Migdal et al, Equation (51)

Time bar (total: 29.3s)

analyze389.0ms (1.3%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%50%1.6%7
52.5%25%22.6%0.1%0%50%2.3%8
53.8%25%21.5%0.1%0%50%3.5%9
54.5%25%20.9%0.1%0%50%4.1%10
55.3%25%20.2%0.1%0%50%4.8%11
55.7%25%19.9%0.1%0%50%5.1%12
Compiler

Compiled 19 to 14 computations (26.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 217.0ms
ival-pow: 92.0ms (42.4% of total)
ival-mult: 42.0ms (19.4% of total)
ival-div: 39.0ms (18% of total)
ival-sqrt: 24.0ms (11.1% of total)
ival-sub: 10.0ms (4.6% of total)
ival-pi: 7.0ms (3.2% of total)
const: 3.0ms (1.4% of total)
backward-pass: 0.0ms (0% of total)

sample8.8s (30%)

Results
3.8s3991×5exit
2.2s8256×0valid
1.1s1956×1invalid
78.0ms426×0invalid
64.0ms212×0unsamplable
Precisions
Click to see histograms. Total time spent on operations: 5.5s
ival-pow: 1.7s (30.7% of total)
ival-mult: 1.1s (20% of total)
ival-sqrt: 790.0ms (14.3% of total)
ival-div: 782.0ms (14.2% of total)
backward-pass: 564.0ms (10.2% of total)
ival-sub: 294.0ms (5.3% of total)
ival-pi: 218.0ms (4% of total)
const: 69.0ms (1.3% of total)
Bogosity

preprocess190.0ms (0.6%)

Algorithm
2×egg-herbie
Rules
1106×fnmadd-define
930×fma-define
846×fmsub-define
760×fnmsub-define
680×sum3-define
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03392
19388
220888
341483
474282
5148682
6209182
7266182
8355982
9371182
10377082
11381482
12382282
01314
13014
24714
36914
49013
511313
614913
718813
821413
922813
1022913
022913
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
Outputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Call 2
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))
Outputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(* (rsqrt k) (pow (* 2 (* (PI) n)) (fnmsub k 1/2 -1/2)))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(* (rsqrt (neg k)) (pow (* 2 (* (PI) n)) (fnmsub k -1/2 -1/2)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(* (rsqrt k) (pow (* (PI) (* n -2)) (fnmsub k 1/2 -1/2)))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(fnmsub (rsqrt (neg k)) (pow (* 2 (* (PI) n)) (fnmsub k -1/2 -1/2)) 0)
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(* (pow (* (PI) (* n -2)) (fnmsub k 1/2 -1/2)) (neg (rsqrt k)))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))
(* (rsqrt n) (pow (* k (* 2 (PI))) (fnmsub n 1/2 -1/2)))

explain314.0ms (1.1%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
3218(1.0224594167278261e-197 2.7626518367625316e-188)0-(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
00-0-(*.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)
00-0-(*.f64 #s(literal 2 binary64) (PI.f64))
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
00-0-(-.f64 #s(literal 1 binary64) k)
00-0-#s(literal 2 binary64)
00-0-(sqrt.f64 k)
00-0-(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
00-0-#s(literal 1 binary64)
00-0-(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
00-0-n
00-0-k
Results
191.0ms512×0valid
Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 107.0ms
ival-pow: 35.0ms (32.7% of total)
ival-mult: 26.0ms (24.3% of total)
ival-div: 24.0ms (22.4% of total)
ival-sqrt: 9.0ms (8.4% of total)
ival-sub: 7.0ms (6.5% of total)
ival-pi: 4.0ms (3.7% of total)
const: 2.0ms (1.9% of total)
backward-pass: 0.0ms (0% of total)

eval1.0ms (0%)

Compiler

Compiled 16 to 12 computations (25% saved)

prune3.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶99.4%
(*.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 34 to 25 computations (26.5% saved)

simplify26.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓cost-diff0
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 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
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff128
(*.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))))
Rules
64×sum3-define
64×*-lowering-*.f32
64×*-lowering-*.f64
48×+-lowering-+.f64
48×+-lowering-+.f32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02098
13898
25898
37898
410092
512992
617092
720292
823192
923592
023592
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/ 1 (sqrt k))
1
(sqrt k)
k
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(* (* 2 (PI)) n)
(* 2 (PI))
2
(PI)
n
(/ (- 1 k) 2)
(- 1 k)
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(- 1/2 (/ k 2))
1/2
(/ k 2)
k
(sqrt k)
Outputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/ 1 (sqrt k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
1
#s(literal 1 binary64)
(sqrt k)
(sqrt.f64 k)
k
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(* (* 2 (PI)) n)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(* 2 (PI))
(*.f64 #s(literal 2 binary64) (PI.f64))
2
#s(literal 2 binary64)
(PI)
(PI.f64)
n
(/ (- 1 k) 2)
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(- 1 k)
(-.f64 #s(literal 1 binary64) k)
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(* 2 (* (PI) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(- 1/2 (/ k 2))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ k 2)
(/.f64 k #s(literal 2 binary64))
k
(sqrt k)
(sqrt.f64 k)

localize232.0ms (0.8%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(PI.f64)
✓accuracy99.7%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓accuracy99.7%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy99.7%
(*.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))))
✓accuracy99.7%
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓accuracy99.6%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
Results
165.0ms256×0valid
Compiler

Compiled 105 to 21 computations (80% saved)

Precisions
Click to see histograms. Total time spent on operations: 94.0ms
ival-pow: 34.0ms (36.3% of total)
ival-div: 23.0ms (24.5% of total)
ival-mult: 22.0ms (23.5% of total)
ival-sub: 6.0ms (6.4% of total)
ival-sqrt: 4.0ms (4.3% of total)
ival-pi: 2.0ms (2.1% of total)
const: 1.0ms (1.1% of total)
backward-pass: 0.0ms (0% of total)

series235.0ms (0.8%)

Counts
10 → 156
Calls
Call 1
Inputs
#<alt (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))>
#<alt (/ 1 (sqrt k))>
#<alt (sqrt k)>
#<alt (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))>
#<alt (/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))>
#<alt (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))>
#<alt (* 2 (* (PI) n))>
#<alt (* (PI) n)>
#<alt (* (* 2 (PI)) n)>
#<alt (PI)>
Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
Calls

