Migdal et al, Equation (51)

Time bar (total: 15.7s)

analyze195.0ms (1.2%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%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: 126.0ms
ival-pow: 76.0ms (60.2% of total)
ival-mult: 17.0ms (13.5% of total)
ival-div: 14.0ms (11.1% of total)
ival-sqrt: 8.0ms (6.3% of total)
ival-pi: 5.0ms (4% of total)
ival-sub: 5.0ms (4% of total)
const: 1.0ms (0.8% of total)
backward-pass: 0.0ms (0% of total)

sample4.6s (29.3%)

Results
2.0s3919×5exit
1.1s8256×0valid
572.0ms1976×1invalid
70.0ms507×0invalid
38.0ms242×0unsamplable
Precisions
Click to see histograms. Total time spent on operations: 2.5s
ival-pow: 763.0ms (30.2% of total)
ival-mult: 477.0ms (18.9% of total)
ival-div: 375.0ms (14.9% of total)
backward-pass: 369.0ms (14.6% of total)
ival-sqrt: 206.0ms (8.2% of total)
ival-sub: 169.0ms (6.7% of total)
ival-pi: 126.0ms (5% of total)
const: 39.0ms (1.5% of total)
Bogosity

preprocess94.0ms (0.6%)

Algorithm
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
iter limit
saturated
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)))

explain199.0ms (1.3%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
3223(2.5985308456311224e-47 1.0994244550744063e-294)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
113.0ms512×0valid
Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 49.0ms
ival-pow: 15.0ms (30.5% of total)
ival-mult: 11.0ms (22.3% of total)
ival-div: 10.0ms (20.3% of total)
ival-sqrt: 7.0ms (14.2% of total)
ival-sub: 3.0ms (6.1% of total)
ival-pi: 2.0ms (4.1% of total)
const: 1.0ms (2% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 16 to 12 computations (25% saved)

prune1.0ms (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))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 34 to 25 computations (26.5% saved)

simplify14.0ms (0.1%)

Algorithm
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
iter limit
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)

localize120.0ms (0.8%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(PI.f64)
accuracy99.8%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
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%
(*.f64 (PI.f64) n)
accuracy99.8%
(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 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%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
Results
93.0ms256×0valid
Compiler

Compiled 105 to 21 computations (80% saved)

Precisions
Click to see histograms. Total time spent on operations: 45.0ms
ival-pow: 15.0ms (33.4% of total)
ival-div: 10.0ms (22.3% of total)
ival-mult: 8.0ms (17.8% of total)
ival-sqrt: 7.0ms (15.6% of total)
ival-sub: 3.0ms (6.7% of total)
ival-pi: 1.0ms (2.2% of total)
const: 1.0ms (2.2% of total)
backward-pass: 0.0ms (0% of total)

series94.0ms (0.6%)

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
35.0ms
n
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
23.0ms
n
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
14.0ms
n
@-inf
(* (PI) n)
9.0ms
n
@inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms
k
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite382.0ms (2.4%)

Algorithm
batch-egg-rewrite
Rules
3146×*-lowering-*.f32
3146×*-lowering-*.f64
2906×pow-lowering-pow.f64
2906×pow-lowering-pow.f32
1394×pow-unpow
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02068
110068
247864
3327564
0826264
Stop Event
iter limit
node limit
Counts
10 → 624
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 #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 #s(literal -1/2 binary64) (log.f64 k))))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.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) (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (neg.f64 (/.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)))))))
(neg.f64 (neg.f64 (/.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)))))))
(neg.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #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))))))
(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 (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) 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)))))
(/.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 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 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 (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 (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))))) #s(literal 1 binary64))
(/.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 #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)))) (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
(/.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 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (*.f64 (/.f64 #s(literal -1 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 k #s(literal 2 binary64))))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
(/.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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (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))))
(/.f64 (-.f64 #s(literal 0 binary64) (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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (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) (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))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (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 -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) (*.f64 (/.f64 #s(literal -1 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 k #s(literal 2 binary64))))))
(/.f64 (*.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)) (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) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) #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) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) #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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
(/.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 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 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 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 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 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64))) (-.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 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 n (/.f64 k #s(literal 2 binary64))))
(/.f64 (*.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)))) (-.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) (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 0 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)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.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 (-.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))))) #s(literal -1 binary64)) (sqrt.f64 k))
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64)))) (pow.f64 n (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k)) (pow.f64 n (/.f64 k #s(literal 2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (/.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))))) #s(literal 1 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))
(pow.f64 (/.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 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (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)) (sqrt.f64 k))) #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 #s(literal -1/2 binary64) (/.f64 k #s(literal -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)))
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(*.f64 (neg.f64 (-.f64 #s(literal 0 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 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
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(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 n)) (pow.f64 n (/.f64 k #s(literal -2 binary64))))
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(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 2 binary64)))
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(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
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(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
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(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)) (PI.f64))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(PI.f64)
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(+.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 (*.f64 #s(literal 3 binary64) (log.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)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (PI.f64))) #s(literal 1/2 binary64)))
(fabs.f64 (PI.f64))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(-.f64 (log.f64 (exp.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (PI.f64))))) #s(literal 1 binary64))
(-.f64 (log.f64 (exp.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))))
(fma.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64) #s(literal -1 binary64))
(expm1.f64 (log1p.f64 (PI.f64)))
(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 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 3/2 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)))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 6 binary64))
(pow.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 2/3 binary64))
(pow.f64 (pow.f64 (E.f64) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))))
(pow.f64 (pow.f64 (E.f64) #s(literal 1/3 binary64)) (*.f64 #s(literal 3 binary64) (log.f64 (PI.f64))))
(pow.f64 (pow.f64 (E.f64) #s(literal 3 binary64)) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.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)) (log.f64 (exp.f64 (cbrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (log.f64 (pow.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
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(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))))
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(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 8/3 binary64)) #s(literal 1/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
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(*.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 8/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 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 5/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 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)))

simplify268.0ms (1.7%)

