiled 195 to 42 computations (78.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 71.0ms
ival-mult: 24.0ms (33.6% of total)
ival-pow: 19.0ms (26.6% of total)
ival-div: 13.0ms (18.2% of total)
ival-sqrt: 10.0ms (14% of total)
ival-add: 2.0ms (2.8% of total)
ival-pi: 1.0ms (1.4% of total)
ival-sub: 1.0ms (1.4% of total)
exact: 1.0ms (1.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series47.0ms (0.5%)

Memory
-9.6MiB live, 90.1MiB allocated
Counts
21 → 81
Calls
Call 1
Inputs
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))
(sqrt.f64 (+.f64 (PI.f64) (PI.f64)))
(+.f64 (PI.f64) (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
(sqrt.f64 n)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
#s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
(-.f64 #s(literal 1 binary64) k)
(PI.f64)
(sqrt.f64 (PI.f64))
(/.f64 (PI.f64) k)
(sqrt.f64 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 (* 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)))
0
(* (sqrt (/ (PI) k)) (sqrt 2))
(exp (+ (log 0) (* 20 (log k))))
(+ (exp (+ (log 0) (* 20 (log k)))) (* k (* (exp (+ (log 0) (* 20 (log k)))) (+ (NAN) (* -1 (+ (log 0) (* 20 (log k))))))))
(+ (exp (+ (log 0) (* 20 (log k)))) (* k (+ (* k (* (exp (+ (log 0) (* 20 (log k)))) (+ (* -1 (NAN)) (+ (* 1/2 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (NAN) (* -1 (+ (log 0) (* 20 (log k))))) 2)))))) (* (exp (+ (log 0) (* 20 (log k)))) (+ (NAN) (* -1 (+ (log 0) (* 20 (log k)))))))))
(+ (exp (+ (log 0) (* 20 (log k)))) (* k (+ (* k (+ (* k (* (exp (+ (log 0) (* 20 (log k)))) (+ (* -1/2 (+ (NAN) (* -1 (NAN)))) (+ (* 1/6 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (NAN) (* -1 (+ (log 0) (* 20 (log k))))) 3)) (* (+ (NAN) (* -1 (+ (log 0) (* 20 (log k))))) (+ (* -1 (NAN)) (* 1/2 (+ (NAN) (* -1 (NAN))))))))))) (* (exp (+ (log 0) (* 20 (log k)))) (+ (* -1 (NAN)) (+ (* 1/2 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (NAN) (* -1 (+ (log 0) (* 20 (log k))))) 2))))))) (* (exp (+ (log 0) (* 20 (log k)))) (+ (NAN) (* -1 (+ (log 0) (* 20 (log k)))))))))
(* (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)
(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)))))))
1
(+ 1 (* -1 k))
(/ (PI) k)
(sqrt k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log 0) (- 1 k)))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (- 1 k)))))
(exp (* 1/8 (* (log 0) (- 1 k))))
(* -1 k)
(* k (- (/ 1 k) 1))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (PI) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(exp (* (log 0) (+ 1 (* -1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (+ 1 (* -1 k))))))
(exp (* 1/8 (* (log 0) (+ 1 (* -1 k)))))
(* -1 (* k (- 1 (/ 1 k))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(sqrt n)
(* (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))))))
(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 (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 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))))))
(+ (* 1/8 (* (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))))))
(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 (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(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) (pow (sqrt -1) 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 (/ (+ (* -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))))))
(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 (/ (+ (* -1 (/ (* (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)))
(+ (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)))
Calls

6 calls:

TimeVariablePointExpression
12.0ms
n
@-inf
((* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (+ (* -1/2 k) 1/2)) (/ 0 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (+ (PI) (PI))) (sqrt k)) (sqrt (+ (PI) (PI))) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k)))) (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k))) (pow 0 (- 1 k)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (- 1 k) (PI) (sqrt (PI)) (/ (PI) k) (sqrt k))
9.0ms
n
@inf
((* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (+ (* -1/2 k) 1/2)) (/ 0 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (+ (PI) (PI))) (sqrt k)) (sqrt (+ (PI) (PI))) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k)))) (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k))) (pow 0 (- 1 k)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (- 1 k) (PI) (sqrt (PI)) (/ (PI) k) (sqrt k))
9.0ms
n
@0
((* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (+ (* -1/2 k) 1/2)) (/ 0 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (+ (PI) (PI))) (sqrt k)) (sqrt (+ (PI) (PI))) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k)))) (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k))) (pow 0 (- 1 k)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (- 1 k) (PI) (sqrt (PI)) (/ (PI) k) (sqrt k))
9.0ms
k
@-inf
((* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (+ (* -1/2 k) 1/2)) (/ 0 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (+ (PI) (PI))) (sqrt k)) (sqrt (+ (PI) (PI))) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k)))) (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k))) (pow 0 (- 1 k)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (- 1 k) (PI) (sqrt (PI)) (/ (PI) k) (sqrt k))
3.0ms
k
@0
((* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (+ (* -1/2 k) 1/2)) (/ 0 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (+ (PI) (PI))) (sqrt k)) (sqrt (+ (PI) (PI))) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k)))) (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k))) (pow 0 (- 1 k)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (- 1 k) (PI) (sqrt (PI)) (/ (PI) k) (sqrt k))

simplify153.0ms (1.5%)