39 calls:

TimeVariablePointExpression
119.0ms
n
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
67.0ms
n
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
17.0ms
n
@inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
4.0ms
k
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms
k
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite868.0ms (3%)

Algorithm
1×batch-egg-rewrite
Rules
5664×*-lowering-*.f32
5664×*-lowering-*.f64
3066×/-lowering-/.f32
3066×/-lowering-/.f64
1334×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02068
113268
285164
0861864
Stop Event
1×iter limit
1×node limit
Counts
10 → 740
Calls
Call 1
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/ 1 (sqrt k))
(sqrt k)
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(* 2 (* (PI) n))
(* (PI) n)
(* (* 2 (PI)) n)
(PI)
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1 binary64)) (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (neg.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1 binary64))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (neg.f64 (neg.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (/.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)))
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(*.f64 (pow.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal 1/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64))) (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))

simplify785.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
5256×*-lowering-*.f32
5256×*-lowering-*.f64
2382×+-lowering-+.f64
2382×+-lowering-+.f32
1472×associate-*r*
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01392132
13852104
211891816
341751732
477401732
081111732
Stop Event
1×iter limit
1×node limit
Counts
156 → 156
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)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 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)))))
(* (sqrt (/ 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)))))
(* (sqrt (/ 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)))))
(* (sqrt (/ 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)))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 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 (* (+ (log n) (log (* 2 (PI)))) (- 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 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 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 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 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 (* 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)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 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)) (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 (* (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 (* (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 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 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)))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -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)) (+.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (*.f64 (*.f64 (*.f64 k #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) #s(literal -1/48 binary64))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) #s(literal 1/8 binary64)))) (*.f64 k k)) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
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(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #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)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal 1/8 binary64)) (log.f64 (*.f64 n (*.f64 (PI.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)))
(+.f64 (*.f64 k (*.f64 (*.f64 k (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (*.f64 (*.f64 k #s(literal -1/48 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 1/8 binary64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))

eval320.0ms (1.1%)

Compiler

Compiled 21499 to 2036 computations (90.5% saved)

prune270.0ms (0.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New97514989
Fresh000
Picked022
Done000
Total97516991
Accuracy
100.0%
Counts
991 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.3%
(/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
99.5%
(/.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
64.7%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 binary64)))
✓99.5%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶96.1%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
99.5%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
▶99.7%
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
73.9%
(/.f64 (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (sqrt.f64 k))
▶52.1%
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
99.7%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
96.0%
(/.f64 (exp.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
99.5%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
77.4%
(*.f64 (pow.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))))
✓99.4%
(*.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))))
▶40.8%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶99.5%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 538 to 385 computations (28.4% saved)

simplify72.0ms (0.2%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓cost-diff6528
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
✓cost-diff6528
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
✓cost-diff0
(sqrt.f64 (*.f64 n (PI.f64)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
✓cost-diff0
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 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
(/.f64 #s(literal 1 binary64) k)
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓cost-diff0
(*.f64 n (PI.f64))
✓cost-diff0
(/.f64 (*.f64 n (PI.f64)) k)
✓cost-diff0
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓cost-diff0
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
✓cost-diff0
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Rules
200×*-lowering-*.f32
200×*-lowering-*.f64
120×fmsub-define
116×fma-lowering-fma.f32
116×fma-lowering-fma.f64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
036237
163235
292234
3109234
4134228
5165228
6210228
7245228
8282228
9291228
10299228
11341228
12426228
13500228
14540228
15569228
16587228
17591228
0591228
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2))) (sqrt k))
(/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2)))
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(pow (* 2 (* (PI) n)) (/ k 2))
(/ k 2)
k
(sqrt k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
n
(PI)
k
(sqrt 2)
2
(* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(sqrt (/ 1 k))
(/ 1 k)
1
k
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(* (* 2 (PI)) n)
(* 2 (PI))
2
(PI)
n
(/ (- 1 k) 2)
(- 1 k)
(/ (* (sqrt 2) (sqrt (* n (PI)))) (sqrt k))
(* (sqrt 2) (sqrt (* n (PI))))
(sqrt 2)
2
(sqrt (* n (PI)))
(* n (PI))
n
(PI)
(sqrt k)
k
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k))))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(- 1/2 (/ k 2))
1/2
(/ k 2)
k
(exp (* 1/2 (log k)))
(* 1/2 (log k))
(log k)
Outputs
(/ (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2))) (sqrt k))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(sqrt (* 2 (* (PI) n)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(* 2 (* (PI) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(pow (* 2 (* (PI) n)) (/ k 2))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))
(/ k 2)
(/.f64 k #s(literal 2 binary64))
k
(sqrt k)
(sqrt.f64 k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(/ (* n (PI)) k)
(*.f64 (PI.f64) (/.f64 n k))
(* n (PI))
(*.f64 (PI.f64) n)
n
(PI)
(PI.f64)
k
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
1
#s(literal 1 binary64)
k
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(* (* 2 (PI)) n)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(* 2 (PI))
(*.f64 #s(literal 2 binary64) (PI.f64))
2
#s(literal 2 binary64)
(PI)
(PI.f64)
n
(/ (- 1 k) 2)
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))
(- 1 k)
(-.f64 #s(literal 1 binary64) k)
(/ (* (sqrt 2) (sqrt (* n (PI)))) (sqrt k))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(* (sqrt 2) (sqrt (* n (PI))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 (PI.f64) n))
(* n (PI))
(*.f64 (PI.f64) n)
n
(PI)
(PI.f64)
(sqrt k)
(sqrt.f64 k)
k
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(* 2 (* (PI) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(- 1/2 (/ k 2))
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ k 2)
(/.f64 k #s(literal 2 binary64))
k
(exp (* 1/2 (log k)))
(sqrt.f64 k)
(* 1/2 (log k))
(*.f64 #s(literal 1/2 binary64) (log.f64 k))
(log k)
(log.f64 k)

localize793.0ms (2.7%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.7%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓accuracy94.4%
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
✓accuracy76.9%
(PI.f64)
✓accuracy99.7%
(*.f64 n (PI.f64))
✓accuracy99.5%
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
✓accuracy99.5%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
✓accuracy76.9%
(PI.f64)
✓accuracy99.7%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓accuracy99.7%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.7%
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓accuracy76.9%
(PI.f64)
✓accuracy99.7%
(*.f64 n (PI.f64))
✓accuracy99.4%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy88.4%
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓accuracy76.9%
(PI.f64)
✓accuracy99.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓accuracy99.7%
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy76.9%
(PI.f64)
Results
349.0ms61×5exit
290.0ms195×0valid
Compiler