Algorithm
egg-herbie
Rules
5256×*-lowering-*.f32
5256×*-lowering-*.f64
2382×+-lowering-+.f64
2382×+-lowering-+.f32
1466×associate-*r*
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01392132
13852094
211921806
341691722
477331722
081041722
Stop Event
iter limit
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 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (*.f64 k (*.f64 k k))))) (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 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (*.f64 k (*.f64 k k))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 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 (PI.f64) (*.f64 n (*.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)))))
(*.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 (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 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 (PI))) (* -1 (log (/ 1 n)))) (- 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 (PI))) (* -1 (log (/ 1 n)))) (- 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 (PI))) (* -1 (log (/ 1 n)))) (- 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 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
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(sqrt (/ 1 k))
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(sqrt (/ 1 k))
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(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 k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
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(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
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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 (* 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)))

eval106.0ms (0.7%)

Compiler

Compiled 17595 to 1734 computations (90.1% saved)

prune90.0ms (0.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New85811869
Fresh000
Picked112
Done000
Total85912871
Accuracy
100.0%
Counts
871 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (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.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))
96.3%
(/.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))))
98.9%
(/.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)))
99.6%
(/.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)))))
98.9%
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
73.3%
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.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))))
99.6%
(*.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)))
74.0%
(*.f64 (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 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)))
73.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.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))))
35.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
99.6%
(*.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 434 to 298 computations (31.3% saved)

simplify149.0ms (0.9%)

Algorithm
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-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)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
cost-diff6528
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
cost-diff0
(/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
cost-diff0
(sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.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
(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
(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
(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 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
Rules
3560×fnmadd-define
3258×fma-define
1958×fma-lowering-fma.f32
1958×fma-lowering-fma.f64
1036×*-lowering-*.f32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
040259
169255
2111253
3197253
4370244
51119244
63540244
76576244
08306244
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))))
(pow k -1/2)
k
-1/2
(pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(- -1/2 (/ k -2))
(/ k -2)
-2
(* (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)
(* (/ 1 (sqrt (/ k (* 2 (* (PI) n))))) (pow (* 2 (* (PI) n)) (/ k -2)))
(/ 1 (sqrt (/ k (* 2 (* (PI) n)))))
1
(sqrt (/ k (* 2 (* (PI) n))))
(/ k (* 2 (* (PI) n)))
k
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(pow (* 2 (* (PI) n)) (/ k -2))
(/ k -2)
-2
(/ (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
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.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)) (- -1/2 (/ k -2)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(* 2 (* (PI) n))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
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)))
(/ k -2)
(/.f64 k #s(literal -2 binary64))
-2
#s(literal -2 binary64)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/ (* n (PI)) k)
(/.f64 (*.f64 (PI.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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)))
(* (* 2 (PI)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (PI))
(*.f64 #s(literal 2 binary64) (PI.f64))
2
#s(literal 2 binary64)
(PI)
(PI.f64)
n
(/ (- 1 k) 2)
(+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))
(- 1 k)
(-.f64 #s(literal 1 binary64) k)
(* (/ 1 (sqrt (/ k (* 2 (* (PI) n))))) (pow (* 2 (* (PI) n)) (/ k -2)))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/ 1 (sqrt (/ k (* 2 (* (PI) n)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
1
#s(literal 1 binary64)
(sqrt (/ k (* 2 (* (PI) n))))
(sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(/ k (* 2 (* (PI) n)))
(/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
k
(* 2 (* (PI) n))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(pow (* 2 (* (PI) n)) (/ k -2))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal -2 binary64)))
(/ k -2)
(/.f64 k #s(literal -2 binary64))
-2
#s(literal -2 binary64)
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k))))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)))
(* 2 (* (PI) n))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
2
#s(literal 2 binary64)
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(- 1/2 (/ k 2))
(+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 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)

localize481.0ms (3.1%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy99.8%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
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)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
accuracy94.4%
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
accuracy75.0%
(PI.f64)
accuracy99.7%
(/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
accuracy99.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
accuracy88.6%
(sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
accuracy75.0%
(PI.f64)
accuracy99.8%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy99.8%
(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 (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))))
accuracy75.0%
(PI.f64)
accuracy99.7%
(/.f64 (*.f64 n (PI.f64)) k)
accuracy99.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
accuracy88.1%
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
accuracy75.0%
(PI.f64)
accuracy99.8%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))
accuracy99.8%
(*.f64 (PI.f64) n)
accuracy99.8%
(/.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)))))
accuracy75.0%
(PI.f64)
Results
231.0ms64×5exit
162.0ms190×0valid
1.0ms0invalid
Compiler

Compiled 269 to 41 computations (84.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 161.0ms
ival-pow: 66.0ms (41% of total)
backward-pass: 34.0ms (21.1% of total)
ival-div: 19.0ms (11.8% of total)
ival-mult: 18.0ms (11.2% of total)
ival-sqrt: 9.0ms (5.6% of total)
ival-sub: 5.0ms (3.1% of total)
ival-log: 4.0ms (2.5% of total)
ival-exp: 3.0ms (1.9% of total)
const: 1.0ms (0.6% of total)
ival-pi: 1.0ms (0.6% of total)

series52.0ms (0.3%)

Counts
22 → 408
Calls
Call 1
Inputs
#<alt (/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))))>
#<alt (pow k -1/2)>
#<alt (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))>
#<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 (* (/ 1 (sqrt (/ k (* 2 (* (PI) n))))) (pow (* 2 (* (PI) n)) (/ k -2)))>
#<alt (/ 1 (sqrt (/ k (* 2 (* (PI) n)))))>
#<alt (sqrt (/ k (* 2 (* (PI) n))))>
#<alt (/ k (* 2 (* (PI) n)))>
#<alt (exp (* 1/2 (log k)))>
#<alt (/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (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)) (/ 1 (sqrt 1/2)))>
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#<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 (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 (/ 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 (* (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 (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<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 (* (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 (* 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