Memory
36.0MiB live, 255.0MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04073264
115422859
082022689
Stop Event
iter limit
node limit
Counts
81 → 81
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)))
0
(* (sqrt (/ (PI) k)) (sqrt 2))
(exp (+ (log 0) (* 20 (log k))))
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(* (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)
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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)))))))
1
(+ 1 (* -1 k))
(/ (PI) k)
(sqrt k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log 0) (- 1 k)))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (- 1 k)))))
(exp (* 1/8 (* (log 0) (- 1 k))))
(* -1 k)
(* k (- (/ 1 k) 1))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (PI) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(exp (* (log 0) (+ 1 (* -1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (+ 1 (* -1 k))))))
(exp (* 1/8 (* (log 0) (+ 1 (* -1 k)))))
(* -1 (* k (- 1 (/ 1 k))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(sqrt n)
(* (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))))))
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
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(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))))
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
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(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 (/ (+ (* -1 (/ (* (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)))
(+ (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)))
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 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #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 (PI.f64) n) 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)
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(*.f64 (sqrt.f64 n) #s(literal 1 binary64))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))
(*.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)))
(+ (* -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))))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (*.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 (NAN.f64) n)) (*.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))))
(+ (* -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))))))
(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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (*.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))) (NAN.f64) (*.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 (*.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))) n))) (neg.f64 n)))
(+ (* -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))))))
(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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (*.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))) (NAN.f64))) (-.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 (NAN.f64) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n))) (neg.f64 n))) (neg.f64 n)))
(exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 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)))
(+ (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)))
(fma.f64 (*.f64 (*.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 (NAN.f64) n)) #s(literal -1/8 binary64) (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))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (* (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)))
(-.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 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.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))) (NAN.f64) (*.f64 (neg.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 (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))) n))) n))
(+ (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)))
(-.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 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.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))) (NAN.f64))) (-.f64 #s(literal 1 binary64) k) (/.f64 (fma.f64 (neg.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 (fma.f64 (pow.f64 (*.f64 (NAN.f64) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n) (*.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))) (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))))) (neg.f64 n))) n))

rewrite302.0ms (3%)

Memory
-1.7MiB live, 348.9MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
047217
070273
122676
2118048
0827248
Stop Event
iter limit
node limit
iter limit
Counts
21 → 254
Calls
Call 1
Inputs
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))
(sqrt.f64 (+.f64 (PI.f64) (PI.f64)))
(+.f64 (PI.f64) (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
(sqrt.f64 n)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
#s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
(-.f64 #s(literal 1 binary64) k)
(PI.f64)
(sqrt.f64 (PI.f64))
(/.f64 (PI.f64) k)
(sqrt.f64 k)
Outputs
#s(literal 0 binary64)
(/.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64)) (sqrt.f64 k))
(neg.f64 (/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))))
#s(literal 0 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))))
#s(literal 0 binary64)
#s(literal 0 binary64)
#s(literal 0 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))))
#s(literal 0 binary64)
(*.f64 (neg.f64 (pow.f64 n #s(literal 1/4 binary64))) (neg.f64 (pow.f64 n #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 n #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 n #s(literal 1/4 binary64))))
(*.f64 (pow.f64 n #s(literal 1/4 binary64)) (pow.f64 n #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 n)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 n n) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 n #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 n #s(literal 1/2 binary64))
(sqrt.f64 n)
(exp.f64 (*.f64 (log.f64 n) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 n) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 n) #s(literal 1/2 binary64))))
#s(literal 0 binary64)
#s(literal 0 binary64)
(/.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64)) (sqrt.f64 k))
(neg.f64 (/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))))
(*.f64 (/.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (+.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 k (-.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 k k k) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 k k k)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 k k k) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 k k k) (-.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (fma.f64 (neg.f64 k) k #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) 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 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))))) (+.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 k (/.f64 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 k (/.f64 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 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) (*.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 k (/.f64 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)))
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(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (PI.f64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (PI.f64)))
(+.f64 (sinh.f64 (log.f64 (PI.f64))) (cosh.f64 (log.f64 (PI.f64))))
(+.f64 (cosh.f64 (log.f64 (PI.f64))) (+.f64 (sinh.f64 (log.f64 (PI.f64))) #s(literal 0 binary64)))
(+.f64 (cosh.f64 (log.f64 (PI.f64))) (sinh.f64 (log.f64 (PI.f64))))
(+.f64 #s(literal 0 binary64) (PI.f64))
(+.f64 (PI.f64) #s(literal 0 binary64))
(log.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (PI.f64)))))
(log.f64 (exp.f64 (PI.f64)))
(PI.f64)
(*.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (neg.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (fabs.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/6 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3/2 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))
(pow.f64 (PI.f64) #s(literal 1/2 binary64))
(sqrt.f64 (PI.f64))
(fabs.f64 (neg.f64 (sqrt.f64 (PI.f64))))
(fabs.f64 (sqrt.f64 (PI.f64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (PI.f64))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (PI.f64)))) (sinh.f64 (log.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) k) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) k))
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) k) (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (cbrt.f64 (PI.f64)) k) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (cbrt.f64 (PI.f64)) k) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (sqrt.f64 (PI.f64)))
(*.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (/.f64 (cbrt.f64 (PI.f64)) (neg.f64 k)))
(*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (/.f64 (cbrt.f64 (PI.f64)) k)))
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 k)))
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) k))
(*.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)) k)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) k)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)))
(*.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) k))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) k))
(/.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) k)
(/.f64 (neg.f64 (PI.f64)) (neg.f64 k))
(/.f64 (/.f64 (PI.f64) k) #s(literal 1 binary64))
(/.f64 (PI.f64) k)
(neg.f64 (/.f64 (neg.f64 (PI.f64)) k))
(+.f64 (/.f64 (cosh.f64 (log.f64 (PI.f64))) k) (/.f64 (sinh.f64 (log.f64 (PI.f64))) k))
(*.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))))