Compiled 246 to 37 computations (85% saved)

Precisions
Click to see histograms. Total time spent on operations: 288.0ms
ival-pow: 68.0ms (23.6% of total)
ival-mult: 55.0ms (19.1% of total)
backward-pass: 52.0ms (18.1% of total)
ival-div: 38.0ms (13.2% of total)
ival-sqrt: 32.0ms (11.1% of total)
ival-log: 24.0ms (8.3% of total)
ival-sub: 8.0ms (2.8% of total)
ival-exp: 7.0ms (2.4% of total)
ival-pi: 3.0ms (1% of total)
const: 1.0ms (0.3% of total)

series76.0ms (0.3%)

Counts
22 → 360
Calls
Call 1
Inputs
#<alt (/ (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2))) (sqrt k))>
#<alt (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2)))>
#<alt (sqrt (* 2 (* (PI) n)))>
#<alt (* 2 (* (PI) n))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))>
#<alt (sqrt (/ 1 k))>
#<alt (/ 1 k)>
#<alt (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))>
#<alt (/ (* (sqrt 2) (sqrt (* n (PI)))) (sqrt k))>
#<alt (* (sqrt 2) (sqrt (* n (PI))))>
#<alt (sqrt 2)>
#<alt (sqrt (* n (PI)))>
#<alt (/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k))))>
#<alt (exp (* 1/2 (log k)))>
#<alt (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))>
#<alt (PI)>
#<alt (* (PI) n)>
#<alt (* (* 2 (PI)) n)>
Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
Calls

90 calls:

TimeVariablePointExpression
6.0ms
k
@-inf
(/ (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2))) (sqrt k))
5.0ms
n
@0
(/ (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2))) (sqrt k))
5.0ms
n
@inf
(/ (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2))) (sqrt k))
5.0ms
k
@inf
(/ (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2))) (sqrt k))
4.0ms
n
@-inf
(/ (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2))) (sqrt k))

rewrite870.0ms (3%)

Algorithm
1×batch-egg-rewrite
Rules
4622×/-lowering-/.f32
4622×/-lowering-/.f64
4204×*-lowering-*.f32
4204×*-lowering-*.f64
1792×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036147
1208143
21263137
08246137
Stop Event
1×iter limit
1×node limit
Counts
22 → 1126
Calls
Call 1
Inputs
(/ (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2))) (sqrt k))
(/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2)))
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
(* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(sqrt (/ 1 k))
(/ 1 k)
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(/ (* (sqrt 2) (sqrt (* n (PI)))) (sqrt k))
(* (sqrt 2) (sqrt (* n (PI))))
(sqrt 2)
(sqrt (* n (PI)))
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k))))
(exp (* 1/2 (log k)))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(PI)
(* (PI) n)
(* (* 2 (PI)) n)
Outputs
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))))
(exp.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))))))
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(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(*.f64 (pow.f64 (PI.f64) (+.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) n) (+.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (PI.f64) (+.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (+.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (PI.f64) (+.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (PI.f64) (+.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) n) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 n (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 n (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 4 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 4 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 4 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 4 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (exp.f64 (*.f64 (/.f64 k #s(literal -2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))
(expm1.f64 (log1p.f64 (PI.f64)))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)))))
(log1p.f64 (expm1.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
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(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 (*.f64 n #s(literal 1 binary64)) (PI.f64))
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))

simplify841.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
6274×*-lowering-*.f32
6274×*-lowering-*.f64
2684×+-lowering-+.f64
2684×+-lowering-+.f32
1466×times-frac
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02244468
17234339
227303887
364123838
087333838
Stop Event
1×iter limit
1×node limit
Counts
360 → 360
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* (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 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
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(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
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(/ (+ (* -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)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 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)))))
(* (sqrt (/ 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)))))
(* (sqrt (/ 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)))))
(* (sqrt (/ 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)))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 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 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 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 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 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 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 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 (* 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)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 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)) (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 (* (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 (* (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 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 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)))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
Outputs
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal 1/2 binary64)))))
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(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 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)))
(+.f64 (*.f64 k (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64))) (*.f64 k (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) k))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64))))) (*.f64 k k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))

eval600.0ms (2%)

Compiler

Compiled 36345 to 2994 computations (91.8% saved)

prune480.0ms (1.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New1802161818
Fresh729
Picked505
Done112
Total1815191834
Accuracy
100.0%
Counts
1834 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
42.1%
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
77.1%
(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
99.5%
(/.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
✓99.5%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶99.5%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
77.0%
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
▶99.7%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
52.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
42.0%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
40.8%
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
77.0%
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
▶42.0%
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
52.2%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
40.7%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
52.2%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
▶52.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
▶40.9%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
40.9%
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
38.4%
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
Compiler

Compiled 540 to 410 computations (24.1% saved)