102 calls:

TimeVariablePointExpression
7.0ms
k
@inf
(sqrt (/ k (* 2 (* (PI) n))))
2.0ms
k
@0
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))))
1.0ms
n
@0
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))))
1.0ms
n
@inf
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))))
1.0ms
n
@-inf
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))))

rewrite407.0ms (2.6%)

Algorithm
batch-egg-rewrite
Rules
5090×*-lowering-*.f32
5090×*-lowering-*.f64
3042×/-lowering-/.f32
3042×/-lowering-/.f64
1980×sum5-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040165
1190156
2953149
37300149
08311149
Stop Event
iter limit
node limit
Counts
22 → 2012
Calls
Call 1
Inputs
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))))
(pow k -1/2)
(pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))
(* 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))
(* (/ 1 (sqrt (/ k (* 2 (* (PI) n))))) (pow (* 2 (* (PI) n)) (/ k -2)))
(/ 1 (sqrt (/ k (* 2 (* (PI) n)))))
(sqrt (/ k (* 2 (* (PI) n))))
(/ k (* 2 (* (PI) n)))
(exp (* 1/2 (log k)))
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k))))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(PI)
(* (PI) n)
(* (* 2 (PI)) n)
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (log.f64 k))))
(exp.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) (*.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 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 #s(literal 1/2 binary64) (-.f64 (log.f64 k) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))) #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 -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal -2 binary64) k))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal -2 binary64) k)) (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)))))))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 k) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))))
(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))) (/.f64 #s(literal -2 binary64) k)) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))))))
(exp.f64 (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) 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 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 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))))))
(-.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 -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 -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 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (neg.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)))))
(neg.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #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 #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) (/.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 (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 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 (/.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))))) #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 -1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (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 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #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 (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 (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 (pow.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
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(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 n (sqrt.f64 (PI.f64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) n))
(*.f64 (-.f64 #s(literal 0 binary64) n) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
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(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))) n)
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) n)) (PI.f64))
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(*.f64 (*.f64 (*.f64 n (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)))
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
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(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(-.f64 #s(literal 0 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal -2 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))
(/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal -2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 (PI.f64) (/.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)))
(*.f64 (PI.f64) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) n)))
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(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
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simplify382.0ms (2.4%)

Algorithm
egg-herbie
Rules
5380×*-lowering-*.f32
5380×*-lowering-*.f64
2876×+-lowering-+.f64
2876×+-lowering-+.f32
1388×fma-lowering-fma.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02945071
19354812
233074497
375714481
080384481
Stop Event
iter limit
node limit
Counts
408 → 408
Calls
Call 1
Inputs
(* (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)
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(/ (+ (* 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)
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(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(sqrt (/ 1 k))
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(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
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(/ 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)) (/ 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 (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (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 (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt -1)) (sqrt -1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt -1)) (sqrt -1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt -1)) (sqrt -1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt -1)) (sqrt -1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 1/2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt -1)) (sqrt -1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt -1)) (sqrt -1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt -1)) (sqrt -1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (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 (/ (* 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 (/ 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))))
(* (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)))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(* 1/2 (/ k (* n (PI))))
(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)))
(* (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))))
(* 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)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k (*.f64 (*.f64 k k) n))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 1/2 binary64)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (+.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (+.f64 (*.f64 (/.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)))) (*.f64 (-.f64 #s(literal 0 binary64) k) (+.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (*.f64 #s(literal -1/24 binary64) (sqrt.f64 (*.f64 k (*.f64 k k))))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/8 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))))))))) k)
(* (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 n (*.f64 (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 n (*.f64 (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 n (*.f64 (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 n (*.f64 (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 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
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eval509.0ms (3.2%)

Compiler

Compiled 62216 to 5392 computations (91.3% saved)

prune639.0ms (4.1%)

Pruning

29 alts after pruning (25 fresh and 4 done)

PrunedKeptTotal
New2956252981
Fresh606
Picked235
Done011
Total2964292993
Accuracy
100.0%
Counts
2993 → 29
Alt Table
Click to see full alt table
StatusAccuracyProgram
36.1%
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
88.0%
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
74.1%
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))) #s(literal -1/2 binary64))
73.4%
(/.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
98.9%
(/.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 1/2 binary64) (*.f64 (PI.f64) n))))
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))
96.3%
(/.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))))
99.6%
(/.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)))))
47.2%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
35.3%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
99.6%
(/.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)))))
47.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
36.0%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
36.0%
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64)))
47.2%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64))))
47.2%
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
47.1%
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64)))
35.9%
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64)))
47.2%
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
47.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))
47.2%
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
74.4%
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))))
35.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
35.5%
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
47.2%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
35.4%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
47.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
35.6%
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
33.4%
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64)))
Compiler

Compiled 757 to 594 computations (21.5% saved)

simplify21.0ms (0.1%)

Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))
cost-diff0
(*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
cost-diff128
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
cost-diff0
(/.f64 k #s(literal 2 binary64))
cost-diff0
(sqrt.f64 (/.f64 k #s(literal 2 binary64)))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64))))
cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))
cost-diff0
(/.f64 n k)
cost-diff0
(*.f64 (/.f64 n k) (PI.f64))
cost-diff0
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
cost-diff0
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(*.f64 (PI.f64) n)
cost-diff0
(/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
cost-diff0
(/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)
cost-diff0
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
cost-diff0
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 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 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
Rules
148×sum3-define
130×fma-define
120×*-lowering-*.f32
120×*-lowering-*.f64
86×/-lowering-/.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037189
166186
2111185
3165183
4205183
5238183
6288183
7326183
8343183
9373183
10472183
0472183
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))))
(sqrt (/ 1 k))
(/ 1 k)
1
k
(pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))
(* n (* (PI) 2))
n
(* (PI) 2)
(PI)
2
(+ -1/2 (* k 1/2))
-1/2
(* k 1/2)
1/2
(sqrt (/ (/ (* (PI) n) 1/2) k))
(/ (/ (* (PI) n) 1/2) k)
(/ (* (PI) n) 1/2)
(* (PI) n)
(PI)
n
1/2
k
(* (sqrt (* (/ n k) (PI))) (sqrt 2))
(sqrt (* (/ n k) (PI)))
(* (/ n k) (PI))
(/ n k)
n
k
(PI)
(sqrt 2)
2
(* (/ 1 (sqrt (/ k 2))) (sqrt (* (PI) n)))
(/ 1 (sqrt (/ k 2)))
1
(sqrt (/ k 2))
(/ k 2)
k
2
(sqrt (* (PI) n))
(* (PI) n)
(PI)
n
(/ -1 (* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k))))
-1
(* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k)))
(sqrt (/ 1/2 (* (PI) n)))
(/ 1/2 (* (PI) n))
1/2
(* (PI) n)
(PI)
n
(- 0 (sqrt k))
0
(sqrt k)
k
Outputs
(/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))))
(/.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))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
1
#s(literal 1 binary64)
k
(pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))
(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) 2))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
n
(* (PI) 2)
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(+ -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))
1/2
#s(literal 1/2 binary64)
(sqrt (/ (/ (* (PI) n) 1/2) k))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) k))
(/ (/ (* (PI) n) 1/2) k)
(/.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) k)
(/ (* (PI) n) 1/2)
(/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))
(* (PI) n)
(*.f64 n (PI.f64))
(PI)
(PI.f64)
n
1/2
#s(literal 1/2 binary64)
k
(* (sqrt (* (/ n k) (PI))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (* (/ n k) (PI)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(* (/ n k) (PI))
(*.f64 (PI.f64) (/.f64 n k))
(/ n k)
(/.f64 n k)
n
k
(PI)
(PI.f64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* (/ 1 (sqrt (/ k 2))) (sqrt (* (PI) n)))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 k #s(literal 2 binary64))))
(/ 1 (sqrt (/ k 2)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64))))
1
#s(literal 1 binary64)
(sqrt (/ k 2))
(sqrt.f64 (/.f64 k #s(literal 2 binary64)))
(/ k 2)
(/.f64 k #s(literal 2 binary64))
k
2
#s(literal 2 binary64)
(sqrt (* (PI) n))
(sqrt.f64 (*.f64 n (PI.f64)))
(* (PI) n)
(*.f64 n (PI.f64))
(PI)
(PI.f64)
n
(/ -1 (* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))
-1
#s(literal -1 binary64)
(* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(sqrt (/ 1/2 (* (PI) n)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))
(/ 1/2 (* (PI) n))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
1/2
#s(literal 1/2 binary64)
(* (PI) n)
(*.f64 n (PI.f64))
(PI)
(PI.f64)
n
(- 0 (sqrt k))
(-.f64 #s(literal 0 binary64) (sqrt.f64 k))
0
#s(literal 0 binary64)
(sqrt k)
(sqrt.f64 k)
k

localize799.0ms (5.1%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy99.7%
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
accuracy99.7%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
accuracy99.7%
(/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))
accuracy75.0%
(PI.f64)
accuracy99.8%
(*.f64 (PI.f64) n)
accuracy99.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64))))
accuracy99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))
accuracy75.0%
(PI.f64)
accuracy99.7%
(*.f64 (/.f64 n k) (PI.f64))
accuracy99.5%
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy88.1%
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
accuracy75.0%
(PI.f64)
accuracy99.8%
(*.f64 (PI.f64) n)
accuracy99.7%
(/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)
accuracy88.1%
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
accuracy75.0%
(PI.f64)
accuracy99.8%
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
accuracy99.8%
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy99.8%
(/.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)))))
accuracy75.0%
(PI.f64)
Results
547.0ms64×5exit
174.0ms190×0valid
1.0ms0invalid
Compiler

Compiled 202 to 38 computations (81.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 144.0ms
ival-sqrt: 58.0ms (40.2% of total)
backward-pass: 32.0ms (22.2% of total)
ival-div: 21.0ms (14.5% of total)
ival-mult: 17.0ms (11.8% of total)
ival-pow: 10.0ms (6.9% of total)
ival-sub: 2.0ms (1.4% of total)
ival-add: 2.0ms (1.4% of total)
const: 1.0ms (0.7% of total)
ival-pi: 1.0ms (0.7% of total)

series26.0ms (0.2%)

Counts
22 → 384
Calls
Call 1
Inputs
#<alt (/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))))>
#<alt (sqrt (/ 1 k))>
#<alt (/ 1 k)>
#<alt (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))>
#<alt (sqrt (/ (/ (* (PI) n) 1/2) k))>
#<alt (/ (/ (* (PI) n) 1/2) k)>
#<alt (/ (* (PI) n) 1/2)>
#<alt (* (PI) n)>
#<alt (* (sqrt (* (/ n k) (PI))) (sqrt 2))>
#<alt (sqrt (* (/ n k) (PI)))>
#<alt (* (/ n k) (PI))>
#<alt (/ n k)>
#<alt (* (/ 1 (sqrt (/ k 2))) (sqrt (* (PI) n)))>
#<alt (/ 1 (sqrt (/ k 2)))>
#<alt (sqrt (/ k 2))>
#<alt (/ k 2)>
#<alt (/ -1 (* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k))))>
#<alt (* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k)))>
#<alt (sqrt (/ 1/2 (* (PI) n)))>
#<alt (/ 1/2 (* (PI) n))>
#<alt (PI)>
#<alt (* n (* (PI) 2))>
Outputs
#<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 (/ 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 (* (+ (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 (* (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 (* 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 (* (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 k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n 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 (* (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 (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 (/ 1 k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt k) (sqrt 1/2))>
#<alt (* (sqrt k) (sqrt 1/2))>
#<alt (* (sqrt k) (sqrt 1/2))>
#<alt (* (sqrt k) (sqrt 1/2))>
#<alt (* (sqrt k) (sqrt 1/2))>
#<alt (* (sqrt k) (sqrt 1/2))>
#<alt (* (sqrt k) (sqrt 1/2))>
#<alt (* (sqrt k) (sqrt 1/2))>
#<alt (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))>
#<alt (* 1/2 k)>
#<alt (* 1/2 k)>
#<alt (* 1/2 k)>
#<alt (* 1/2 k)>
#<alt (* 1/2 k)>
#<alt (* 1/2 k)>
#<alt (* 1/2 k)>
#<alt (* 1/2 k)>
#<alt (* 1/2 k)>
#<alt (* 1/2 k)>
#<alt (* 1/2 k)>
#<alt (* 1/2 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)) (/ 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 (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (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 (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))>
#<alt (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* 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 (PI)))>
Calls