eval277.0ms (2.8%)

Memory
23.5MiB live, 359.0MiB allocated
Compiler

Compiled 30 562 to 4 383 computations (85.7% saved)

prune32.0ms (0.3%)

Memory
-5.9MiB live, 84.2MiB allocated
Pruning

21 alts after pruning (13 fresh and 8 done)

PrunedKeptTotal
New8562858
Fresh01111
Picked145
Done044
Total85721878
Accuracy
100.0%
Counts
878 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
55.5%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
99.5%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
99.6%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
55.7%
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))) (sqrt.f64 k))
29.9%
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))
54.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
19.5%
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
54.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
5.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
11.6%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
5.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
55.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
54.9%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
54.9%
#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))))
5.2%
#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 (PI.f64) k))))
39.9%
#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))))
55.0%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))))
40.0%
#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))))
40.1%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
9.4%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
5.2%
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (+ (PI) (PI))) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
Compiler

Compiled 1 443 to 613 computations (57.5% saved)

regimes48.0ms (0.5%)

Memory
3.6MiB live, 102.4MiB allocated
Counts
38 → 1
Calls
Call 1
Inputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (+ (PI) (PI))) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (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 (PI.f64) n) 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) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (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)) (PI.f64))) (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 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.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 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 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(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 (/.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(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #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) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (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 (*.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)))))
(*.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))))
(*.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 (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 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -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 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
(*.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))))
Calls

4 calls:

13.0ms
(*.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))))
12.0ms
k
10.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
10.0ms
n
Results
AccuracySegmentsBranch
99.6%1k
99.6%1n
99.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 23 to 23 computations (0% saved)

regimes52.0ms (0.5%)

Memory
11.8MiB live, 57.7MiB allocated
Counts
33 → 1
Calls
Call 1
Inputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (+ (PI) (PI))) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (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 (PI.f64) n) 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) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (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)) (PI.f64))) (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 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.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 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 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(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 (/.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(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #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) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (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 (*.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)))))
Outputs
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
Calls

4 calls:

25.0ms
n
9.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
9.0ms
k
8.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%1k
99.6%1n
99.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 23 to 23 computations (0% saved)

regimes44.0ms (0.4%)

Memory
6.2MiB live, 51.6MiB allocated
Counts
23 → 2
Calls
Call 1
Inputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (+ (PI) (PI))) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (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 (PI.f64) n) 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) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (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)) (PI.f64))) (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 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.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 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
Calls

4 calls:

23.0ms
(*.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))))
7.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms
n
6.0ms
k
Results
AccuracySegmentsBranch
98.9%2k
61.1%2n
98.9%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
61.1%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 23 to 23 computations (0% saved)

regimes17.0ms (0.2%)

Memory
-17.8MiB live, 32.8MiB allocated
Counts
21 → 3
Calls
Call 1
Inputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (+ (PI) (PI))) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (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 (PI.f64) n) 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) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (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)) (PI.f64))) (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 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.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 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
Outputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))
Calls

2 calls:

10.0ms
k
6.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
98.8%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
84.2%3k
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes15.0ms (0.2%)

Memory
-7.4MiB live, 38.1MiB allocated
Counts
19 → 2
Calls
Call 1
Inputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (+ (PI) (PI))) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (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 (PI.f64) n) 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) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (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)) (PI.f64))) (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 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.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 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
Outputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
Calls

2 calls:

8.0ms
k
6.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
71.9%2k
72.1%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 17 to 15 computations (11.8% saved)

regimes15.0ms (0.1%)

Memory
39.6MiB live, 39.6MiB allocated
Counts
10 → 3
Calls
Call 1
Inputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (+ (PI) (PI))) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (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 (PI.f64) n) 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) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
Outputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
Calls

4 calls:

4.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms
n
3.0ms
k
3.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
47.9%2n
47.9%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
57.1%2k
59.4%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 23 to 23 computations (0% saved)

regimes5.0ms (0%)

Memory
-37.9MiB live, 6.9MiB allocated
Counts
4 → 2
Calls
Call 1
Inputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
Outputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
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
57.2%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
28.0MiB live, 28.0MiB allocated
Counts
3 → 2
Calls
Call 1
Inputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
Outputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
Calls

4 calls:

2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
2.0ms
n
2.0ms
k
Results
AccuracySegmentsBranch
24.2%2n
24.2%2(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
26.3%2k
26.4%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 23 to 23 computations (0% saved)

regimes8.0ms (0.1%)

Memory
-21.2MiB live, 23.6MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
Outputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
Calls

4 calls:

3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms
n
1.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
1.0ms
k
Results
AccuracySegmentsBranch
19.5%1n
19.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
19.5%1k
19.5%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))))
Compiler

Compiled 23 to 23 computations (0% saved)

bsearch32.0ms (0.3%)

Memory
3.7MiB live, 105.2MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
29.0ms
5.3992085673560354e-14
2.3005238183322123
Samples
22.0ms160×0valid
Compiler

Compiled 509 to 428 computations (15.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-div: 4.0ms (29.6% of total)
ival-pow: 4.0ms (29.6% of total)
ival-mult: 3.0ms (22.2% of total)
ival-pi: 1.0ms (7.4% of total)
ival-sub: 1.0ms (7.4% of total)
ival-sqrt: 1.0ms (7.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
2.7MiB live, 2.7MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
3.987243498737837e+284
+inf
0.0ms
4.325395907374826e-227
9.80229732164679e-126
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
4.325395907374826e-227
9.80229732164679e-126
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch1.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.5173560213464794e+153
1.3342575182450216e+159
0.0ms
4.325395907374826e-227
9.80229732164679e-126
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
4.325395907374826e-227
9.80229732164679e-126
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
4.325395907374826e-227
9.80229732164679e-126
Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify27.0ms (0.3%)

Memory
-12.3MiB live, 77.9MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
079412
1104392
2119392
3139392
4156392
5175392
6209392
7276392
8307392
9340392
10350392
Stop Event
saturated
Calls
Call 1
Inputs
(*.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))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 3170534137668829/576460752303423488 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #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 499999999999999990079578960260221425096554759926423605900012855280825179991269042612044308093073246922143074698610725186309660447719446848973826083227612667029686373206874073603221710445876270310293765181110136931503450775547995353849221420762954771236422294344040540188066309300289536 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) (/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #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 1999999999999999999466806008246307489711078038236873372571680376048739359044847523345839519129134316887338757648057420040785188188258060440266031719514112 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #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 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
Outputs
(*.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))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 3170534137668829/576460752303423488 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #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 499999999999999990079578960260221425096554759926423605900012855280825179991269042612044308093073246922143074698610725186309660447719446848973826083227612667029686373206874073603221710445876270310293765181110136931503450775547995353849221420762954771236422294344040540188066309300289536 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) (/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 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 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #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 499999999999999990079578960260221425096554759926423605900012855280825179991269042612044308093073246922143074698610725186309660447719446848973826083227612667029686373206874073603221710445876270310293765181110136931503450775547995353849221420762954771236422294344040540188066309300289536 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) (/.f64 #s(approx (/ 0 (sqrt k)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))))
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#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))

soundness1.4s (13.7%)

Memory
26.6MiB live, 1 226.9MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0120502
1378489
21377453
34131453
08166441
04073264
115422859
082022689
051272
085257
1251241
21233241
08250241
0153716
1500695
21855625
35611613
08462601
042236
065228
1200218
2904170
09162170
04003260
114572974
271752791
080282677
01338
02238
18335
244635
3400729
0892129
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 986 to 514 computations (47.9% saved)

preprocess49.0ms (0.5%)

Memory
-7.8MiB live, 81.1MiB allocated
Compiler

Compiled 886 to 184 computations (79.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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