simplify21.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 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 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(/.f64 k (*.f64 (PI.f64) n))
✓cost-diff0
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))
✓cost-diff0
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))
✓cost-diff0
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
✓cost-diff0
(sqrt.f64 n)
✓cost-diff0
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
✓cost-diff0
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓cost-diff64
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))
✓cost-diff64
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
Rules
84×*-lowering-*.f32
84×*-lowering-*.f64
32×*-commutative
30×/-lowering-/.f32
30×/-lowering-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029201
146201
264201
382201
489201
089201
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)
(* (pow (* 2 (* (PI) n)) k) k)
(pow (* 2 (* (PI) n)) k)
k
1/2
(sqrt (/ (* 2 (* (PI) n)) k))
(/ (* 2 (* (PI) n)) k)
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
k
(* (sqrt n) (sqrt (* (/ (PI) k) 2)))
(sqrt n)
n
(sqrt (* (/ (PI) k) 2))
(* (/ (PI) k) 2)
(/ (PI) k)
(PI)
k
2
(* (pow (/ k (* (PI) n)) -1/2) (sqrt 2))
(pow (/ k (* (PI) n)) -1/2)
(/ k (* (PI) n))
k
(* (PI) n)
(PI)
n
-1/2
(sqrt 2)
2
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- (/ k 2) 1/2)))
(pow k -1/2)
k
-1/2
(pow (* 2 (* (PI) n)) (- (/ k 2) 1/2))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(- (/ k 2) 1/2)
(/ k 2)
1/2
Outputs
(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(sqrt (* 2 (* (PI) n)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(* 2 (* (PI) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)
(sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(* (pow (* 2 (* (PI) n)) k) k)
(*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(pow (* 2 (* (PI) n)) k)
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
k
1/2
#s(literal 1/2 binary64)
(sqrt (/ (* 2 (* (PI) n)) k))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(/ (* 2 (* (PI) n)) k)
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
(* 2 (* (PI) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
k
(* (sqrt n) (sqrt (* (/ (PI) k) 2)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt n)
(sqrt.f64 n)
n
(sqrt (* (/ (PI) k) 2))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))
(* (/ (PI) k) 2)
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(PI)
(PI.f64)
k
2
#s(literal 2 binary64)
(* (pow (/ k (* (PI) n)) -1/2) (sqrt 2))
(*.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(pow (/ k (* (PI) n)) -1/2)
(pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64))
(/ k (* (PI) n))
(/.f64 (/.f64 k n) (PI.f64))
k
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
-1/2
#s(literal -1/2 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- (/ k 2) 1/2)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(pow k -1/2)
(pow.f64 k #s(literal -1/2 binary64))
k
-1/2
#s(literal -1/2 binary64)
(pow (* 2 (* (PI) n)) (- (/ k 2) 1/2))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(* 2 (* (PI) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(- (/ k 2) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(/ k 2)
(/.f64 k #s(literal 2 binary64))
1/2
#s(literal 1/2 binary64)

localize690.0ms (2.4%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))
✓accuracy99.7%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy76.9%
(PI.f64)
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.4%
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy89.7%
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))
✓accuracy76.9%
(PI.f64)
✓accuracy99.8%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
✓accuracy99.8%
(/.f64 (PI.f64) k)
✓accuracy99.6%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
✓accuracy76.9%
(PI.f64)
✓accuracy99.7%
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy88.4%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
✓accuracy76.9%
(PI.f64)
✓accuracy99.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓accuracy99.7%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy76.9%
(PI.f64)
Results
309.0ms61×5exit
247.0ms195×0valid
Compiler

Compiled 206 to 30 computations (85.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 275.0ms
ival-pow: 132.0ms (48% of total)
backward-pass: 46.0ms (16.7% of total)
ival-mult: 33.0ms (12% of total)
ival-div: 28.0ms (10.2% of total)
ival-sqrt: 27.0ms (9.8% of total)
ival-sub: 4.0ms (1.5% of total)
ival-pi: 3.0ms (1.1% of total)
const: 1.0ms (0.4% of total)

series109.0ms (0.4%)

Counts
19 → 336
Calls
Call 1
Inputs
#<alt (/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))>
#<alt (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)>
#<alt (sqrt (* 2 (* (PI) n)))>
#<alt (* 2 (* (PI) n))>
#<alt (sqrt (/ (* 2 (* (PI) n)) k))>
#<alt (/ (* 2 (* (PI) n)) k)>
#<alt (* (PI) n)>
#<alt (* (sqrt n) (sqrt (* (/ (PI) k) 2)))>
#<alt (sqrt n)>
#<alt (sqrt (* (/ (PI) k) 2))>
#<alt (* (/ (PI) k) 2)>
#<alt (* (pow (/ k (* (PI) n)) -1/2) (sqrt 2))>
#<alt (pow (/ k (* (PI) n)) -1/2)>
#<alt (/ k (* (PI) n))>
#<alt (/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- (/ k 2) 1/2)))>
#<alt (pow k -1/2)>
#<alt (pow (* 2 (* (PI) n)) (- (/ k 2) 1/2))>
#<alt (PI)>
#<alt (/ (PI) k)>
Outputs
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (sqrt k)>
#<alt (+ (sqrt k) (* 1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI)))))))>
#<alt (+ (sqrt k) (* (pow k 2) (+ (* 1/4 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))))))>
#<alt (+ (sqrt k) (* (pow k 2) (+ (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))) (* k (+ (* 1/4 (* (sqrt (/ 1 k)) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt k) (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/4 (/ (pow (log (* 2 (* n (PI)))) 2) k))))))))))>
#<alt (sqrt (* k (pow (* 2 (* n (PI))) k)))>
#<alt (sqrt (* k (pow (* 2 (* n (PI))) k)))>
#<alt (sqrt (* k (pow (* 2 (* n (PI))) k)))>
#<alt (sqrt (* k (pow (* 2 (* n (PI))) k)))>
#<alt (* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (* -1 (* (sqrt n) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt n) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt n) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt n) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)>
#<alt (/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))>
#<alt (+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))>
#<alt (+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
Calls

84 calls:

TimeVariablePointExpression
7.0ms
k
@0
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- (/ k 2) 1/2)))
6.0ms
n
@-inf
(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
6.0ms
n
@inf
(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
6.0ms
k
@0
(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
4.0ms
n
@0
(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))

rewrite913.0ms (3.1%)