96 calls:

TimeVariablePointExpression
3.0ms
k
@inf
(sqrt (/ (/ (* (PI) n) 1/2) k))
1.0ms
n
@-inf
(/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))))
1.0ms
n
@-inf
(sqrt (/ (/ (* (PI) n) 1/2) k))
1.0ms
n
@inf
(/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))))
1.0ms
n
@0
(/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))))

rewrite421.0ms (2.7%)

Algorithm
batch-egg-rewrite
Rules
4656×*-lowering-*.f32
4656×*-lowering-*.f64
2640×/-lowering-/.f32
2640×/-lowering-/.f64
1376×sum4-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037130
1171126
2918125
36906125
08222125
Stop Event
iter limit
node limit
Counts
22 → 1533
Calls
Call 1
Inputs
(/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))))
(sqrt (/ 1 k))
(/ 1 k)
(pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))
(sqrt (/ (/ (* (PI) n) 1/2) k))
(/ (/ (* (PI) n) 1/2) k)
(/ (* (PI) n) 1/2)
(* (PI) n)
(* (sqrt (* (/ n k) (PI))) (sqrt 2))
(sqrt (* (/ n k) (PI)))
(* (/ n k) (PI))
(/ n k)
(* (/ 1 (sqrt (/ k 2))) (sqrt (* (PI) n)))
(/ 1 (sqrt (/ k 2)))
(sqrt (/ k 2))
(/ k 2)
(/ -1 (* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k))))
(* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k)))
(sqrt (/ 1/2 (* (PI) n)))
(/ 1/2 (* (PI) n))
(PI)
(* n (* (PI) 2))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k)))))
(exp.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))))
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(/.f64 #s(literal 1 binary64) (exp.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))
(/.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) n))
(/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)))
(/.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) n))
(/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))
(/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(/.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))))
(/.f64 (-.f64 #s(literal 0 binary64) n) (/.f64 #s(literal -1/2 binary64) (PI.f64)))
(/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (exp.f64 (log.f64 (*.f64 n (PI.f64)))) (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) (*.f64 n (PI.f64))))) (exp.f64 (log.f64 #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(*.f64 n (/.f64 (PI.f64) #s(literal 1/2 binary64)))
(*.f64 n (/.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 n (neg.f64 (*.f64 (PI.f64) #s(literal -2 binary64))))
(*.f64 n (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -2 binary64)))
(*.f64 (PI.f64) (/.f64 n #s(literal 1/2 binary64)))
(*.f64 (PI.f64) (exp.f64 (log.f64 (/.f64 n #s(literal 1/2 binary64)))))
(*.f64 (PI.f64) (*.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (PI.f64) (/.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) n)
(*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) n) #s(literal -1 binary64)))
(*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n #s(literal 1 binary64)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(*.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1 binary64))
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(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 n #s(literal 1/2 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))) n))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 n (PI.f64))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal -2 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))) #s(literal -1 binary64)))
(*.f64 #s(literal -2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 n (PI.f64))) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) n) (*.f64 (PI.f64) #s(literal -2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) n) (/.f64 (PI.f64) #s(literal -1/2 binary64)))
(*.f64 (/.f64 n #s(literal 1/2 binary64)) (PI.f64))
(*.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 (PI.f64) #s(literal 1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 n #s(literal -1/2 binary64)))
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(*.f64 (/.f64 n #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 n (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))))
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(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) (sqrt.f64 (PI.f64)))
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(*.f64 (exp.f64 (log.f64 (*.f64 n (PI.f64)))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1 binary64)) (PI.f64))
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(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (/.f64 (PI.f64) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) n)
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(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal -2 binary64) n) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 (*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) n)) (PI.f64))
(*.f64 (*.f64 (/.f64 n #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (PI.f64))) (-.f64 #s(literal 0 binary64) n))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 n #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64))
(*.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))

simplify274.0ms (1.7%)

Algorithm
egg-herbie
Rules
3362×*-lowering-*.f32
3362×*-lowering-*.f64
1960×fnmadd-define
1820×fma-lowering-fma.f32
1820×fma-lowering-fma.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01773303
15373196
218423106
353743094
080803094
Stop Event
iter limit
node limit
Counts
384 → 384
Calls
Call 1
Inputs
(* (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)))))))
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(* (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))
(/ 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 (* (+ (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)))
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(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 k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n 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)))
(* (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 (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 (/ 1 k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))
(* (sqrt k) (sqrt 1/2))
(* (sqrt k) (sqrt 1/2))
(* (sqrt k) (sqrt 1/2))
(* (sqrt k) (sqrt 1/2))
(* (sqrt k) (sqrt 1/2))
(* (sqrt k) (sqrt 1/2))
(* (sqrt k) (sqrt 1/2))
(* (sqrt k) (sqrt 1/2))
(* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))
(* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))
(* 1/2 k)
(* 1/2 k)
(* 1/2 k)
(* 1/2 k)
(* 1/2 k)
(* 1/2 k)
(* 1/2 k)
(* 1/2 k)
(* 1/2 k)
(* 1/2 k)
(* 1/2 k)
(* 1/2 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)) (/ 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 (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (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))))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* 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 (PI)))
Outputs
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (+.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (-.f64 (*.f64 (/.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) (*.f64 k (+.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) #s(literal -1/24 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/8 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))))))))) k)
(* (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 n (*.f64 (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 n (*.f64 (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 n (*.f64 (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 n (*.f64 (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #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 n (*.f64 (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 n (*.f64 (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 n (*.f64 (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 n (*.f64 (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 n (*.f64 (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 n (*.f64 (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 n (*.f64 (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 n (*.f64 (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)))
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
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(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #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)))))
(* (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)))))
(* (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)))))
(* (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)))))
(* (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)))))
(* (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)))))
(* (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)))))
(* (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)))))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.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)))

eval339.0ms (2.2%)

Compiler

Compiled 31960 to 4489 computations (86% saved)

prune303.0ms (1.9%)

Pruning

51 alts after pruning (45 fresh and 6 done)

PrunedKeptTotal
New2184312215
Fresh61420
Picked145
Done224
Total2193512244
Accuracy
100.0%
Counts
2244 → 51
Alt Table
Click to see full alt table
StatusAccuracyProgram
36.0%
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
74.1%
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))) #s(literal -1/2 binary64))
73.4%
(/.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
35.3%
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
35.8%
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
99.5%
(/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
47.3%
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)))
98.9%
(/.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 1/2 binary64) (*.f64 (PI.f64) n))))
96.3%
(/.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))))
47.2%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
47.2%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
35.3%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
99.6%
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
99.6%
(/.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)))))
47.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
36.0%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
36.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
35.5%
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
35.9%
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
47.2%
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
99.6%
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
47.2%
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
47.2%
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
47.1%
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64)))
47.2%
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
47.2%
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
47.1%
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
47.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))
47.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n)))
47.2%
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
74.4%
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))))
35.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
35.4%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
47.2%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
35.5%
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
35.4%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
47.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
47.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
35.6%
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
35.5%
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
35.6%
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
35.6%
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k))
35.5%
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
35.6%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
35.6%
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k)))
35.5%
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n))))
35.6%
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n))
35.6%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
35.6%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
35.6%
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))))
33.4%
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64)))
Compiler

Compiled 1275 to 1001 computations (21.5% saved)

simplify12.0ms (0.1%)

Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(PI.f64)
cost-diff0
(/.f64 (PI.f64) #s(literal 1/2 binary64))
cost-diff0
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
cost-diff64
(pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 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 1/2 binary64)))
cost-diff0
(/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))
cost-diff0
(/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))
cost-diff0
(sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
cost-diff0
(*.f64 n (PI.f64))
cost-diff0
(/.f64 #s(literal 2 binary64) k)
cost-diff0
(*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))
cost-diff0
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
cost-diff0
(pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 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 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
Rules
116×*-lowering-*.f32
116×*-lowering-*.f64
74×/-lowering-/.f32
74×/-lowering-/.f64
46×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
032170
153170
281170
3113170
4132170
5142170
6142170
0142170
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))))
(sqrt (/ 1 k))
(/ 1 k)
1
k
(pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))
(/ 1/2 (* n (PI)))
1/2
(* n (PI))
n
(PI)
(+ 1/2 (/ k -2))
(/ k -2)
-2
(sqrt (* (/ 2 k) (* n (PI))))
(* (/ 2 k) (* n (PI)))
(/ 2 k)
2
k
(* n (PI))
n
(PI)
(/ 1 (sqrt (/ k (/ n (/ 1/2 (PI))))))
1
(sqrt (/ k (/ n (/ 1/2 (PI)))))
(/ k (/ n (/ 1/2 (PI))))
k
(/ n (/ 1/2 (PI)))
n
(/ 1/2 (PI))
1/2
(PI)
(/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
n
(PI)
k
(sqrt 1/2)
1/2
(/ (pow (/ (PI) 1/2) 1/2) (pow (/ k n) 1/2))
(pow (/ (PI) 1/2) 1/2)
(/ (PI) 1/2)
(PI)
1/2
(pow (/ k n) 1/2)
(/ k n)
k
n
Outputs
(/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.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 (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
1/2
#s(literal 1/2 binary64)
(* n (PI))
(*.f64 n (PI.f64))
n
(PI)
(PI.f64)
(+ 1/2 (/ k -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))
(/ k -2)
(/.f64 k #s(literal -2 binary64))
-2
#s(literal -2 binary64)
(sqrt (* (/ 2 k) (* n (PI))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k)))
(* (/ 2 k) (* n (PI)))
(*.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
2
#s(literal 2 binary64)
k
(* n (PI))
(*.f64 n (PI.f64))
n
(PI)
(PI.f64)
(/ 1 (sqrt (/ k (/ n (/ 1/2 (PI))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))))
1
#s(literal 1 binary64)
(sqrt (/ k (/ n (/ 1/2 (PI)))))
(sqrt.f64 (/.f64 k (/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))))
(/ k (/ n (/ 1/2 (PI))))
(/.f64 k (/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))
k
(/ n (/ 1/2 (PI)))
(/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))
n
(/ 1/2 (PI))
(/.f64 #s(literal 1/2 binary64) (PI.f64))
1/2
#s(literal 1/2 binary64)
(PI)
(PI.f64)
(/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(* n (PI))
(*.f64 n (PI.f64))
n
(PI)
(PI.f64)
k
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(/ (pow (/ (PI) 1/2) 1/2) (pow (/ k n) 1/2))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64))) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
(pow (/ (PI) 1/2) 1/2)
(sqrt.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)))
(/ (PI) 1/2)
(/.f64 (PI.f64) #s(literal 1/2 binary64))
(PI)
(PI.f64)
1/2
#s(literal 1/2 binary64)
(pow (/ k n) 1/2)
(pow.f64 (/.f64 k n) #s(literal 1/2 binary64))
(/ k n)
(/.f64 k n)
k
n