Algorithm
1×batch-egg-rewrite
Rules
4694×*-lowering-*.f32
4694×*-lowering-*.f64
3780×/-lowering-/.f32
3780×/-lowering-/.f64
1590×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029132
1169129
21062121
08357121
Stop Event
1×iter limit
1×node limit
Counts
19 → 782
Calls
Call 1
Inputs
(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
(pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
(sqrt (/ (* 2 (* (PI) n)) k))
(/ (* 2 (* (PI) n)) k)
(* (PI) n)
(* (sqrt n) (sqrt (* (/ (PI) k) 2)))
(sqrt n)
(sqrt (* (/ (PI) k) 2))
(* (/ (PI) k) 2)
(* (pow (/ k (* (PI) n)) -1/2) (sqrt 2))
(pow (/ k (* (PI) n)) -1/2)
(/ k (* (PI) n))
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- (/ k 2) 1/2)))
(pow k -1/2)
(pow (* 2 (* (PI) n)) (- (/ k 2) 1/2))
(PI)
(/ (PI) k)
Outputs
(exp.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (*.f64 #s(literal -1/2 binary64) (log.f64 k))))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))))
(exp.f64 (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64))))
(exp.f64 (neg.f64 (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (*.f64 #s(literal 1/2 binary64) (log.f64 k)))))
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))))
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))))
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (/.f64 k #s(literal 2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))) #s(literal 2 binary64))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 (/.f64 k #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(*.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
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(*.f64 (pow.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))))
(*.f64 (pow.f64 n (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))) (pow.f64 n (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))) (pow.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 n (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(*.f64 (exp.f64 (*.f64 (/.f64 k #s(literal 2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 n (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64))) (sqrt.f64 n)))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 n)))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 n)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (pow.f64 n (/.f64 k #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))) (/.f64 (pow.f64 n (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (+.f64 (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (+.f64 (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) #s(literal 1 binary64)))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (exp.f64 (PI.f64)))))
(+.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))
(expm1.f64 (log1p.f64 (PI.f64)))
(neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) (PI.f64))) #s(literal 1 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (cbrt.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 k (PI.f64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (-.f64 #s(literal 0 binary64) k)))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) k) (/.f64 #s(literal 1 binary64) k))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) k)) (/.f64 (PI.f64) (-.f64 #s(literal 0 binary64) k)))
(neg.f64 (/.f64 (PI.f64) (-.f64 #s(literal 0 binary64) k)))
(/.f64 (PI.f64) k)
(/.f64 #s(literal 1 binary64) (/.f64 k (PI.f64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) k))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 k (PI.f64))))
(pow.f64 (/.f64 k (PI.f64)) #s(literal -1 binary64))
(*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) k))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) k))
(*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64))
(*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (PI.f64) (-.f64 #s(literal 0 binary64) k)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)))))
(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))) k))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) k))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal -1 binary64)) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) #s(literal -1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k))

simplify775.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
6316×*-lowering-*.f32
6316×*-lowering-*.f64
3548×+-lowering-+.f64
3548×+-lowering-+.f32
1052×distribute-rgt-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02663665
18493530
232153327
083713327
Stop Event
1×iter limit
1×node limit
Counts
336 → 336
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* (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)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt k)
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(+ (sqrt k) (* (pow k 2) (+ (* 1/4 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))))))
(+ (sqrt k) (* (pow k 2) (+ (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))) (* k (+ (* 1/4 (* (sqrt (/ 1 k)) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt k) (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/4 (/ (pow (log (* 2 (* n (PI)))) 2) k))))))))))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
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(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
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(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
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(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
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(* 2 (* n (PI)))
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(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(sqrt n)
(sqrt n)
(sqrt n)
(sqrt n)
(sqrt n)
(sqrt n)
(sqrt n)
(sqrt n)
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
Outputs
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 n (PI.f64)) k) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 n (PI.f64)) k) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 n (PI.f64)) k) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 n (PI.f64)) k) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* (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)
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(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(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)) (pow (sqrt -1) 2))
(neg.f64 (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)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+.f64 (*.f64 k (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) k)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+.f64 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal 1/48 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) k))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/8 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)

eval561.0ms (1.9%)

Compiler

Compiled 26611 to 3112 computations (88.3% saved)

prune463.0ms (1.6%)

Pruning

35 alts after pruning (32 fresh and 3 done)

PrunedKeptTotal
New1531241555
Fresh5813
Picked325
Done011
Total1539351574
Accuracy
100.0%
Counts
1574 → 35
Alt Table
Click to see full alt table
StatusAccuracyProgram
40.7%
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
42.1%
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
30.6%
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
89.6%
(pow.f64 (*.f64 (/.f64 k #s(literal 2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
▶99.5%
(/.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
✓99.5%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓99.5%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
40.7%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
▶52.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
42.0%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
▶40.8%
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
42.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
77.0%
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
42.0%
(*.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
40.6%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
52.2%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
88.3%
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
40.7%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
40.7%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
52.2%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
52.2%
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
▶52.1%
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))))
52.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
✓52.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
52.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
40.9%
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
40.9%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
40.8%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) n)) k))
40.9%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
88.4%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
40.9%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
40.9%
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
40.9%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
▶40.9%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
38.4%
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
Compiler

Compiled 880 to 678 computations (23% saved)

simplify148.0ms (0.5%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓cost-diff0
(sqrt.f64 n)
✓cost-diff128
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))))
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓cost-diff0
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
✓cost-diff0
(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
✓cost-diff0
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))
✓cost-diff0
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
✓cost-diff128
(/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))
✓cost-diff128
(*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n)))
✓cost-diff128
(pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
✓cost-diff128
(/.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
Rules
1950×sum3-define
920×fnmadd-define
736×fmsub-define
494×fma-define
476×fmm-def
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033183
160180
286180
3115180
4167180
5240180
6315180
7360180
8431180
9515180
10634180
11952180
121209180
131545180
143360180
153480180
163480180
03480180
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ (pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2))) (sqrt k))
(pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2)))
(* (PI) (/ -2 (/ -1 n)))
(PI)
(/ -2 (/ -1 n))
-2
(/ -1 n)
-1
n
(+ 1/2 (* k -1/2))
1/2
(* k -1/2)
k
-1/2
(sqrt k)
(sqrt (* (* 2 (PI)) (/ n k)))
(* (* 2 (PI)) (/ n k))
(* 2 (PI))
2
(PI)
(/ n k)
n
k
(/ 1 (pow (/ (* 2 (* (PI) n)) k) -1/2))
1
(pow (/ (* 2 (* (PI) n)) k) -1/2)
(/ (* 2 (* (PI) n)) k)
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
k
-1/2
(/ (sqrt (* 2 (* (PI) n))) (sqrt k))
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(sqrt k)
k
(* (sqrt n) (/ 1 (sqrt (/ k (* 2 (PI))))))
(sqrt n)
n
(/ 1 (sqrt (/ k (* 2 (PI)))))
1
(sqrt (/ k (* 2 (PI))))
(/ k (* 2 (PI)))
k
(* 2 (PI))
2
(PI)
Outputs
(/ (pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2))) (sqrt k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2)))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(* (PI) (/ -2 (/ -1 n)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(PI)
(PI.f64)
(/ -2 (/ -1 n))
(*.f64 n #s(literal 2 binary64))
-2
#s(literal -2 binary64)
(/ -1 n)
(/.f64 #s(literal -1 binary64) n)
-1
#s(literal -1 binary64)
n
(+ 1/2 (* k -1/2))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(* k -1/2)
(*.f64 k #s(literal -1/2 binary64))
k
-1/2
#s(literal -1/2 binary64)
(sqrt k)
(sqrt.f64 k)
(sqrt (* (* 2 (PI)) (/ n k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(* (* 2 (PI)) (/ n k))
(/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))
(* 2 (PI))
(*.f64 (PI.f64) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(PI)
(PI.f64)
(/ n k)
(/.f64 n k)
n
k
(/ 1 (pow (/ (* 2 (* (PI) n)) k) -1/2))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)) #s(literal -1/2 binary64)))
1
#s(literal 1 binary64)
(pow (/ (* 2 (* (PI) n)) k) -1/2)
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)) #s(literal -1/2 binary64))
(/ (* 2 (* (PI) n)) k)
(/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))
(* 2 (* (PI) n))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
k
-1/2
#s(literal -1/2 binary64)
(/ (sqrt (* 2 (* (PI) n))) (sqrt k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(sqrt (* 2 (* (PI) n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))
(* 2 (* (PI) n))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(sqrt k)
(sqrt.f64 k)
k
(* (sqrt n) (/ 1 (sqrt (/ k (* 2 (PI))))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt n)
(sqrt.f64 n)
n
(/ 1 (sqrt (/ k (* 2 (PI)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))))
1
#s(literal 1 binary64)
(sqrt (/ k (* 2 (PI))))
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))))
(/ k (* 2 (PI)))
(/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))
k
(* 2 (PI))
(*.f64 (PI.f64) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(PI)
(PI.f64)