localize397.0ms (2.5%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy99.4%
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
accuracy98.8%
(pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
accuracy88.6%
(pow.f64 (/.f64 k n) #s(literal 1/2 binary64))
accuracy75.0%
(PI.f64)
accuracy99.7%
(/.f64 (*.f64 n (PI.f64)) k)
accuracy99.4%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy88.1%
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
accuracy75.0%
(PI.f64)
accuracy99.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
accuracy99.6%
(/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))
accuracy88.6%
(sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))
accuracy75.0%
(PI.f64)
accuracy99.8%
(*.f64 n (PI.f64))
accuracy99.6%
(*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))
accuracy88.1%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
accuracy75.0%
(PI.f64)
accuracy99.8%
(*.f64 n (PI.f64))
accuracy99.8%
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
accuracy99.7%
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
accuracy75.0%
(PI.f64)
Results
231.0ms64×5exit
111.0ms190×0valid
1.0ms0invalid
Compiler

Compiled 182 to 33 computations (81.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 103.0ms
ival-div: 35.0ms (34% of total)
backward-pass: 25.0ms (24.3% of total)
ival-pow: 22.0ms (21.4% of total)
ival-sqrt: 11.0ms (10.7% of total)
ival-mult: 4.0ms (3.9% of total)
ival-add: 2.0ms (1.9% of total)
const: 1.0ms (1% of total)
ival-pi: 1.0ms (1% of total)

series86.0ms (0.5%)

Counts
21 → 360
Calls
Call 1
Inputs
#<alt (/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))))>
#<alt (sqrt (/ 1 k))>
#<alt (/ 1 k)>
#<alt (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))>
#<alt (sqrt (* (/ 2 k) (* n (PI))))>
#<alt (* (/ 2 k) (* n (PI)))>
#<alt (/ 2 k)>
#<alt (* n (PI))>
#<alt (/ 1 (sqrt (/ k (/ n (/ 1/2 (PI))))))>
#<alt (sqrt (/ k (/ n (/ 1/2 (PI)))))>
#<alt (/ k (/ n (/ 1/2 (PI))))>
#<alt (/ n (/ 1/2 (PI)))>
#<alt (/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (/ (* n (PI)) k)>
#<alt (pow (/ (PI) 1/2) 1/2)>
#<alt (/ (pow (/ (PI) 1/2) 1/2) (pow (/ k n) 1/2))>
#<alt (/ (PI) 1/2)>
#<alt (PI)>
#<alt (/ 1/2 (* n (PI)))>
#<alt (pow (/ k n) 1/2)>
Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (/ (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (/ 1/2 (* 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 (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)>
#<alt (/ (+ (* k (+ (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/48 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/2 (* (log (/ 1/2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))))>
#<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 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (+ (* -1/2 (* (* k (* (log (/ 1/2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* 1/8 (* (* k (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))>
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 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)) (* (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 (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 (* 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 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 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 (* (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 (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 (/ 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 (* (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 (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* n (PI))))>
#<alt (* 1/2 (/ k (* 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)))>
#<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)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (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 (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 (* (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)) 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)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (sqrt (/ k n))>
#<alt (* (sqrt (/ k n)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k n)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k n)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k n)) (pow (sqrt -1) 2))>
Calls

90 calls:

TimeVariablePointExpression
42.0ms
n
@0
(/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))))
17.0ms
n
@-inf
(/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))))
7.0ms
n
@inf
(/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))))
3.0ms
k
@-inf
(/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))))
2.0ms
k
@0
(pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))

rewrite357.0ms (2.3%)

Algorithm
batch-egg-rewrite
Rules
4518×*-lowering-*.f32
4518×*-lowering-*.f64
3152×/-lowering-/.f32
3152×/-lowering-/.f64
972×sum5-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
032124
1183120
21057120
37701120
08207120
Stop Event
iter limit
node limit
Counts
21 → 1764
Calls
Call 1
Inputs
(/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))))
(sqrt (/ 1 k))
(/ 1 k)
(pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))
(sqrt (* (/ 2 k) (* n (PI))))
(* (/ 2 k) (* n (PI)))
(/ 2 k)
(* n (PI))
(/ 1 (sqrt (/ k (/ n (/ 1/2 (PI))))))
(sqrt (/ k (/ n (/ 1/2 (PI)))))
(/ k (/ n (/ 1/2 (PI))))
(/ n (/ 1/2 (PI)))
(/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(pow (/ (PI) 1/2) 1/2)
(/ (pow (/ (PI) 1/2) 1/2) (pow (/ k n) 1/2))
(/ (PI) 1/2)
(PI)
(/ 1/2 (* n (PI)))
(pow (/ k n) 1/2)
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))))
(exp.f64 (+.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k)))))
(exp.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal -1/2 binary64) (PI.f64)))) (*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (neg.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64))))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1 binary64)) (*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))
(/.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (/.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.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 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) #s(literal 1 binary64))
(*.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.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 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (pow.f64 (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))))
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simplify262.0ms (1.7%)

Algorithm
egg-herbie
Rules
3708×*-lowering-*.f32
3708×*-lowering-*.f64
1900×fma-lowering-fma.f32
1900×fma-lowering-fma.f64
1518×sum3-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01693229
15063049
217793022
354762950
080972950
Stop Event
iter limit
node limit
Counts
360 → 360
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/ (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
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(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))))
(sqrt (/ 1 k))
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
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(* (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))))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
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(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
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(* n (PI))
(* n (PI))
(* n (PI))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))
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(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
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(/ (* n (PI)) k)
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(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
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(/ (* n (PI)) k)
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(/ (* n (PI)) k)
(/ (* n (PI)) k)
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(/ (* n (PI)) k)
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(/ (* n (PI)) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(/ 1/2 (* n (PI)))
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(/ 1/2 (* n (PI)))
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(sqrt (/ k n))
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(sqrt (/ k n))
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Outputs
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(/ (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
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(/.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)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 k n))
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 k n))
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 k n))
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(sqrt (/ k n))
(sqrt.f64 (/.f64 k n))
(* (sqrt (/ k n)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k n)))
(* (sqrt (/ k n)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k n)))
(* (sqrt (/ k n)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k n)))
(* (sqrt (/ k n)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k n)))

eval319.0ms (2%)

Compiler

Compiled 35827 to 5375 computations (85% saved)

prune305.0ms (1.9%)

Pruning

64 alts after pruning (56 fresh and 8 done)

PrunedKeptTotal
New2460282488
Fresh122840
Picked235
Done156
Total2475642539
Accuracy
100.0%
Counts
2539 → 64
Alt Table
Click to see full alt table
StatusAccuracyProgram
36.0%
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
74.1%
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))) #s(literal -1/2 binary64))
72.9%
(/.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))
35.3%
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64)))
35.9%
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #s(literal -1/2 binary64))))
35.8%
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n)))
99.5%
(/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
47.3%
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)))
98.9%
(/.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 1/2 binary64) (*.f64 (PI.f64) n))))
96.3%
(/.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))))
47.2%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
99.6%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
47.2%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
35.3%
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
35.3%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
35.3%
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64)))
35.3%
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
99.6%
(/.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)))))
35.4%
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
47.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
47.3%
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))))
36.0%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
47.1%
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
47.2%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n)))
35.5%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
47.2%
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
35.9%
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
35.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k))))
36.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
36.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
36.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
36.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k)))
33.9%
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))))
99.6%
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
47.2%
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
47.2%
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
47.2%
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
47.2%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))
47.1%
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
47.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))
47.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n)))
47.2%
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
74.4%
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))))
35.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
47.2%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n))
35.4%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
47.2%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
35.5%
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
35.4%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
47.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
35.5%
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
35.6%
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
35.6%
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
35.6%
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k))
35.5%
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
35.6%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
35.6%
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k)))
35.5%
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n))))
35.6%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
35.6%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k)))
35.6%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
35.5%
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
33.4%
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64)))
33.9%
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64)))
Compiler

Compiled 1994 to 977 computations (51% saved)

regimes118.0ms (0.8%)

Counts
97 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n)))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n)))
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #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 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
(*.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 (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)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(/.f64 (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.f64 k))
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))) #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))))
(/.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.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 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.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 (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 (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 1/2 binary64) (*.f64 (PI.f64) n))))
(/.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 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Outputs
(/.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)))))
Calls

4 calls:

31.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
27.0ms
n
27.0ms
k
24.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%1k
99.6%1n
99.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes109.0ms (0.7%)

Counts
83 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n)))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n)))
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #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 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
(*.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))))
Outputs
(/.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)))))
Calls

4 calls:

26.0ms
n
26.0ms
k
23.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
21.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%1k
99.6%1n
99.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes54.0ms (0.3%)

Counts
78 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n)))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n)))
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #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 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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:

23.0ms
k
20.0ms
n
Results
AccuracySegmentsBranch
99.6%1k
99.6%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes71.0ms (0.5%)

Counts
76 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n)))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n)))
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #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 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.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:

22.0ms
n
20.0ms
k
Results
AccuracySegmentsBranch
99.5%1k
99.5%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes52.0ms (0.3%)

Counts
74 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n)))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n)))
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))))
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #s(literal -1/2 binary64))))
Outputs
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))))
Calls

2 calls:

21.0ms
n
20.0ms
k
Results
AccuracySegmentsBranch
47.3%1n
47.3%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes26.0ms (0.2%)

Counts
38 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
Calls

2 calls:

11.0ms
n
11.0ms
k
Results
AccuracySegmentsBranch
47.2%1k
47.2%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes19.0ms (0.1%)

Counts
29 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
Calls

2 calls:

8.0ms
n
8.0ms
k
Results
AccuracySegmentsBranch
47.2%1n
47.2%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes20.0ms (0.1%)

Counts
28 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
Outputs
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
Calls

2 calls:

8.0ms
n
8.0ms
k
Results
AccuracySegmentsBranch
36.1%1n
36.1%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts
13 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
Outputs
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
Calls

2 calls:

5.0ms
n
4.0ms
k
Results
AccuracySegmentsBranch
36.0%1k
36.0%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts
12 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k)))
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
Outputs
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
Calls

2 calls:

4.0ms
n
4.0ms
k
Results
AccuracySegmentsBranch
35.6%1k
35.6%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 #s(literal 2 binary64) (/.f64 k n))))
Outputs
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
Calls

2 calls:

4.0ms
k
1.0ms
n
Results
AccuracySegmentsBranch
35.5%1k
35.5%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify11.0ms (0.1%)

Algorithm
egg-herbie
Rules
32×*-commutative_binary64
18×+-commutative_binary64
14×sub-neg_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
059121
179121
293121
3103121
4111121
5114121
Stop Event
saturated
Calls
Call 1
Inputs
(/.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)))))
(/.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)))) (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 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
Outputs
(/.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)))))
(/.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)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.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)))) (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 n (PI.f64))) (+.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))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 n #s(literal 2 binary64))) (PI.f64)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))

soundness2.4s (15.4%)

Rules
5380×*-lowering-*.f32
5380×*-lowering-*.f64
5256×*-lowering-*.f32
5256×*-lowering-*.f64
5090×*-lowering-*.f32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
032124
1183120
21057120
37701120
08207120
02068
110068
247864
3327564
0826264
040165
1190156
2953149
37300149
08311149
01314
13014
24714
36914
49013
511313
614913
718813
821413
922813
1022913
022913
037130
1171126
2918125
36906125
08222125
01392132
13852094
211921806
341691722
477331722
081041722
02945071
19354812
233074497
375714481
080384481
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
saturated
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 385 to 271 computations (29.6% saved)

preprocess67.0ms (0.4%)

Compiler

Compiled 282 to 142 computations (49.6% saved)

end0.0ms (0%)

Profiling

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