localize492.0ms (1.7%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.8%
(sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓accuracy99.6%
(/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy99.5%
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))))
✓accuracy100.0%
(PI.f64)
✓accuracy99.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy99.4%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
✓accuracy99.7%
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy77.5%
(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (PI.f64))
✓accuracy100.0%
(PI.f64)
✓accuracy99.6%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))
✓accuracy77.5%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
✓accuracy99.7%
(/.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
✓accuracy99.7%
(pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
✓accuracy99.6%
(/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))
✓accuracy99.6%
(*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n)))
Results
369.0ms256×0valid
Compiler

Compiled 199 to 34 computations (82.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 175.0ms
ival-div: 83.0ms (47.3% of total)
ival-pow: 32.0ms (18.3% of total)
ival-mult: 30.0ms (17.1% of total)
ival-sqrt: 22.0ms (12.5% of total)
ival-add: 3.0ms (1.7% of total)
ival-pi: 2.0ms (1.1% of total)
const: 2.0ms (1.1% of total)
backward-pass: 0.0ms (0% of total)

series113.0ms (0.4%)

Counts
20 → 324
Calls
Call 1
Inputs
#<alt (/ (pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2))) (sqrt k))>
#<alt (pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2)))>
#<alt (* (PI) (/ -2 (/ -1 n)))>
#<alt (/ -2 (/ -1 n))>
#<alt (sqrt (* (* 2 (PI)) (/ n k)))>
#<alt (* (* 2 (PI)) (/ n k))>
#<alt (* 2 (PI))>
#<alt (PI)>
#<alt (/ 1 (pow (/ (* 2 (* (PI) n)) k) -1/2))>
#<alt (pow (/ (* 2 (* (PI) n)) k) -1/2)>
#<alt (/ (* 2 (* (PI) n)) k)>
#<alt (* 2 (* (PI) n))>
#<alt (/ (sqrt (* 2 (* (PI) n))) (sqrt k))>
#<alt (sqrt (* 2 (* (PI) n)))>
#<alt (* (PI) n)>
#<alt (* (sqrt n) (/ 1 (sqrt (/ k (* 2 (PI))))))>
#<alt (sqrt n)>
#<alt (/ 1 (sqrt (/ k (* 2 (PI)))))>
#<alt (sqrt (/ k (* 2 (PI))))>
#<alt (/ k (* 2 (PI)))>
Outputs
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (sqrt n)>
#<alt (* -1 (* (sqrt n) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt n) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt n) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt n) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ k (PI))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (PI))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (PI))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (PI))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (PI))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (PI))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (PI))) (sqrt 1/2))>
#<alt (* (sqrt (/ k (PI))) (sqrt 1/2))>
#<alt (* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
#<alt (* 1/2 (/ k (PI)))>
Calls

81 calls:

TimeVariablePointExpression
61.0ms
k
@-inf
(pow (/ (* 2 (* (PI) n)) k) -1/2)
2.0ms
n
@0
(/ (pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2))) (sqrt k))
2.0ms
n
@-inf
(/ 1 (pow (/ (* 2 (* (PI) n)) k) -1/2))
2.0ms
n
@0
(/ 1 (pow (/ (* 2 (* (PI) n)) k) -1/2))
2.0ms
n
@-inf
(* (sqrt n) (/ 1 (sqrt (/ k (* 2 (PI))))))

rewrite995.0ms (3.4%)

Algorithm
1×batch-egg-rewrite
Rules
6556×*-lowering-*.f32
6556×*-lowering-*.f64
2322×/-lowering-/.f32
2322×/-lowering-/.f64
1586×pow-lowering-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033125
1183122
21139122
08924122
Stop Event
1×iter limit
1×node limit
Counts
20 → 1465
Calls
Call 1
Inputs
(/ (pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2))) (sqrt k))
(pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2)))
(* (PI) (/ -2 (/ -1 n)))
(/ -2 (/ -1 n))
(sqrt (* (* 2 (PI)) (/ n k)))
(* (* 2 (PI)) (/ n k))
(* 2 (PI))
(PI)
(/ 1 (pow (/ (* 2 (* (PI) n)) k) -1/2))
(pow (/ (* 2 (* (PI) n)) k) -1/2)
(/ (* 2 (* (PI) n)) k)
(* 2 (* (PI) n))
(/ (sqrt (* 2 (* (PI) n))) (sqrt k))
(sqrt (* 2 (* (PI) n)))
(* (PI) n)
(* (sqrt n) (/ 1 (sqrt (/ k (* 2 (PI))))))
(sqrt n)
(/ 1 (sqrt (/ k (* 2 (PI)))))
(sqrt (/ k (* 2 (PI))))
(/ k (* 2 (PI)))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))))
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal -2 binary64))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal -2 binary64))) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (/.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) (/.f64 k #s(literal -2 binary64))) (/.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal -2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) (sqrt.f64 k)))
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(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64))))
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(/.f64 (neg.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))))) (neg.f64 (sqrt.f64 (PI.f64))))
(pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))))
(*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 (PI.f64) k) #s(literal -1 binary64)))
(*.f64 k (/.f64 #s(literal 1/2 binary64) (PI.f64)))
(*.f64 #s(literal -1/2 binary64) (/.f64 k (-.f64 #s(literal 0 binary64) (PI.f64))))
(*.f64 (/.f64 k #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))))
(*.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) k) (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) k)
(*.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)))
(*.f64 (/.f64 k #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64)))
(*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64))
(*.f64 (/.f64 (/.f64 k #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal 1 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) k)) (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (/.f64 k (cbrt.f64 (PI.f64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (PI.f64))) (/.f64 k (*.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) (/.f64 k #s(literal -2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 k (*.f64 (cbrt.f64 (PI.f64)) #s(literal -2 binary64))))
(*.f64 (/.f64 k (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal 1/2 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 k (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (/.f64 k (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 k (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (/.f64 #s(literal 1 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))))

simplify749.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
4478×*-lowering-*.f32
4478×*-lowering-*.f64
1686×sum4-define
1592×+-lowering-+.f64
1592×+-lowering-+.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01503074
14313020
213253004
335192858
457192858
084032858
Stop Event
1×iter limit
1×node limit
Counts
324 → 324
Calls
Call 1
Inputs
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 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 (* -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 (* -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 (* -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 (/ (* 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)) (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 (* (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 (* (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 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* (sqrt (* 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)))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(sqrt n)
(sqrt n)
(sqrt n)
(sqrt n)
(sqrt n)
(sqrt n)
(sqrt n)
(sqrt n)
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
(* 1/2 (/ k (PI)))
Outputs
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64)))
(sqrt n)
(sqrt.f64 n)
(sqrt n)
(sqrt.f64 n)
(sqrt n)
(sqrt.f64 n)
(sqrt n)
(sqrt.f64 n)
(sqrt n)
(sqrt.f64 n)
(sqrt n)
(sqrt.f64 n)
(sqrt n)
(sqrt.f64 n)
(sqrt n)
(sqrt.f64 n)
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(sqrt.f64 n)
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(sqrt.f64 n)
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(sqrt.f64 n)
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(sqrt.f64 n)
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal -1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal -1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal -1/2 binary64)))
(* (sqrt (/ (PI) k)) (/ (sqrt -1) (sqrt -1/2)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal -1/2 binary64)))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(* (sqrt (/ k (PI))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ k (PI))) (* (sqrt -1) (sqrt -1/2))))
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))
(* 1/2 (/ k (PI)))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64))

eval733.0ms (2.5%)

Compiler

Compiled 33638 to 4757 computations (85.9% saved)

prune750.0ms (2.6%)

Pruning

52 alts after pruning (47 fresh and 5 done)

PrunedKeptTotal
New2162272189
Fresh72027
Picked235
Done123
Total2172522224
Accuracy
100.0%
Counts
2224 → 52
Alt Table
Click to see full alt table
StatusAccuracyProgram
41.9%
(pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
19.4%
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
42.1%
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
30.6%
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
89.6%
(pow.f64 (*.f64 (/.f64 k #s(literal 2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
✓99.5%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓99.5%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
52.1%
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
52.1%
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) n))) (sqrt.f64 k))
40.7%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
52.2%
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64)))) (sqrt.f64 k))
✓52.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
52.2%
(/.f64 (sqrt.f64 n) (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
42.0%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
41.9%
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
40.8%
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
40.8%
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
42.0%
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
40.8%
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
40.8%
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
42.0%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
52.1%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
42.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
38.4%
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))))))))
77.0%
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
52.2%
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 n))
40.6%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
52.2%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
88.3%
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
40.7%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
40.7%
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
40.7%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
52.2%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
52.2%
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
52.1%
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal -1/2 binary64))))
✓52.1%
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))))
52.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
52.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
40.9%
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
40.9%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
40.9%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
40.9%
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
40.9%
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
40.9%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
40.9%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
40.9%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
40.9%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
88.4%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
40.9%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
✓40.9%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
40.8%
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
38.4%
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
Compiler

Compiled 1690 to 826 computations (51.1% saved)

regimes152.0ms (0.5%)

Counts
83 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 n))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 n) (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) n))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) n)) k))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 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 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 (/.f64 k #s(literal 2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (exp.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
(/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))))
(/.f64 (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (sqrt.f64 k))
Outputs
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Calls

4 calls:

33.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
33.0ms
k
31.0ms
(*.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))))
31.0ms
n
Results
AccuracySegmentsBranch
99.7%1k
99.7%1n
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes152.0ms (0.5%)

Counts
80 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 n))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 n) (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) n))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) n)) k))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 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 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 (/.f64 k #s(literal 2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (exp.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
(/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
Outputs
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
Calls

4 calls:

40.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
32.0ms
n
32.0ms
k
29.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.7%1k
99.7%1n
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes140.0ms (0.5%)

Counts
78 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 n))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 n) (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) n))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) n)) k))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 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 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 (/.f64 k #s(literal 2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (exp.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
(/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
Outputs
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
Calls

4 calls:

31.0ms
n
31.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
30.0ms
(*.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))))
30.0ms
k
Results
AccuracySegmentsBranch
99.5%1n
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.5%1k
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes71.0ms (0.2%)

Counts
63 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 n))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 n) (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) n))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) n)) k))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
Outputs
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
Calls

2 calls:

28.0ms
n
25.0ms
k
Results
AccuracySegmentsBranch
99.5%1k
99.5%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes67.0ms (0.2%)

Counts
62 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 n))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 n) (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) n))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) n)) k))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Outputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Calls

2 calls:

28.0ms
k
24.0ms
n
Results
AccuracySegmentsBranch
99.5%1k
99.5%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes63.0ms (0.2%)

Counts
61 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 n))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 n) (pow.f64 (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) n))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) n)) k))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 k))
Outputs
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
Calls

2 calls:

28.0ms
n
25.0ms
k
Results
AccuracySegmentsBranch
58.8%2k
52.2%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes51.0ms (0.2%)

Counts
38 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
Calls

1 calls:

43.0ms
k
Results
AccuracySegmentsBranch
58.8%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes19.0ms (0.1%)

Counts
29 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
Calls

1 calls:

13.0ms
k
Results
AccuracySegmentsBranch
58.8%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes41.0ms (0.1%)

Counts
28 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
Outputs
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64))
Calls

2 calls:

23.0ms
n
13.0ms
k
Results
AccuracySegmentsBranch
42.1%1n
48.7%2k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes30.0ms (0.1%)

Counts
26 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k n) (*.f64 (PI.f64) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) n) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 k (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))) n)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) n)) (PI.f64))) k) #s(literal -1/2 binary64)))
Outputs
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
Calls

2 calls:

12.0ms
k
12.0ms
n
Results
AccuracySegmentsBranch
42.1%1n
42.1%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes15.0ms (0.1%)

Counts
11 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
Outputs
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
Calls

2 calls:

6.0ms
n
6.0ms
k
Results
AccuracySegmentsBranch
40.9%1k
40.9%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0%)

Counts
7 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
Outputs
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
Calls

2 calls:

5.0ms
n
5.0ms
k
Results
AccuracySegmentsBranch
40.9%1k
40.9%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0%)

Counts
6 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
Outputs
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
Calls

2 calls:

7.0ms
k
4.0ms
n
Results
AccuracySegmentsBranch
40.9%1k
40.9%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0%)

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

2 calls:

3.0ms
k
3.0ms
n
Results
AccuracySegmentsBranch
40.9%1k
40.9%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

2 calls:

2.0ms
n
2.0ms
k
Results
AccuracySegmentsBranch
40.8%1k
40.8%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch69.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
61.0ms
3.1576722363398875e+157
4.365693087883307e+168
Results
46.0ms160×0valid
Compiler

Compiled 333 to 247 computations (25.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 34.0ms
ival-pow: 13.0ms (38.8% of total)
ival-mult: 8.0ms (23.9% of total)
ival-div: 5.0ms (14.9% of total)
ival-sqrt: 3.0ms (9% of total)
ival-sub: 2.0ms (6% of total)
ival-pi: 1.0ms (3% of total)
const: 1.0ms (3% of total)
backward-pass: 0.0ms (0% of total)

bsearch75.0ms (0.3%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
68.0ms
3.1576722363398875e+157
4.365693087883307e+168
Results
50.0ms160×0valid
Compiler

Compiled 323 to 237 computations (26.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 40.0ms
ival-pow: 14.0ms (35% of total)
ival-div: 11.0ms (27.5% of total)
ival-mult: 8.0ms (20% of total)
ival-sqrt: 3.0ms (7.5% of total)
ival-sub: 2.0ms (5% of total)
ival-pi: 1.0ms (2.5% of total)
const: 1.0ms (2.5% of total)
backward-pass: 0.0ms (0% of total)

bsearch68.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
61.0ms
3.1576722363398875e+157
4.365693087883307e+168
Results
46.0ms160×0valid
Compiler

Compiled 323 to 237 computations (26.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 34.0ms
ival-pow: 13.0ms (38.7% of total)
ival-mult: 8.0ms (23.8% of total)
ival-div: 5.0ms (14.9% of total)
ival-sqrt: 3.0ms (8.9% of total)
ival-sub: 2.0ms (5.9% of total)
ival-pi: 1.0ms (3% of total)
const: 1.0ms (3% of total)
backward-pass: 0.0ms (0% of total)

bsearch50.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
45.0ms
8.193052119549399e+149
1.5726568381322546e+151
Results
34.0ms112×0valid
Compiler

Compiled 233 to 171 computations (26.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-pow: 9.0ms (38.3% of total)
ival-mult: 5.0ms (21.3% of total)
ival-div: 4.0ms (17% of total)
ival-sqrt: 2.0ms (8.5% of total)
ival-pi: 1.0ms (4.3% of total)
ival-sub: 1.0ms (4.3% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify30.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
38×*-commutative_binary64
12×+-commutative_binary64
8×sub-neg_binary64
6×neg-sub0_binary64
6×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
074243
194243
2103243
3109243
4114243
5116243
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 31999999999999999467493767142135094865931912800559057163744243662734989360032401745007292062270039736039596427019619362161104235141266359470896331850434740224 binary64)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64))) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 31999999999999999467493767142135094865931912800559057163744243662734989360032401745007292062270039736039596427019619362161104235141266359470896331850434740224 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 31999999999999999467493767142135094865931912800559057163744243662734989360032401745007292062270039736039596427019619362161104235141266359470896331850434740224 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 15500000000000001065774348727042225933865500007478443205990605846109914766951141499831288376172534092030102022432413510758517012882813886574995343147008 binary64)) (pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
Outputs
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 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 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 31999999999999999467493767142135094865931912800559057163744243662734989360032401745007292062270039736039596427019619362161104235141266359470896331850434740224 binary64)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64))) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 31999999999999999467493767142135094865931912800559057163744243662734989360032401745007292062270039736039596427019619362161104235141266359470896331850434740224 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64))) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 31999999999999999467493767142135094865931912800559057163744243662734989360032401745007292062270039736039596427019619362161104235141266359470896331850434740224 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 31999999999999999467493767142135094865931912800559057163744243662734989360032401745007292062270039736039596427019619362161104235141266359470896331850434740224 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 31999999999999999467493767142135094865931912800559057163744243662734989360032401745007292062270039736039596427019619362161104235141266359470896331850434740224 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 15500000000000001065774348727042225933865500007478443205990605846109914766951141499831288376172534092030102022432413510758517012882813886574995343147008 binary64)) (pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (*.f64 k k)) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))

soundness4.2s (14.3%)

Rules
6556×*-lowering-*.f32
6556×*-lowering-*.f64
5664×*-lowering-*.f32
5664×*-lowering-*.f64
5256×*-lowering-*.f32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
036147
1208143
21263137
08246137
01392132
13852104
211891816
341751732
477401732
081111732
033125
1183122
21139122
08924122
029132
1169129
21062121
08357121
01314
13014
24714
36914
49013
511313
614913
718813
821413
922813
1022913
022913
02068
113268
285164
0861864
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×saturated
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 723 to 457 computations (36.8% saved)

preprocess318.0ms (1.1%)

Compiler

Compiled 526 to 174 computations (66.9% saved)

end0.0ms (0%)

Profiling

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